K–12 Session 4.3Standards for Mathematical Practices

Part 3: Looking for the Practices through Observation

Module 1:A Closer Look at the Common

Core State Standards for Mathematics

Expected Outcomes

• Build understanding of the standards for mathematical practice.

• Enhance skills in identifying the extent to which students exhibit the standards for mathematical practice.

• Generate ideas for how teachers can integrate the standards for mathematical practice with instruction to support student proficiency.

Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement.

Richard Elmore, Ph.D., Harvard Graduate School of Education

Principle #2: If you change one element of the instructional core, you have to change the other two.

The Instructional Core

Adapted from the Public Education Leadership Project at Harvard University

STRUCTURES

POLICIES, PROCESSES & PROCEDURES

RESOURCES

HUMAN, MATERIAL, M

ONEY

STAKEHOLDERS

CULTURE

Organizational Elements

The 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.

-Common Core State Standards for Mathematics, page 6

5

The Standards for Mathematical Practice1. 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.

6

Grouping of Math Practices

Reasoning and Explaining2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others

Modeling and Using Tools4. Model with mathematics5. Use appropriate tools strategically Seeing Structure and Generalizing7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Overarching Habits of Mind of a Productive Mathematical Thinker1. Make sense of problems and persevere in solving them6. Attend to precision

Adapted from (McCallum, 2011)

7

Articulating Student Dispositions & Teacher Strategies

Making your own “Look-For” toolActivity 5

Small Group Task

• Identify 3-5 student dispositions that you look for in a classroom as evidence of students engaging in the practices– What would students be communicating?– What would students be doing?

• Identify 3-5 teaching strategies that would give students the opportunity to engage in the practices– What would students be communicating?– What would students be doing?

9

Large Group Discussion

• Share student dispositions. – Discuss if the dispositions need refinement– Record dispositions on “look-for” tool

• Share teacher strategies. – Discuss if the dispositions need refinement– Record dispositions on “look-for” tool

10

Observing Instruction: Task 1

Looking for the CCSSM Practices in the Classroom

Activity 6A

Review Task #1

• What important mathematical concepts would a student need to understand in order to be successful with this task?

• When engaged in this task, what would it look like for a student to demonstrate proficiency in the mathematical practice standard that we are studying?

12

Viewing Task #1

•Practice 1•Practice 2•Practice 3•Practice 4

•Practice 5•Practice 6•Practice 7•Practice 8

13

Choose one lesson and watch approximately 5-7 minutes of instruction using your rubric. Have a discussion on evidence of the two math practices you have been talking about in this module

Whole Group Discussion 1

• What mathematical concepts are being addressed in this lesson?

• To what extent are individual students demonstrating proficiency with either of the two practice standards that we just studied? What is your evidence?

• How do the instructional decisions support student learning?

14

Observing Instruction: Task 2

Looking for the CCSSM Practices in the Classroom

Activity 6B

Review Task #2

• What important mathematical concepts would a student need to understand in order to be successful with this task?

• When engaged in this task, what would it look like for a student to demonstrate proficiency in the mathematical practice standard that we are studying?

16

Viewing Task #2

•Practice 1•Practice 2•Practice 3•Practice 4

•Practice 5•Practice 6•Practice 7•Practice 8

17

Choose one lesson and watch approximately 5-7 minutes of instruction using your rubric. Have a discussion on evidence of the two math practices you have been talking about in this module

Whole Group Discussion 2

• What mathematical concepts are being addressed in this lesson?

• To what extent are individual students demonstrating proficiency with either of the two practice standards that we just studied? What is your evidence?

• How do the instructional decisions support student learning?

18

Review Outcomes

• Build understanding of the standards for mathematical practice.

• Enhance skills in identifying the extent to which students exhibit the standards for mathematical practice.

• Generate ideas for how teachers can integrate the standards for mathematical practice with instruction to support student proficiency.

19

Reflection

• What practices do you see as being able to implement immediately in your classroom?

• What challenges to you see in engaging students in the math practices?

• What needs to you have to support engaging students in the math practices? (e.g. - content knowledge, activities, coaching, etc.?)

• How will you communicate these needs to school, district, and state leadership?