Mathematics Summit Southern Indiana Deanery: Focus on Mathematics Instruction
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Mathematics Summit
Southern Indiana Deanery: Focus on Mathematics Instruction
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Standards for the Day
• Deepen understanding of creating a mathematically literate classroom
• Apply a variety of strategies to support and promote the learning of mathematics
• Promote own and others’ learning through community conversation, collaboration and reflection
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Agenda
DAY I• Grant Overview/Introduction• Mini-lesson: connecting Mathematical Literacy • Vocabulary Development Routines- GOs and Word Walls• Developing Classroom Discourse for Deeper Understanding
DAY II• Analysis of New Common Core State Standards• Using Multiple Representations to Develop Deeper Understanding • Using Number lines and manipulatives to support conceptual understanding
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Introductions
• Introduce yourself, let us know– School, grade, experience (if you want)– Something interesting you did or are going to
do this summer– Anything else you want to share!
• Be sure you have a name tag and have signed in
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Project Overview- Part 1
• 6 days of PD during the year
• Developing curriculum, instructional practices, and resources that support mathematics instruction
• Provide teachers with feedback through: coaching, analysis of student work, & informal discussion
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Project Overview- Part 2
• 2 days of summer training• 1st Semester:
– 1 cadre day to be held at a school, during September/early October
– 2 x 1 day grade level coaching for each group (5/6, 7/8), late October/early November
• 2nd Semester: – 1 cadre day, during late February/early March
• Distance support for mathematics teachers
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Take a few moments to compare the
NCTM Processes and CCSS Practice Standards
Guiding Questions:
How are the processes and practices similar?
How do they differ?
What do the new practices mean for my instruction?
Indiana Transition Info
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
8
NCTM Standards for Mathematics
Content
NumberAlgebraGeometry &
MeasurementProbability & Statistics
Process
Problem Solving
Reasoning & Proof
Communication
Connections
Representations
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
9
Instructional Programs Pre K-12 Should Enable All Students To:
• Organize & consolidate their mathematical thinking through communication
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
• Analyze & evaluate the mathematical thinking & strategies of others
• Use the language of mathematics to express mathematical ideas precisely
(NCTM Standards, p. 269)
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CCSS Content for Mathematics
Number and Operations k – 12 Algebra k – 5, 9 – 12 Measurement & Data k – 5 Geometry k – 12 Expressions & Equations 6 – 8 Proportionality 6 – 7 Statistics & Probability 6 – 12 Functions 8 – 12 Modeling 9 – 12
CCSS Mathematics Standards
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CCSS Practices for Mathematics
Make sense of problems/persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Take a few moments to compare the
NCTM Processes and CCSS Practice Standards
Guiding Questions:
How are the processes and practices similar?
How do they differ?
What do the new practices mean for my instruction?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
"The ability to read, listen, think creatively, and communicate about problem situations, mathematical representations, and the validation of solution will help students to develop and deepen their understanding of mathematics."
(NCTM Standards, p. 80)
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
What are the necessary ingredients to communicate
mathematics effectively?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
“Students should be encouraged to increase their ability to express themselves clearly and coherently. As they become older, their styles of argument and dialogue should more closely adhere to established conventions, and students should become more aware of, and responsive to, their audience. The ability to write about mathematics should be particularly nurtured across the grades.”
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
“Students should be encouraged to increase their ability to express themselves clearly and coherently. As they become older, their styles of argument and dialogue should more closely adhere to established conventions, and students should become more aware of, and responsive to, their audience. The ability to write about mathematics should be particularly nurtured across the grades.”
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
“Students should be encouraged to increase their ability to express themselves clearly and coherently. As they become older, their styles of argument and dialogue should more closely adhere to established conventions, and students should become more aware of, and responsive to, their audience. The ability to write about mathematics should be particularly nurtured across the grades.”
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
18
Mathematics as a Language
• Includes Elements, Notation, and Syntax
• Is the language (science) of patterns and change
• Is a way of thinking about the world
• Is a necessary ingredient for developing & demonstrating understanding – both oral & written language
(Sensible, Sense-Making Mathematics, by Steve Leinwand)
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
How do we represent in mathematics?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
20
How many ways can we say or represent 12 ÷ 4 mathematically?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Multiple Representations of the Same Idea
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Literacy in Mathematics
Vocabulary Development
Reading
Writing2Speaking/ Listening
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
“Research in the past ten years reveals that vocabulary knowledge is the single most important factor contributing to reading comprehension.”
Teaching Reading in the Content Areas, Billmeyer & Barton
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
“Reading mathematics means decoding and comprehending not only words but mathematical signs, symbols, and diagrams/graphs.”
“Consequently, students need to learn the meaning of each symbol and to connect each symbol, the idea that the symbol represents, and the written or spoken word(s) that correspond to that idea.”
(McREL, Teaching Reading in Mathematics)
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
26
The Precise Language of Mathematics
Graphic Organizers that allow for multiple representations/interactions
Frayer Model, VVWA, Alphablocks, Foldables
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Gradual Release Model• I Do, You Watch
• I Do, You Help
• You Do, I Help
• You Do, I Watch
• Extended Scaffolding– I Suggest, You Do– You Decide to Do
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
28
“The Mathematical Communication Standard is closely tied to problem solving and reasoning. Thus as students’ mathematical language develops, so does their ability to reason and solve problems. Additionally, problem-solving situations provide a setting for the development & extension of communication skills & reasoning ability.”
(NCTM Standards, pp 80)
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Something that squared with your beliefs
Something going ‘round and ‘round in your head
Three points you want to remember
Exit Slip
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Developing Discourse in the Classroom
• Choose an article to read
• We are using two reading strategies as we read:– Text coding– Margin notes
• You have 30 minutes to read the article
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Sample Margin Notes
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Text Coding
!- Important Idea
?- I have a question
- I disagree with
- agrees with my thinking
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Discourse Discussion
• In similar article groups discuss the main idea of the article and the appropriate guiding questions
• In mixed groups we are going to have a
Café Conversation
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Something that squared with your beliefs
Something going ‘round and ‘round in your head
Three points you want to remember
Exit Slip
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