Empowering Young Learners through the Standards for Mathematical Practice

1. Empowering Young Learners through the Standards for Mathematical Practice Juli K. Dixon, Ph.D. University of Central Florida juli.dixon@ucf.edu

2. Solve this…

3. Perspective… What do you think fourth grade students would do? How might they solve 4 x 7 x 25?

4. Perspective… Are you observing this sort of mathematics talk in classrooms? Is this sort of math talk important?

5. Perspective… What does this have to do with the Common Core State Standards for Mathematics (CCSSM)?

6. Background of the CCSSM • Published by the National Governor’s Association and the Council of Chief State School Officers in June 2010 • Result of collaboration from 48 states • Provides a focused curriculum with an emphasis on teaching for depth

7. Background of the CCSSM • “… standards must address the problem of a curriculum that is ‘a mile wide and an inch deep.’ These Standards are a substantial answer to that challenge” (CCSS, 2010, p. 3). • We’ve already met this challenge in Florida. How can we use our momentum to take us further and deeper?

8. NGSSS Content Standards Wordle

9. CCSSM Content Standards Wordle

10. Background of the CCSSM The CCSSM consist of Content Standards and 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” (CCSS), 2010, p. 6).

11. Making Sense of the Mathematical Practices The Standards for Mathematical Practice are based on: • The National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics (NCTM, 2000), and • The National Research Council’s (NRC) Adding It Up (NRC, 2001).

12. Making Sense of the Mathematical Practices NCTM Process Standards: • Problem Solving • Reasoning and Proof • Communication • Representation • Connections

13. Making Sense of the Mathematical Practices NRC Strands of Mathematical Proficiency: • Adaptive Reasoning • Strategic Competence • Conceptual Understanding • Procedural Fluency • Productive Disposition

14. Standards of Mathematical Practice Wordle

15. Perspective… According to a recommendation from the Center for the Study of Mathematics Curriculum (CSMC, 2010), we should lead with the Mathematical Practices. Florida is positioned well to do this.

16. Making Sense of the Mathematical Practices The 8 Standards for Mathematical Practice: Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

17. We will only address 4 today The 8 Standards for Mathematical Practice: Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

18. Impact on Depth… (NGSSS) Grade 4 Big Idea 1: Develop quick recall of multiplication facts and related division facts and fluency with whole number multiplication. MA.4.A.1.2: Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm, and checking for reasonableness of results, including solving real-world problems.

19. Impact on Depth… (CCSS) Grade 4 Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.5: Multiply multi-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.

20. Impact on Depth… What does it mean to use strategies to multiply? When do students begin to develop these strategies?

21. Impact on Depth… (NGSSS) Grade 3 Big Idea 1: Develop understanding of multiplication and division and strategies for basic multiplication facts and related division facts. MA.3.A.1.2: Solve multiplication and division fact problems by using strategies that result form applying number properties.

22. Impact on Depth… (CCSS) Grade 3 Cluster: Understand properties of multiplication… 3.OA.5: Apply properties of operations as strategies to multiply and divide. Grade 3 Cluster: Multiply and divide within 100 3.OA.7: Fluently multiply within 100, using strategies such as the relationship between multiplication and division or properties of operations.

23. What does it mean to use strategies to multiply? Consider 6 x 7 How can using strategies to multiply these factors help students look for and make use of structure? (SMP7) What strategies can we use? • How might this sort of thinking influence the order in which facts are introduced in grade 3?

24. Now solve 4 x 7 x 25… The Standards for Mathematical Practice help us to focus on processes, not just products.

25. Empowering Young Learners Reasoning abstractly and quantitatively often involves making sense of mathematics in real-world contexts. Word problems can provide examples of mathematics in real-world contexts. We need to help students make sense of them. Not just solve them.

26. Empowering Young Learners Consider the following problems: Jessica has 7 key chains. Calvin has 8 key chains. How many key chains do they have all together? Jessica has 7 key chains. Alex has 15 key chains. How many more key chains does Alex have than Jessica? Key words seem helpful, or are they….

27. Empowering Young Learners Now consider this problem: Jessica has 7 key chains. How many more key chains does she need to have 15 key chains all together? How would a child who has been conditioned to use key words solve it?

28. Empowering Young Learners We need students to make sense of problem situations as well as each other’s thinking. Consider these students as they reason about division.

29. Empowering Young Learners We need students to make sense of problem situations as well as each other’s thinking. Consider these students as they reason about division. Notice how the teacher’s questions focus on making sense of the problem.

30. Empowering Young Learners We need students to make sense of problem situations as well as each other’s thinking. Consider these students as they reason about remainders. Notice how they need support to construct viable arguments and critique the reasoning of others.

31. How might you change your practice to address these now? The 8 Standards for Mathematical Practice: Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

32. How do we support this empowerment? • Teachers need content knowledge for teaching mathematics to know the tasks to provide, the questions to ask, and how to assess for understanding. • Math Talk needs to be supported in the classroom. • Social norms need to be established in classroom and professional development settings to address misconceptions in respectful ways.