3/23/2016 Using Writing to Enhance Students’ Mathematical Understanding April 5, 2016 Dennis C. Cullen M.A., BCBA Judd Pittman M.S. and M.Ed Pennsylvania Training and Technical Assistance Network PaTTAN’s Mission The mission of the Pennsylvania Training and Technical Assistance Network (PaTTAN) is to support the efforts and initiatives of the Bureau of Special Education, and to build the capacity of local educational agencies to serve students who receive special education services. 1
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Transcript
3232016
Using Writing to Enhance Studentsrsquo Mathematical
Understanding April 5 2016
Dennis C Cullen MA BCBA Judd Pittman MS and MEd
Pennsylvania Training and Technical Assistance Network
PaTTANrsquos Mission
The mission of the Pennsylvania Training and Technical Assistance
Network (PaTTAN) is to support the efforts and initiatives of the Bureau of
Special Education and to build the capacity of local educational agencies to serve students who receive special
education services
1
3232016
PDErsquos Commitment to Least Restrictive Environment (LRE)
Our goal for each child is to ensure Individualized Education Program (IEP)
teams begin with the general education setting with the use of Supplementary Aids and Services
before considering a more restrictive environment
Grade 5 PSSA Release Item
2
3232016
Using the Chat Box
You will notice the chat box that is likely on the right hand side of your screen We will be asking for your participation from time to time
You will type your responses in the chat box
Hello
Agenda
bull Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
3
bull
3232016
Mathematical Literacy
Mathematical Literacy
Disciplinary Literacy Science Literacy
Historical Literacy
Each discipline has its own specific vocabulary text types and ways of communicatinghelliphellip Students who are literate in a
discipline(math science social studies language arts) can read write speak listen and think critically about the discipline (Hillman 2014)
Mathematical Literacy Mathematical Practices
bull bull
Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct vial arguments and critique the reasoning of others
bull Model with mathematics bull Use appropriate tools strategically bull Attend to precision bull Look for and make use of structure bull Look for and express regularity in repeated reasoning
4
3232016
Mathematical Literacy Importance of Text
Mathematics is its own language
Vocabulary ldquooverlap phenomenonrdquo
Text Structure
Mathematical Literacy Importance of Text
Disciplinary Literacy Mathematical Literacy
Text 8+9=17
Expand the understanding of text to include bull Algorithm bull Equation bull Proof bull Chart bull Graph bull Multimedia
12
Mx + b = y
5
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
PDErsquos Commitment to Least Restrictive Environment (LRE)
Our goal for each child is to ensure Individualized Education Program (IEP)
teams begin with the general education setting with the use of Supplementary Aids and Services
before considering a more restrictive environment
Grade 5 PSSA Release Item
2
3232016
Using the Chat Box
You will notice the chat box that is likely on the right hand side of your screen We will be asking for your participation from time to time
You will type your responses in the chat box
Hello
Agenda
bull Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
3
bull
3232016
Mathematical Literacy
Mathematical Literacy
Disciplinary Literacy Science Literacy
Historical Literacy
Each discipline has its own specific vocabulary text types and ways of communicatinghelliphellip Students who are literate in a
discipline(math science social studies language arts) can read write speak listen and think critically about the discipline (Hillman 2014)
Mathematical Literacy Mathematical Practices
bull bull
Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct vial arguments and critique the reasoning of others
bull Model with mathematics bull Use appropriate tools strategically bull Attend to precision bull Look for and make use of structure bull Look for and express regularity in repeated reasoning
4
3232016
Mathematical Literacy Importance of Text
Mathematics is its own language
Vocabulary ldquooverlap phenomenonrdquo
Text Structure
Mathematical Literacy Importance of Text
Disciplinary Literacy Mathematical Literacy
Text 8+9=17
Expand the understanding of text to include bull Algorithm bull Equation bull Proof bull Chart bull Graph bull Multimedia
12
Mx + b = y
5
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Using the Chat Box
You will notice the chat box that is likely on the right hand side of your screen We will be asking for your participation from time to time
You will type your responses in the chat box
Hello
Agenda
bull Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
3
bull
3232016
Mathematical Literacy
Mathematical Literacy
Disciplinary Literacy Science Literacy
Historical Literacy
Each discipline has its own specific vocabulary text types and ways of communicatinghelliphellip Students who are literate in a
discipline(math science social studies language arts) can read write speak listen and think critically about the discipline (Hillman 2014)
Mathematical Literacy Mathematical Practices
bull bull
Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct vial arguments and critique the reasoning of others
bull Model with mathematics bull Use appropriate tools strategically bull Attend to precision bull Look for and make use of structure bull Look for and express regularity in repeated reasoning
4
3232016
Mathematical Literacy Importance of Text
Mathematics is its own language
Vocabulary ldquooverlap phenomenonrdquo
Text Structure
Mathematical Literacy Importance of Text
Disciplinary Literacy Mathematical Literacy
Text 8+9=17
Expand the understanding of text to include bull Algorithm bull Equation bull Proof bull Chart bull Graph bull Multimedia
12
Mx + b = y
5
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
bull
3232016
Mathematical Literacy
Mathematical Literacy
Disciplinary Literacy Science Literacy
Historical Literacy
Each discipline has its own specific vocabulary text types and ways of communicatinghelliphellip Students who are literate in a
discipline(math science social studies language arts) can read write speak listen and think critically about the discipline (Hillman 2014)
Mathematical Literacy Mathematical Practices
bull bull
Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct vial arguments and critique the reasoning of others
bull Model with mathematics bull Use appropriate tools strategically bull Attend to precision bull Look for and make use of structure bull Look for and express regularity in repeated reasoning
4
3232016
Mathematical Literacy Importance of Text
Mathematics is its own language
Vocabulary ldquooverlap phenomenonrdquo
Text Structure
Mathematical Literacy Importance of Text
Disciplinary Literacy Mathematical Literacy
Text 8+9=17
Expand the understanding of text to include bull Algorithm bull Equation bull Proof bull Chart bull Graph bull Multimedia
12
Mx + b = y
5
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy Importance of Text
Mathematics is its own language
Vocabulary ldquooverlap phenomenonrdquo
Text Structure
Mathematical Literacy Importance of Text
Disciplinary Literacy Mathematical Literacy
Text 8+9=17
Expand the understanding of text to include bull Algorithm bull Equation bull Proof bull Chart bull Graph bull Multimedia
12
Mx + b = y
5
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy
bull Focus on writing ndash Mathematical writing is succinct ndash How mathematicians communicate ndash Supports mathematical reasoning and problem
solving ndash Practical skill
bull Writing up estimates bull Explanation of proceduresplans bull Invoices
Agenda
Mathematical Literacy bull The Complex Skill of Writing bull Vocabulary in Mathematics
6
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Of language-dependent skills ndash longest to learn mastered by the fewest
bull Mental juggling act ndash Composing ndash Transcribing ndash Editing
(Moats 2012)
The Complex Skill of Writing
7
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Scope and Sequence ndash Micro Level (Mechanics)
bull Transcription skills ndash spelling handwriting (keyboarding)
bull Capitalization and Punctuation bull Parts of SpeechSentence Parts
The Complex Skill of Writing
bull Scope and Sequence bull Revision and Publication ndash Macro Level
ndash Revision (Composition) ndash Presenting work for bull Quality of Writing
Publication ndash Focus
ndash Content
ndash Organization ndash Style
bull Purpose of Writing ndash Narrative Writing ndash Informational Writing ndash OpinionArgumentative
Writing
8
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Framework for Meeting the PA Core Writing Standards
MicrostructureFoundational skills bull Handwriting- accuracy and
fluency bull Keyboarding (fluencyndash transition) bull Spelling- accuracy and fluency bull Vocabulary bull Sentences structure bull Mechanics
Macrostructure processing skills bull Writing process plan
writetranscribeedit and revise and provide feedback (collaboration)
bull Requires central executive function
bull Higher level reasoning bull Synthesizing bull Sentences combining and
complexity
The Complex Skill of Writing
bull Writing relies on ndash Subskills ndash Cognitive abilities ndash Self-management strategies ndash Memory functions ndash Attention resources
(Moats 2012)
9
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull The READING brain ndash Four parts
bull Phonological processor ndash part of the brain that recognizes SOUNDS of spoken words skwar
bull Orthographic processor ndash part of the brain that recognizes SYMBOLS of written word ldquos q u a r erdquo
bull Meaning processor ndash part of the brain that recognizes various meanings of the word ldquosquarerdquo
bull Context processor ndash part of the brain that recognizes which meaning to select based on the sentence and structure
(Moats 2012)
The Complex Skill of Writing
10
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
ndash Grapho ndash related to written language
3232016
The Complex Skill of Writing
bull Mr Collins asked the students to tell the reasons that a square is different than a triangle
bull Ms Burns taught the class how to calculate the square root of a number
bull The team realized the error put them back at square one
bull When they won the Powerball they divided the winnings fair and square
The Complex Skill of Writing
bull The graphomotor process
ndash Motor ndash related to coordination of movement
ndash During Writing graphomotor skills control bull Direction bull Spatial proportion bull Flow bull Size of letters
(Moats 2012)
11
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
12
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
Three Parts of Writing
Planning Translating Reviewing
(Hayes and Flower 1980)
The Complex Skill of Writing
bull Three Parts of Writing ndash Planning
bull Generating and organizing ideas bull Purpose of writing bull Organizational structure bull Audience
ldquoWhat do I want to say and how will I say itrdquo
(Moats 2012)
13
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Three Parts of Writing ndash Translating
bull Ideas turn into specific words bull Transcribed into written form bull Ideas may be reorganized reworked or discarded bull Syntactic formulation ndash putting together words and
sentences that convey intended meaning ndash Spelling ndash Grammar ndash Punctuation
(Moats 2012)
The Complex Skill of Writing
bull Three Parts of Writing ndash Reviewing
bull Editing rewriting text bull Can occur while translating bull Requires writer to examine hisher work from the
point of view of the reader bull Determines how it will be interpreted
(Moats 2012)
14
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Writing involves both ldquohigher levelrdquo and ldquolower levelrdquo skills
bull Places heavy demands on the brain
(Moats 2012)
The Complex Skill of Writing
bull Higher Level bull Lower Level
Spelling irregular high frequency words
Keeping the purpose for writing in mind
Conveying the sequence of steps used
Writing symbols + - x divide =
Writing left to right
Selecting precise vocabulary
Checking for clarity of exposition
15
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Beginning writers have to learn both lower level skills and higher level skills simultaneously
bull Failure to learn lower level skills limits the acquisition of higher level skills
(Moats 2012)
The Complex Skill of Writing
bull Memory and the Writing Process
Three Kinds of Memory bull Long-term memory ndash permanent mental storage bull Short-term memory ndash temporary storage unit
ndash Make sense of information and decide what to do with it
bull Working memory - works to connect information in short-term memory to information stored in longshyterm memory
(Baddeley 2000)
16
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Working Memory and the Writing Process
Central Executive
Phonological Loop Visuospatial Sketchpad Episodic Buffer
Directs the production of spelling
words
Holds the
speech sounds
Holds the graphemes and allows the hand to
move
Limited capacity
temporary storage system
(Baddeley 2000 Moats 2012)
The Complex Skill of Writing
bull Working Memory is engaged in every phase ndash Planning
bull Setting a goal bull Choosing a format bull Imagining the finished product
ndash Selection bull Word bull Phrase bull Sentence bull Paragraph
Does this match the
plan
(Moats 2012)
17
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill of Writing
bull Novice writers ndash Working memory may be taxed by concentration
on the formation of letters or spelling ndash May not remember words long enough to write
them down ndash May need years of practice to coordinate the
activities required for writing
(Moats 2012)
The Complex Skill of Writing
bull Supporting Students with Writing ndash Practice handwriting ndash Write high frequency words from dictation ndash Combine onsets and rimes
bulllap
bullmap
bulltrap
ndash Write the alphabet numbers
(Moats 2012)
18
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
The Complex Skill or Writing
ndash Create model of finished product ndash Provide organizers to place ideas in order
bull Supporting Students with Writing ndash Provide goal ndash Use prompts
ndash Model with students (write down what they say) ndash Use sentence starters ndash Encourage self-talk andor partner talk ndash Model editing and revising
(Moats 2012)
Check In
Working Memory is involved only in the translating stage of writing a True b False
Students with dysgraphia have unusual difficulty with handwriting and spelling but those deficits generally wonrsquot impact other aspects of writing a True b False
38
19
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Agenda
Mathematical Literacy The Complex Skill of Writing bull Vocabulary in Mathematics
MATH LITERACY VOCABULARY FOCUS
40
20
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
What is Vocabulary
Pick which one best matches your thoughts
1 Knowledge of and memory for word meanings 2 Words that students can name or read in print 3 Instructional practices that create
understanding of various words 4 Lists of words that are necessary to know in
order to pass state and local assessments 41
Vocabulary Research
bull ldquoWords are not just words They are the nexus-the interface-between communication and thoughtrdquo (Adams 2009 p 180)
bull Our knowledge of words determines how we understand texts define ourselves for others and define the way we see the world (Bloom 2001 Pinker 2007)
42
21
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy Tiers of Vocabulary
43
X+Y=Z Linear-Function Quadratic-Function Addition Subtraction Numerator Denominator Multiply Divide Absolute-Value Slope Fraction Common-Denominator Geometry Triangle Square
Math Vocabulary
Tiers for Word Selection amp Instruction
Tier 1 most basic words
Tier 2 rich useful words
Tier 3 important difficult words
high-frequency high-utility words (across all subjects)
low-frequency words content-specific words (specific subject area)
common words usually known
Deep Instruction
Building Background Knowledge
(Beck et al 2002)
44
22
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Tier 2 Words
High frequency words for mature language use-- coincide analysis complementary correlation synthesis hypothesis integratedndash and thus instruction in these words can add productively to an individualrsquos language ability
(Beck McKeown Kucan 2002)
45
The Trouble With Tier 2 Words
Function
Think and write a definition for the word function
Think a write a synonym for the word function
Type thoughts in the chat box
46
23
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Websterrsquos New Word Dictionary 1 professional or official position occupation 2 the action for which a person or thing is specially fitted or used or for which a thing exists purpose 3 any of a group of related actions contributing to a larger action especially the normal and specific contribution of a bodily part to the economy of a living organism 4 an official or formal ceremony or social gathering 5a a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set b a variable (as a quality trait or measurement) that depends on and varies with another ltheight is a function of agegt also result ltillnesses that are a function of stressgt 6 characteristic behavior of a chemical compound due to a particular reactive unit also functional group 7 a computer subroutine specifically one that performs a calculation with variables provided by a program and supplies the program with a single result
47mdash funcmiddottionmiddotless -lәs adjective
Mathematical Literacy Vocabulary
24
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy Caveat
bull Teachers should feel free to use their best judgment based on an understanding of their studentsrsquo needs in selecting words to teach
bull They also should feel free to treat words in different ways Emphasis on what is important
bull Pay attention to those words (whether they meet the criteria for Tier 2 or not) that may require some attention for students to understand
49
Mathematical Literacy Types of Words -- Review
Tier 1 Commonly Used
Tier 2 Academic
Tier 3 Content
real add win
Quantitative Subtrahend Common Denominator Addition Subtraction
Analyze synthesize evidence
50
25
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
Mathematical Literacy Introducing Vocabulary
bull Word Rating Chart (prepopulated) bull Word Rating Chart (blank) bull Fist of Five Word Rating Chart bull Likert Scale for Rating Words
51
How Well Do You Know This Word
0 1 2
I know this word well I can explain it and use it
I know something about this word and can relate
it to a situation
I have seen or
heard the word
I donrsquot know this
word
3
52
3232016
26
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy Teaching Vocabulary
bull Exposure bull Quick Teach bull Explicit Instruction (Vocabulary Routine)
53
Mathematical Literacy Exposure
54
Addition Algorithm
27
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy ldquoQuick Teachrdquo
Use of known words in order to learn new words
Addition ndash Put together or combine
55
Subtraction ndash Take away or separate
Mathematical Literacy Explicit Instruction
A structured systematic and effective methodology for teaching academic skills
An unambiguous and direct approach to teaching that includes both instructional design and delivery procedures
Archer amp Hughes 2011 p 1
56
28
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Mathematical Literacy Explicit Instruction
Students increased their scores by as much as 30 percentile points after receiving direct and meaningful vocabulary instruction
20th percentile 50th percentile
Flynt amp Brozo Walsh 2003 Dunn Bonner amp Haskee 2007
Direct Instruction = 059
Vocabulary = 067
Hattie 2009
57
Check In
58
One evidence based tool for determining which words to explicitly teach ishellip a A word rating chart b Graphic organizer c Semantic feature analysis d None of the above
Tier I words are defined ashellip a Low frequency content specific words b High frequency and high utility words across
subjectcontent areas c Everyday common usually known words d None of the above
Explicit Instruction is a high leverage way to teach Tier III content specific vocabulary a True b False
29
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Vocabulary
THE IMPACT OF MORPHOLOGY ON VOCABULARY INSTRUCTION
59
Morphological Analysis
bull Morpheme ndash meaningful part of a word ndash Ex Geometry ndash Greek origin
bull Ge (earth) metria (procedures or systems)
bull Why study words at the morphemic level ndash Students who are aware of morphemes in words
are better readers ndash Knowledge of common morphemes aids in
decoding unknown words ndash Approximately three-quarters of compounded and
affixed words can be deciphered morphemically
60
30
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
To learn more
61
wwwpattannet Reading initiative Literacy videos
Explicit Instruction
VOCABULARY INSTRUCTION WITH ROUTINES
62
31
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Power of Instructional Routines
bull Students should have organizational structures in place to build organizational routines
bull Each student can create a personal notebook to organize their new words visual depictions and other important information like safety rules
bull Each student should have an ldquoagendardquo to write requirements assignments and other ldquothings to remember to dordquo and to organize their day
63
Vocabulary Instructional Routine
bull Step 1 Introduce the word bull Step 2 Introduce the wordrsquos meaning bull Step 3 Illustrate the word with examples bull Step 4 Check studentsrsquo understanding
ndash Ask deep processing questions ndash Have students discern between examples and non-
examples
ndash Have students generate their own examples ndash Have students generate a sentence (using a sentence
starter)
64
32
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Instructional Routine-Critical Words
65
Addition
66
33
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo ad-di-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo addition
67
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is when two or more sets are combined into one complete set Your Turn Create a student friendly explanation for your students
68
34
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Step 3 Illustrate the Word with Examples
bull Concrete Examples o Show an object o Acting out
bull Visual Examples-show a picture or diagram bull Verbal Examples-explain and discuss when
the word might be used and who might use the word
69
Step 3 Concrete Examples
70
Simple
Complex
35
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Deep Processing Questions
71
Step 4 Check Student Understanding
Option 1 Ask Deep Processing Questions bull When would you use addition bull Begin by saying or writing I would use addition
when I am doing____________
72
36
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Equation
73
Step 1 Introduce the Word
bull Write the word on the board or overhead bull Read and say the word Have students repeat the word bull Have students tap out syllables in the word bull Have students read the word by parts as you loop
under the words bull Have students repeat the pronunciation of the word
Example ldquoThis word is addition What wordrdquo ldquoTap and say the parts of the wordrdquo e-qua-tion
ldquoRead the word by partsrdquo ldquo What wordrdquo equation
74
37
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Step 2 Introduce the Wordrsquos Meaning
Option 1 Present a student-friendly explanation Have students practice telling the student-friendly explanation Example ___________ is a mathematical statement where one quantity equals another quantity Your Turn Create a student friendly explanation for your students
75
Step 3 Visual Examples
Input + Input = Output
Always contains an = sign
Equation
The combining of two or more sets into one complete set
What is it
What are some steps
Putting together
Inputs Expression or Quantity
Outputs Expression or Quantity
Joining
X + 5 = Y -7
(Concept Maps Schwartz amp Raphael 1985) 76
What is it like
Concept Mapping = 057
Hattie 2009
38
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
Step 4 Check Student Understanding
Definition Characteristics
Picture Non-examples
Equation
A mathematical statement that says one expression or quantity is equal to another expression or quantity
Inputs Expressions or Quantities
Outputs Expression or Quantities
Always contains an = sign
Expression
Equation
Effect Size 041
77Hattie 2009
Check In
When using direct instruction to teach Tier III vocabulary a high leverage technique is to use an ldquoInstructional Routinerdquo a True b False
Concept mapping andor graphic organizers are high leverage techniques to incorporate into your vocabulary instruction tool belt a True b False
78
39
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
3232016
References
bull Archer A L amp Hughes C A (2011) Explicit instruction Effective and efficient teaching New York NY The Guilford Press
bull Baddeley A (2000) The episodic buffer A new component of working memory Trends in Cognitive Sciences Vol 4 (11) 417-423
bull Beck I L McKeown M G amp Kucan L (2002) Bringing words to life Robust vocabulary instruction New York The Guilford Press
bull Hattie J (2009) Visible learning A synthesis of over 800 meta-analyses relating to achievement New York NY Routledge
bull Hayes JR amp Flowers LS (1980) Identifying the organization of the writing processes In LW Gregg amp ER Steinberg (Eds) Cognitive process in writing (pp 3- 30) Hillsdale NJ Erlbaum
bull Hillman AM (2014) A Literature Review on Disciplinary Literacy How do Secondary Teachers Apprentice into Mathematical Literacy Journal of Adolescent and Adult Literacy Vol 57 (5) 397-406
bull Moats LC (2012) Language essentials for teachers of reading and spelling (Letrs) module 9 Teaching beginning spelling and writing (k-3) (2nd ed) Longmont CO Cambium Learning Sopris
Contact Information wwwpattannet
Dennis Cullen dcullenpattannet 1-800-441-3215 ext 7232
Judd Pittman jpittmanpattannet 1-800-360-7282
Commonwealth of Pennsylvania
Tom Wolf Governor
40
Related Documents
