Instructional Shift in Math

ESC NORTHNetwork Principal Meeting

January, 2013

Objectives Identify the MAJOR, SUPPORTING, and ADDITIONAL

CLUSTERS for a given grade level

Understand how students should CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS in the mathematics classroom (TLF 3b: Using Questioning and Discussion Techniques)

Connect work to the TEACHING AND LEARNING FRAMEWORK (Standards 1d4, 3b1, and 3b2) and to MATH PRACTICE 3 (Constructing viable arguments and critiquing reasoning of others)

CCSS District-wide Goals

By 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 FOCUS areas for mathematics

Begin reviewing current curricular materials to determine where it aligns to the critical areas of FOCUS

Common Core Standards

Standards for Math Content

These DOMAINS connect topics and content between and among grade levels.

Each grade level consists of a set of DOMAINSDOMAINS which are large groups of related standards.

Each domain consists of a set of CLUSTERS.

These CLUSTERS are smaller sets of related standards within the domain.

The CLUSTERS identify the primary ideas to be learned within the domain.

High School

Arranged by cluster (NOT COURSE)Number and QuantityAlgebraFunctionsModelingGeometryProbability and Statistics

The Major Work of the Grade

Some clusters require greater emphasis or FOCUS than others based on the depth of the ideas, the time that they take to master, and/or the demands of college and career readiness.

In addition, an intense FOCUS on the most critical material at each grade level allows depth in learning, which is carried out through the Standards for Mathematical Practice.

The Major Work of the Grade

The list of standards for each grade level is not a flat, one-dimensional checklist.

To make these emphases more transparent and useful, MAJOR, SUPPORTING, and ADDITIONAL clusters have been identified by the CCSS authors.

Activity – Part 1

On Your Own:

Read the instructions and critical areas of the grade level

Mark each bulleted cluster with an M, S, or A to the best of your ability. (Notice the hint…) Use the Individual column for your answers

As you mark each cluster, highlight key words in the text that supports your answer

You will have 5 to 8 minutes for this INDIVIDUAL activity

Handout 1

Activity – Part 2With Your Partner:Compare your answers and mark the clusters where you disagree in the Partner column

For each cluster where you and your partner disagree, one of you will make an argument defending the answer siting specific evidence from the text (Handout 1) to justify your answer

The other partner listens without interruption. Switch roles and let the other partner present while the first partner listens

After the second partner is finished, both partners continue to discuss and try to reach consensus until the facilitator indicates time is up

Answer Key Grade 7

Grade Level Focus Areas

Major Cluster

□Supporting Cluster

• Additional Cluster

All

Major

Clusters

Answer Key Grade 7

Grade Level Focus Areas

Major Cluster

□Supporting Cluster

• Additional Cluster

Additional Clusters

Additional Clusters

Supporting Clusters

Supporting Clusters

Implementation Strategy:

Defending and Critiquing ArgumentsStudents increase their understanding through creating explanations/arguments and listening to/critiquing the reasoning of others

Hip to be SquareActivity:Take 2 minutes to begin working on this problem on your own.

For the next 5 minutes, with a partner, continue to solve the questions.

Challenge one another— How did you get that

answer? How do you know that

your answer makes sense?

How are our solutions the same? Different?

Hip to be Square… 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.

Standards for Mathematical PracticePriority for 2012-13

Standard 1: Make sense of problems and persevere in solving themStandard 2: Reason abstractly and quantitativelyStandard 3: Construct viable arguments and critique the reasoning of othersStandard 4: Model with mathematicsStandard 5: Use appropriate tools strategically

Standard 6: Attend to precisionStandard 7: Look for and make use of structureStandard 8: Look for and express regularity in repeated reasoning

Mathematical Practice 3

MP3: Construct viable arguments and critique the reasoning of 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 solution and discussion of the square problem?

What made for strong arguments? Weaker arguments?

What are students expected to know and be able to do?

Handout 2

Common Core Content ConnectionsStandards for Mathematical Practice

MP3: Construct viable arguments and critique the reasoning of others

Anchor Standards for ELA and Content Literacy

Reading 1: Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

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.

Ties to the Teaching and Learning Framework

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others

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

What does language sound like when constructing viable arguments and critiquing the reasoning of others look like for the age group and ELD levels of students we currently teach?

What student actions/interactions should we see? How do we share these expectations with teachers/students?

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

Implementation Strategy

“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

Questioning-Putting MP3 into Practice

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.

Summary Spending more time on fewer topics allows for deeper

learning and understanding

All CCSS math content standards are important and to be taught, some have greater emphasis and should have more time devoted to them

Students increase their understanding through creating explanations/arguments and listening to/critiquing the reasoning of others

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

Made connections to the Teaching and Learning Framework Rubrics through questioning and discussion techniques

Next StepsWith your grade level/department team:

Engage students in using Mathematical Practice 3 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.

Have faculty review the MAJOR, SUPPORTING, and ADDITIONAL clusters for the grade they teach

In future grade level/department team meetings, begin reviewing your current curricular resources looking for where current units of study correspond to the CCSS areas of emphasis

In future meetings, begin aligning current units of study to what is emphasized in the CCSS and to what degree it is emphasized