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K–12 Session 4.3 Standards for Mathematical Practices Part 3: Looking for the Practices through Observation Module 1: A Closer Look at the Common Core State Standards for Mathematics

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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.

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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

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Adapted from the Public Education Leadership Project at Harvard University STRUCTURES POLICIES, PROCESSES & PROCEDURES RESOURCES HUMAN, MATERIAL, MONEY STAKEHOLDERS CULTURE Organizational Elements

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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

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The 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. 6

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Grouping of Math Practices Reasoning and Explaining 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others Modeling and Using Tools 4. Model with mathematics 5. Use appropriate tools strategically Seeing Structure and Generalizing 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Overarching Habits of Mind of a Productive Mathematical Thinker 1. Make sense of problems and persevere in solving them 6. Attend to precision Adapted from (McCallum, 2011) 7

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Articulating Student Dispositions & Teacher Strategies Making your own “Look-For” tool Activity 5

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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

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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

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Observing Instruction: Task 1 Looking for the CCSSM Practices in the Classroom Activity 6A

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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

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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

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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

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Observing Instruction: Task 2 Looking for the CCSSM Practices in the Classroom Activity 6B

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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

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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

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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

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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

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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?

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