Office of Curriculum, Instruction and School Support

2012

Mathematical Practice 3:Mathematical Practice 3:Construct Viable Arguments and Construct Viable Arguments and Critique the Reasoning of OthersCritique the Reasoning of Others

Mathematics Implementation Module 1

Module ObjectivesModule Objectives

After today’s module on Mathematics Practice 3, teachers will have an understanding of how students should CONSTRUCT VIABLE ARGUMENTS CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF AND CRITIQUE THE REASONING OF OTHERS OTHERS in the mathematics classroom (TLF 3b: Using Questioning and Discussion Techniques)

2

CCSS District-Wide GoalsCCSS District-Wide GoalsBy May 2013, at a minimum, teachers will be expected to:engage all students in using Mathematical Practice 3: CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS

in grade level/department groups, engage in on-going dialogues regarding FOCUSFOCUS areas for mathematics

begin reviewing current curricular materials to determine where it aligns to the critical areas of FOCUSFOCUS

3

The Intersection of The Intersection of Mathematical StandardsMathematical StandardsThe Standards for Mathematical Standards for Mathematical

Practice Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

The Standards for Mathematical Standards for Mathematical Content Content are a balanced combination of procedure and understanding. They define what students should understand and be able to do in their study of mathematics

4

Hip to be …Hip to be …

5MARS Task

ActivityActivity

6

Structure strategy: Guided sharing: Private, Partner, Public

Private: Time to think and work on the problem

Take 3 minutes to solve the problem on your own.

Partner: Time to discuss our pathways and solutions. Need for a discussion prompt: Say a Second Sentence

Ask your partner: How do you know that your answer makes sense? Tell me more.

Public: Select students to participate strategically based on work samples

Select a pair of students/participants who had different approaches.

Hip to be …Hip to be …

Domain: Geometry (7th grade)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard 6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

7

Standards for Standards for Mathematical PracticeMathematical Practice

Standard 1: Make sense of problems and persevere in solving them

Standard 2: Reason abstractly and quantitativelyStandard 3: Construct viable arguments and

critique the reasoning of othersStandard 4: Model with mathematicsStandard 5: Use appropriate tools strategicallyStandard 6: Attend to precisionStandard 7: Look for and make use of structureStandard 8: Look for and express regularity in

repeated reasoning8

Priority for 2012-13

Mathematical Practice 3Mathematical Practice 3

Construct Construct viable viable

arguments arguments and and

critique the critique the reasoning reasoning of othersof others

Activity:Do a close read of Handout 2With a partner, discuss—

What parts of MP3 do you believe you and your partner used in your discussion of the polygon problem?

What made for stronger arguments? Weaker arguments?

9

Common Core Content Common Core Content ConnectionsConnections

Standards for Standards for Mathematical PracticeMathematical Practice

Anchor Standards for Anchor Standards for ELA and Content LiteracyELA and Content Literacy

MP3: Construct viable arguments and critique the reasoning of others

Speaking and Listening 1: Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own

clearly and persuasively.

10

Ties to the Teaching and Ties to the Teaching and Learning FrameworkLearning Framework

11

Mathematical Practice 3:Mathematical Practice 3:Activity:In grade level groups, using Handouts 4 and 5, discuss:

What do language standards look like and sound like for our students?

How do we share these expectations with students?

What actions should we be doing as teachers? How do we model this practice for students?

How do we begin to integrate Math Practice 3 into our lessons and classrooms now?

What commitments will we make to see this happen?

12

Implementation StrategyImplementation StrategyQuestioning-Putting MP3 into Practice

Say a Second Sentence

Ask students to explain how they arrived at an answer to a given math problem. Listen for student understanding not for answer-getting. Ask a student to Say a Second Sentence to explain their thinking.

13

14

“Correct answers are essential…but they’re part of the process, they’re not the product. The product is the mathematics the kids walk away with in their heads…”

-Phil Daro, co-author of CCSSM, 2012

SummarySummaryEngaged in a mathematical problem

intersecting content and practice standards

Discussed the meaning of Mathematical Practice 3: CONSTRUCT VIABLE CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS REASONING OF OTHERS and how to engage students in using this practice

Made links to the Teaching and Learning Framework through questioning and discussion techniques15

Next StepsNext Steps

Engage all students in using Mathematical Practice #3: CONSTRUCT CONSTRUCT VIABLE ARGUMENTS AND VIABLE ARGUMENTS AND CRITIQUE THE REASONING CRITIQUE THE REASONING OF OTHERSOF OTHERS utilizing strategies from this session

16