Developing Mathematical Practices for Algebra in Grades 4-10

Developed by Education Development Center, Inc. with support from the Massachusetts Department of Elementary and Secondary Education

DMPA Course Goals

•Understand the big ideas of the Standards for Mathematical Practice

•Explore how the development those mathematical practices can contribute to students’ conceptual understanding and problem-solving in algebra

DMPA Course Goals cont.

•Understand the concept of cognitive demand

•Understand the relationship between cognitive demand and effective implementation of the Standards for Mathematical Practice, and

•Consider instructional strategies that support students’ development of the Standards for Mathematical Practice

Why Focus on the Eight Math Practices?

“These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms.”

-2011 Massachusetts Curriculum Framework for Mathematics (page 14)

-Common Core State Standards for Mathematics (page 5)

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These Math Practices Define the “Next Step”!

•“The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.”Page 18, 2011 Massachusetts Curriculum

Framework for Mathematics

Who should sign up for this course?•Grades 4-10 mathematics teachers •Special education teachers working in

grades 4-10 math classrooms•Math coaches•Cross-grade school and district teams

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The Participant Experience

Learn about the Eight Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Participant Experience

•Do math and identify their own (and colleagues’) use of the math practices

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Growing Triangles

•Analyze written student work for evidence of math practices and to identify the potential in student thinking

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Participant Experience

A Shift in Emphasis

PedagogyInstructional

Strategies

Mathematics

SMP

MathematicsSMP

PedagogyInstruction

al Strategies

60 hour Course Progression

Tools: Strategies:

• Math Practice Big Ideas • Math Practice “Ask

yourself…” Questions• 3-Column Student Work

Analysis Framework• Cognitive Demand

Framework

• Diagramming for Meaning• Guess-Check-Generalize• Three-Read Problem

Interpretation• Act it Out • Table-Top Math Work

Participant Take-Aways

Course Logistics• 60 hours: equivalent to 8 full day sessions (8:00-3:30)

plus classroom experimentation

• Flexible configuration to meet district or DSAC needs. Options include:▫ 1 week in summer + 3 Saturday Fall follow-ups

• 5 Friday p.m./all day Saturday combinations• 3 February/April vacation days + 3 Fri./Sat. classes

• 3 graduate credits or 67.5 PDPs

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SummerSessions 1-5

FallS6

FallS7

FallS8

Teacher Impact

•Understanding of what the Standards for Mathematical Practice are, how they develop, and how to nurture students’ development of these practices.

•An appreciation of the importance and commitment to providing students a steady diet of high demand tasks that prompt use and development of the SsMP.

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Teacher Impact, continued

Practically speaking, teachers will leave with

•A set of instructional strategies to prompt students’ use and development of the math practices.

•Adaptation strategies they can bring to their current curriculum materials to place more emphasis on the mathematical reasoning personified in the math practices.

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Teacher Impact, continued•The capacity to identify evidence of (or

the potential for) math practice use in their students’ math work.

•Experience co-planning and implementing at least three high demand math lessons based on tasks and/or incorporating strategies worked on in the course.

•Tools and frameworks they can continue to use together during common planning and meeting time.

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