Using Video to Think about What the Math Practices Look Like in K-5 Classrooms

1. Using Video to Think about What the Math Practices Look Like in K-5 Classrooms

2. Overview of This Session • An overview of the Math Practices; in-depth look at Math Practice 1 and 6 • Discuss video from 5 classes (K, 3, 1, 2, 5) • What do the SMPs, particularly SMP 1 and 6, look like in K-5 classrooms? • What’s the role of the student? The teacher? The task? • Connections to content, to other practices • How do we help teachers develop “mathematically proficient students”?

3. Standards for Mathematical Practice Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Reasoning and explaining • Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker Modeling and using tools Model with mathematics Use appropriate tools strategically Look for and make use of structure Look for and express regularity in repeated reasoning Seeing structure and generalizing

4. What’s important? • The math Practices describe “mathematically proficient students…” • Understanding what the Math Practices mean (and don’t mean) in the elementary grades. • Connections to content, and to each other. • “We’re doing all the practices, all the time.”

5. SMP1: Make sense of problems and persevere in solving them Mathematically proficient students (MPS) start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor an evaluate their progress and change course if necessary. MPS can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. …Might rely on using concrete objects or pictures to help conceptualize and solve a problem. MPS check their answers to problems using a different method, they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solve complex problems and identify correspondences between different approaches.

6. SMP1: Make sense of problems and persevere in solving them Mathematically proficient students (MPS) start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor an evaluate their progress and change course if necessary. MPS can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. …Might rely on using concrete objects or pictures to help conceptualize and solve a problem. MPS check their answers to problems using a different method, they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solve complex problems and identify correspondences between different approaches.

7. SMP1 ALWAYS asking yourself does it make sense? Make connections between the words, visuals, numbers and symbols.

8. What does it look like in the classroom? • Who’s using the practice? • What’s the role of: • The task • The teacher • The student • Video Clip #1 (Kindergarten) • Crayons in the Box • Video Clip #2 (3rd Grade) • Visual Arrays 3x9

9. SMP6: Attend to precision MPS try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they research high school they have learned to examine claims and make explicit use of definitions.

10. SMP6: Attend to precision MPS try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they research high school they have learned to examine claims and make explicit use of definitions.

11. Video Clip • Video Clip #3 (1st Grade) • Library Books • Video Clip #1 (2nd Grade) • 69 + 87 • Video Clip #2 (5th Grade) • 85 x 63 Roles of the task, teacher, student

12. Thinking about Implementation • Are the SMPs different in different grades? • What impacts how it looks? • Math content • Time of year • Is it a new idea?

13. The Role of…. • The student • How is the child approaching the problem? • The teacher • “mathematically proficient (teachers)…” • Classroom culture, teaching practices. • Questioning, modeling, explicit teaching • The task/curriculum • Types/variety of tasks-rigor • Connecting the content with concrete • Communication • The interaction/integration of all 3

14. What’s Our Role? • How do we help teachers develop “mathematically proficient students”? • It’s important that teachers: • Know the math and their students • Have images of what the SMPs look/sound like (SMP moments) • Can see/capitalize on opportunities • Have strategies: questioning, modeling, posing • Curriculum that helps them focus on the SMPs

15. The Standards for Mathematical Practice “The mathematical practices describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics.” NCSM, 2011