Mathematical Practices Overview

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Explore the Standards for Mathematical Practice

Identify characteristics of a student and classroom that exemplifies mathematical practice.

Plan professional development to take a closer look to◦ make sense of each mathematical practice. ◦ connect practices to content for rigor and relevance.

Expected Outcomes

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INSTRUCTION

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What does a classroom look and sound like

when all students are engaged in learning

mathematics?

November 2011

Interpreting Distance–Time Graphs

Materials for this activity were obtained through the Mathematics Assessment Project (MAP). Original materials for this lesson can be found at: http://map.mathshell.org/materials/

adapted from the Mathematics Assessment Project (MAP)

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Tom’s journey to the Bus Stop

Write a narrative (describe) what is happening.

Is the graph realistic? Explain.

November 2011

Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.

- Montana Common Core Standards

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NCTM – Principles and Standards for School Mathematics Process Standards

Problem solving Reasoning and proof Connections Communication Representation

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Strands of Proficiency of Mathematical Proficiency

Adding It Up: Helping Children Learn MathematicsBy Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001).Washington, DC: National Academy Press

p. 117

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is an elusive term with multiple meanings. To a pure mathematician, rigor is a mark of excellence. To a K-12 educator, “rigorous” often means “difficult,” as in “AP calculus is rigorous.”

In the Montana Standards for Mathematical Practices . . .

Mathematical Rigor

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◦approach mathematics with a disposition to accept challenge and apply effort;

◦engage in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and

◦emerge fluent in the language of mathematics, proficient with the tools of mathematics, and empowered as mathematical thinkers.

Rigor is a process where students:

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Integration of Practices for Rigor and Relevance Is:

a process, not just one correct answer.

part of each lesson.

not “Problem Solving Fridays”.

not “enrichment” for advanced students.

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

2. Reason abstractly and quantitatively3. 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.

Standards for Mathematical Practice

(CCSS, 2010)

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(McCallum, 2011)

Grouping the Standards for Mathematical Practices

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What opportunities were there for you to engage in the practice standards in the Distance Time Task?

Did explaining give opportunities to engage in additional practices? Or deepen the ones identified above.

Are there any words/phrases you want to add to our list that describe a classroom with students engaged in mathematical practice?

Connections to Practices

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Traditional U.S. ProblemWhich fraction is closer to 1: 4/5 or 5/4 ?

Same problem integrating content and practice standards

4/5 is closer to 1 than is 5/4. Using a number line, explain why this is so.

(Daro, Feb 2011)

Standards for Mathematical Practice in a Classroom

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Math Class Makeover

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Oregon State Mathematical Practice Module 1: Part 1:Making Sense of the Mathematics

◦ Doing mathematics◦ Examining mathematical practice

Part 2: Student dispositions and Teacher Actions◦ Identify student outcomes ◦ Identify teaching strategies

Part 3: Looking for the Practices through Observation◦ Create your own “look for” tool◦ Look for MCCS Mathematical Practice in Classroom videos

http://www.ode.state.or.us/search/page/?id=3406 Oregon DOE

A Closer Look a Mathematical Practice

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Does our list of words/phrases describe a classroom where students are engaged in mathematical practice?

Use Reflection Sheet capture key thoughts about the practice standards

Reflection and Planning

November 2011

Jean Howard

Mathematics Curriculum Specialist(406) 444-0706; jhoward@mt.gov

Cynthia GreenELA Curriculum Specialist(406) 444-0729; cgreen4@mt.gov

Judy SnowState Assessment Director (406) 444-3656; jsnow@mt.gov