1. Facilitating Math Talks for All Students Candace Standley, Culpeper County Schools Carol Walsh, Middlesex County Public Schools March 21, 2016 Southwest Virginia Higher Education Center Session 2B

2. Let’s do some math! 18 X 5

3. How did you solve the problem?

4. How did a group of Stanford freshman solve the problem?

5. What are math talks?

6. 5-10 Minute Mental Math Activity Students Share solution strategies verbally Explain thinking Justify reasoning Make sense of each other’s strategies Teacher Facilitates conversation Asks questions Records responses Ensures mathematics is clear in recordings

7. One Caution... Set Classroom Norms! Errors are gifts, because they promote discussion. The answer is important but it is not the math. Ask questions until ideas make sense. Share a second sentence to connect your thoughts. Talk about each other’s thinking. Think with language and use language to think. Use multiple strategies... multiple representations !

8. “If we use talk to establish a supportive learning environment, but we do not succeed in creating productive talk about the actual content of mathematics, our students are not likely to succeed in learning the mathematics we want them to know. On the other hand, if we fail to build a supportive learning environment – one in which students can talk about their mathematical thinking without fear of ridicule – then many students will not participate at all.” - Chapin, O’Connor, and Anderson (2009)

9. Let’s do some math! 56 + 97

10. WHY DO WE NEED NUMBER TALKS?

11. 5 PROCESS STANDARDS Communication Connections Representations Reasoning Problem Solving

13. “Dialogue is the central aspect of co-intelligence. We can only generate higher levels of intelligence among us if we are doing some high quality talking with each other.” - Tom Atlee, The Tao of Democracy

14. What can students learn from math talks?

15. Composing and decomposing numbers Conceptual understanding of the relationship between numbers (number sense) Computation strategies Reasoning skills and sense- making Multiple strategies/ representations for an answer Value of successes and errors in deepening understanding through problem-solving

16. Let’s do some math ! 56 - 29

17. How are math talks different than other mathematical discourse?

18. Problems are written and read publicly but students solve them mentally Wait time Silent signals Teacher scribes after student explanations Student validates presentation of ideas Questions after student has shared All answers directed up front, including mistakes**

19. “It’s not about right answers. It’s about developing reasoning and the capacity to articulate and communicate.” - Lucy West, Metamorphosis Teaching Learning Communities

21. Each group will chart the ways the group believes students will solve the problem mentally as well as student misconceptions.

23. GROUP #2 15 + 37 + 5

24. GROUP #3 36 + 54

26. GROUP #5 2.6 ÷.2

27. GROUP #6 50% of 120 25% of 120 26% of 120

29. THE BIGGER PICTURE PRINCIPLES TO ACTION Page 11 How do Number Talks connect to our beliefs about teaching and learning mathematics? Next steps to “continue the discussion”?

30. For Questions: Candace Standley, Culpeper County Schools, standley@culpeperschools.org Carol Walsh, Middlesex County Public Schools cwalsh@mcps.k12.va.us

31. References Atlee, T., & Zubizarreta, R. (2003). The Tao of democracy: Using co-intelligence to create a world that works for all. Cranston, RI: Writers' Collective. Chapin, S., & Connor, M. (2009). Classroom discussions: Using math talk to help students learn, grades K-6 (2nd ed.). Sausalito, Calif.: Math Solutions. Harris, P. (2011). Building powerful numeracy for middle and high school students. Portsmouth, NH: Heinemann. Harris, P. (2012). Building powerful numeracy facilitator’s guide. Pam Harris Consulting, LLC. Harris, P. (2014). Lessons and activities for building powerful numeracy. Portsmouth, NH: Heinemann. Humphreys, C., & Parker, R. (2015). Making Number Talks Matter. Portland, ME: Stenhouse Publishers. National Council of Teachers of Mathematics. (2014). Principles to Action: Ensuring Mathematical Success for All. Reston, VA: NCTM. Oakland Unified School District Leadership, Curriculum and Instruction. (2013). Instructional toolkit for mathematics. http://blog.mrmeyer.com/wp- content/uploads/OUSDMathInstructionalToolkit2013-14.pdf

32. References Parrish, S. (2014). Number talks: Helping children build mental math and computation strategies. Sausalito: Math Solutions. Sawyer, W. W. (1961). A Mathematician’s Delight. London: Penguin. Youcubed at Stanford University. (Producer). (n.d.). Number talks. Available from https://www.youcubed.org/category/papers-videos/videos/. https://www.youcubed.org/category/papers-videos/videos/ West, L., & Staub, F. (2003). Content-focused coaching: Transforming mathematics lessons. Portsmouth, NH: Heinemann.