Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them. - Henry David Thoreau
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Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards
Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them. - Henry David Thoreau. Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards. Icebreaker. - PowerPoint PPT Presentation
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Building Stronger Math StudentsBy Building a Stronger FoundationMCPS Adoption of New Internationally-driven Standards
Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them.
- Henry David Thoreau
Icebreaker Do you consider yourself
a “math person?” Do you consider yourself
a reader?
Goals of the
MCPS
Mathem
atics Program
Develop students who love math and see it as sensible and useful to solving problems and making sense of the world.
All students will reach proficiency in math – Understanding, Computing, Applying, Reasoning, and Engaging (UCARE).
Building a Strong Foundation
Proficiency in Number Concepts
Success in Advanced Math
Rankings are for the 26 OECD countries participating in PISA in 2000, 2003, and 2006.
Programme of International Student Assessment (PISA) Results
Subject
2000 Rank
(out of 26)
Math 17th
Science 13th
Reading 14th
Slide Credit: EdTrust.orgData Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results , http://www.oecd.org/
2003 Rank
(out of 26)
22nd
Tied for 17th
14th
2006 Rank
(out of 26)
2009 Rank(out of 26)
22nd Tied 20th
19th 13th
n/a Tied 10th
Why internationally-driven standards?
Slide Credit: EdTrust.orgData Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results , http://www.oecd.org/
Why internationally-driven standards?
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Cana
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lgium
Switz
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aland
Aust
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Czec
h Re
publ
icIce
land
Denm
ark
Fran
ceSw
eden
Aust
riaGe
rman
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land
OECD
Ave
rage
Slova
ck R
epub
licNo
rway
Luxe
mbo
urg
Polan
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ngar
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ainUn
ited
Stat
esPo
rtuga
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lyGr
eece
Turk
eyM
exico
300
350
400
450
500
5502003 PISA - Math
Aver
age
Scal
e Sc
ore
U.S.A.OECD Average
What nations are consistently near the top in math?
Finland KoreaNetherlandsSwitzerlandCanadaJapanNew ZealandBelgiumAustralia
Why internationally-driven standards?
China has not taken PISA as a nation. Certain cities such as Shanghai have joined and are ranking near the top.
What are the Internationally-driven Standards?The Common Core State Standards:
Include rigorous content and application of knowledge through high-order skills
Build upon strengths and lessons of current state standards
Internationally benchmarked so that all students are prepared to succeed in our global economy and society
Based on evidence and research
Learn more: http://www.corestandards.org/
Building a Strong Foundation
2001 MCPS
CCSS/EIC
Rigor ✔ ✔Coherence
✔ ✔
Focus ✔
What is needed in curriculum and instructionto help build a strong foundation?
2001 MCPS
CCSS/EIC
Rigor ✔ ✔Coherence
✔ ✔
Focus ✔
Rigor, Coherence, and Focus Source: Achieve – CCSS
Rigor refers to the degree that sets of standards address key content that prepare students for success beyond high school.
Rigor, Coherence, and Focus Source: Achieve – CCSS
Focus refers to whether the standards create an appropriate balance among: conceptual understanding procedural skill problem solving with an emphasis
on application and modeling
MCPS and CCS
Strand Comparison
Math K
Math 1
Math 2
Math 3
Math 4
Math 5
Math 6
Math 7
Math 8
Final Common Core StandardsNumberAlgebraGeometryMea-sure-mentStatisticsProbability
The CCSS recommend that elementary schools focus on building a strong foundation in number concepts – before accelerating into advanced math.
MCPS Math teachers in advanced level courses in middle school and high school have requested a stronger foundation in number concepts for ALL students, even the most advanced.
So what does
this look
like?
Going Deep in Mathematics2001 Curriculum and CCSS
Understanding
ComputingApplying Reasoning
Engaging
Comprehending Concepts, Operations, & Relations
Carrying out procedures
Formulating and solving mathematical problems
Using logic to explain a solution
Seeing math as sensible, useful, and doable
3 2 32 1
1½ ÷ ½ =
a. ½ b. ¾c. 3d. 1
Write this problemas a questionusing words and
not symbols.
How many halves are in one and one half?
MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN
DEPTH
COMPUTING
UNDERSTANDING
REASONING
1½ ÷ ½ = 3
Describe a situation
requiring use of this
concept.
You have a yard and
a half of ribbon to make bows. Each bow requires ½
yard. How many bows
can you make?
MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN
DEPTH
APPLYING REASONING
Complete the number sentence with <, >, or =
352 360
114 113
MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN
DEPTH
COMPUTING<
>
Same Problems, but requiring Understanding, Computing, Application,
and Reasoning
MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN
DEPTHENGAGEMENTWhen might we need to compare three digit
numbers?Which type of milk will give you the most energy
standards“Spiral” Curriculum – concepts introduced and mastered over several grade levels
Concept introduced and mastered in one grade level
Grade level standards not sufficiently challenging for most students
Many standards are “pulled down” from upper grades.
Language of standards was general and not specific – resulting in teaching to test.
Fewer, higher, clearer standards provide direction for teaching and learning – not testing.
Curriculum developed independently of all other subjects
Curriculum integrated with other content areas and thinking and academic skills
What Makes The EIC Foundation Stronger?
Building a Stronger Foundation
MCPS 2001 Curriculum
EIC / Internationally-driven standards
• Add and subtract two- and three-digit numbers using alternative strategies.
• Add two- and three-digit numbers with regrouping.
• Subtract two-and three-digit numbers with regrouping. *
• Model and use the identity and commutative properties for addition…to solve problems. *
* From a higher grade level
• Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
• Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
• Explain why addition and subtraction strategies work, using place value and the properties of operations.
Comparing Standards on One Topic in Grade 2: Using Place Value to Add and Subtract
Building a Stronger Foundation
Critical Questions For Instructional Planning
1. What do students need to know and be able to do?
2. How will we know they have learned it?
3. What will we do when they haven’t?4. What will we do when they already
know it?
How Do We Plan To Reach ALL Students?
Building a Stronger Foundation
Enriched and Accelerated Instruction in Elementary Math
- Who consistently demonstrate strong mastery in all five strands for an indicator
All Students – In the grade level EIC/CCSS Curriculum• Grade level
expectations are at a higher level
• Fewer topics per grade level
• Enrichment–mastery of the 5 UCARE strands requires greater depth for all students
Few Students – grade level
advancement
Building a Stronger Foundation
Enrichment and Acceleration Implementation PlanSchool Year
Kindergarten, Grade 1, Grade 2
Grade 3, Grade 4, Grade 5
2011-2012 Common Core State Standards/ Elementary Integrated CurriculumGrade Level Math Curriculum with enrichment and acceleration
MCPS 2001 CurriculumContinue acceleration within grade level and next grade level up
School Year
Kindergarten, Grade 1, Grade 2, Grade 3
Grade 4, Grade 5
2012-2013 Common Core State Standards/ Elementary Integrated CurriculumGrade Level Math Curriculum with enrichment and acceleration
MCPS 2001 CurriculumContinue acceleration within grade level and next grade level up
Learning Progressions Enrichment and Acceleration in
Kindergarten
Building a Strong Number Foundation - Kindergarten:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level
Know number names and the count
sequence to 100(KMP1)
Count to tell the number of objectsCompare numbers
(KMP2)
Count forward from a given number
Compare numbers(KMP4)Co
untin
g & Ca
rdin
alit
y
Num
ber &
Op
erat
ion
s Bas
e Te
n
Learning Progression Enrichment
Learning Progression Acceleration
UCARE Enrichment
Decompose numbers less
than or equal to 10 into pairs in more than one way (KMP2)
Decompose numbers less
than or equal to 10 into more
than two parts (KMP2)
Decompose numbers less
than or equal to 20 into pairs in more than one
way (KMP2)
Fluency within 5(KMP4)Op
erat
ions
an
d Al
gebr
aic
Thin
king
Addition – putting together and adding to problems within 10. Subtraction – taking apart and taking from problems within 10
(KMP4)
Addition and subtraction problems unknowns in all positions within 10
(G1MP1)
Foundations for place value:
numbers 11-19 are ten ones and some more ones (KMP4)
Foundations for place value: Ten ones is a unit called a “ten”
Tens can be counted (G1MP1)
Apply place value concepts: Extend
counting sequence to 120 starting at
any number (G1MP1)
Opportunities for Enrichment/Acceleration (Grade K)
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
Enrichment:Geometry
Accel.: Counting
and Cardinality
Marking Period 3Opportunities for Enrichment/Acceleration (Kindergarten)
Marking Period 1
Wee
ks
Wee
ks
Wee
ks
Wee
ksEnrich/ Accel.:
Oper. and Alg.
Thinking
Accel.:Number
and Operations in Base Ten
Accel.:Operations
and Algebraic Thinking
Marking Period 4
Accel.: Counting
and Cardinality
Acceleration: Counting and Cardinality
Accel.: Counting
and Cardinality
Marking Period 2
Enrichment:Meas. and
Data
Foundations for place value: 10 ones is a unit called a “ten”
Tens can be counted (G1MP1)
Count to 120 starting at any
number Compare 2-digit
numbers(G1MP1)
Compare relative positions of three 2-
digit numbers(G1MP1)Nu
mbe
r &
Oper
atio
ns B
ase
Ten
Num
ber &
Op
erat
ion
s Bas
e Te
n Concrete Models: Add 2-digit to 1-
digit, 2-digit to multiple
of 10Subtract multiples
of 10(G1MP3)
Written Methods: Add 2-digit to 1-digit, 2-digit to multiple of
10Subtract multiples of
10(G1MP4)
Written Methods:Add 2-digit numbers
(G2MP2)
Building a Strong Number Foundation – Grade 1:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level
Learning Progression Enrichment
Learning Progression Acceleration
UCARE Enrichment
Add and subtract within 10(G1MP1)
Add and subtract within 20(G1MP2)
Fluently add and subtract within 10(G1MP3)
Fluently add and subtract within 20(G2MP1)
Oper
atio
ns
and
Alge
brai
c Th
inki
ng
Addition and subtraction problems
unknowns in all positions within 10
(G1MP1)
Addition and subtraction problems
unknowns in all positions within 20
(G1MP2)
Addition and subtraction
problems with 3 addends(G1MP2)Add 3
whole numbers within 10(G1MP1)
Opportunities for Enrichment/Acceleration (Grade 1)
* moves students to Number and Operations in Base Ten
Marking Period 2 Marking Period 3 Marking Period 4
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
Acceleration:Number and Operations
in Base Ten
Acceleration:Operations and Algebraic
Thinking/ Number and Operations in Base Ten
Enrichment:Geometry
Enrichment: Number and Operations
in Base Ten
Marking Period 1
Enrichment: Operations and
Algebraic Thinking
Acceleration:Operations and
Algebraic Thinking
Wee
ks
Acceleration: Number and Operations
in Base Ten
Enrichment: Number and Operations
in Base Ten
Enrichment/Acceleration: Operations and
Algebraic Thinking
Wee
ks
Wee
ks
Wee
ks
Enrichment:Measurement and Data
Acceleration:Operations and
Algebraic Thinking*
Meaning of a “hundred”
Count by 1s, 10s, 100s to 1000
Numerals and expanded form
(G2MP1)
Mentally add & subtract 10 or 100
Compare using symbols(G2MP1)
Count by 5s to 1000 from a given
number(G2MP1)Nu
mbe
r &
Oper
atio
ns B
ase
Ten
Num
ber &
Op
erat
ions
Ba
se Te
n
Learning Progressions Enrichment and Acceleration in
Kindergarten
Add & subtract 2-digit numbers
models- drawings- number lines – place
value strategies(G2MP2)
Fluently add & subtract 2-digit numbers
(G2MP2)
Mentally add & subtract within 100
Add four 2-digit numbers within 100(G2MP2)
Learning Progressions Enrichment and Acceleration in
Kindergarten
Add & subtract 3-digit numbersmodels- drawings- number lines – place value
strategies(G2MP4)
Fluently add & subtract 3-digit
numbers(G3)
Oper
atio
ns
and
Alge
brai
c Th
inki
ng Add & subtract
within 20 – mental
strategies(G2MP1)
Add 1-digit addends
from memory(G2MP3)
Repeated addition & rectangula
r arrays(G2MP3)
Repeated addition &
multiple representat
ions(G2MP3)
Fluently add and subtract within 20(G2MP2)
One step +/- word problems
(G2MP1)Include
compare problems (G2MP2)
Two step +/- word problems – 1-digit addends (G2MP2)Two digit addends
(G2MP3)
More complex two step
+/- problem types
(G2MP3)
Generate compare problems(G2MP2)
Enrichment AccelerationUCARE Enrichment
Building a Strong Number Foundation – Grade 2:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level
Opportunities for Enrichment/Acceleration (Grade 2)
Marking Period 3 Marking Period 4
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5Enrichment:
Oper. and Algebraic Thinking
5
6 6 6 6
7 7 7 7
8 8 8 Enrichment:Geometry
8
9 9 9Enrichment:
Oper. and Algebraic Thinking
9
Opportunities for Enrichment/Acceleration (Grade 2)Marking Period 1
Wee
ks
Acceleration: Number and Operations
in Base Ten
Enrichment:Measurement and Data
Wee
ks
Wee
ks
Acceleration:Number and Operationsin Base Ten
Enrichment:Number and Operations
in Base Ten
Acceleration:Oper. and Algebraic
Thinking
Marking Period 2
Enrich.: Number
and Op. in Base Ten
Enrich.: Oper. and
Algebraic Thinking
Accel.: Oper. and
Algebraic Thinking
Accel.: Num. & Op. in
Base Ten
Enrich.: Num. & Op. in
Base Ten
Acceleration:Oper. and
Alg. Thinking W
eeks
Accel.: Oper. and Algebraic Thinking
But is it fair to compare the U.S. to less diverse nations?