1. Coaching for Math GAINS Professional Learning

2. Initial Steps in Math Coaching How going SLOWLY will help you to make significant GAINS FAST.

3. Establishing Norms Start and end on time Electronic devices off except on break

4. Norms Start and end on time. Respond to the signal. Each person gets the chance to speak and listen. Participants direct their discussion to the whole group, not the facilitator. Invest in your own learning and the learning of others. Contribute to a safe environment that encourages risk taking; be kind. Think and act like mathematicians.

5. Overview of the Session Clarify your personal image of what being a mathematics coach involves. View some examples of the math coaching process in action. Practise being a math coach in a safe environment through role play. Identify some next steps for yourself.

6. Some possible questions: - Who are you? Tell me about yourself. - What are your strengths, styles, beliefs, goals …? - What do you want me to know about you as a math teacher? Initial Meeting

7. Coaching Strategies and Stems Paraphrasing Do I understand that… you don’t have access to computers? In other words …you want to try some differentiated instruction? It sounds like …you have explored a variety of resources? Clarifying What do you mean by … the course is too hard? Is it always the case that …the students in the class don’t listen? How is… teaching math same as/different from…teaching science? Interpreting What you are explaining might mean …students rely on formulas Could it mean that … students need more time on this topic? Is it possible that … the following things could result from… ?

8. Now it's your turn … Role play the initial meeting between coach and coachee. Ask questions to lay a foundation for your later work with the teacher. Use the stems to probe more deeply.

9. What does being a math coach involve?

10. What do you think now? In pairs, create a Frayer Model for “Coaching” Definition Characteristics Examples Non-examples Coaching

11. The Non-negotiables "What coaching is not" Your coaching duties do not include …

12. It's all about trust! Sincerity Competence Benevolence Reliability Adapted from: Coaching Leaders to Attain Student Success – Gary Bloom

13. Content-Focused Coaching… Is content specific. Teachers' plans, strategies and methods are discussed in terms of student learning. Is based on a set of core issues of learning and teaching. Fosters professional habits of mind. Enriches and refines teachers' pedagogical content knowledge. Encourages teachers to communicate with each other … in a focused, professional manner. from Content-Focused Coaching: Transforming Mathematics Lessons, by Lucy West, p.3

14. Let's hear from another expert: Cathy Fosnot (Fosnot, 2002) Discuss with a partner any new thoughts about coaching. Re-visit and revise your Frayer model.

15. The “Guide” Aligned with Grades 7-12 Literacy Guide A prototype for other subjects A research framework Find an indicator that addresses one of your foci for the year

16. More Precision www.edugains.ca Library www.tmerc.ca

17. Sharpening the Instructional Focus 37 indicators in The Guide for Administrators and Other Facilitators of Teachers’ Learning for Mathematics Instruction 8 criteria in the Student Success Action Planning Template 3 strategic approaches 1 key focus May 2008 September 2008 2006

18. Sharpening the Instructional Focus Three strategic approaches: Fearless listening and speaking Questioning to evoke and expose thinking Responding to provide appropriate scaffolding and challenge Driver for 2008-09

19. Sharpening the DI Focus Differentiation of content, process, and product based on student readiness, interest, and learning profile Differentiation based on student readiness and differentiation at the concept development stage 2004 - 08 2008 - 09

20. Connecting Foci Questioning DifferentiatingResponding Fearless listening and speaking

21. Differentiating Mathematics Instruction Questioning to Evoke and Expose Thinking Materials adapted from Dr. Marian Small’s presentation August 2008

22. Questioning That Matters You have introduced a counter model for subtracting integers. As you look at each question and it’s answer, think about its purpose. 22

23. Questions That Matter What is (-3) – (-4)? Tell how you calculated (-3) – (-4). Use a diagram or manipulatives to show how to calculate (-3) – (-4) and tell why you do what you do. Why does it make sense that (-3) – (-4) is more than (-3) – 0? Choose two integers and subtract them. What is the difference? How do you know? 23

24. Differences in Intent Do you want students to: be able to get an answer? [What is (-3) – (-4)?] be able to explain an answer? [Explain how you calculated (-3) – (-4).] see how a particular aspect of mathematics connects to what they already know? [Use a diagram or manipulatives to show how to calculate (-3) – (-4) and tell why you do what you do.] 24

25. Differences in Intent Do you want students to: be able to describe why a particular answer makes sense? [Why does it make sense that (-3) – (-4) is more than (-3) – 0? ] be able to provide an answer? [Choose two integers and subtract them. What is the difference? How do you know?] Which of these types of questions are important to you? All of them? Some of them? Why? 25

26. It is important that: even struggling students meet questions with these various intents, including making sense of answers and relating to other math ideas, and meet with success. questions focus on the math that matters. 26

27. Your answer is….? A graph goes through the point (1,0). What could it be? What makes this an accessible, or inclusive, sort of question?

28. Possible responses x = 1 y = 0 y = x- 1 y = x 2 - 1 y = x 3 - 1 y = 3x 2 -2x -1 28 (1,0)

29. What good questions can do Good questions: – Evoke student thinking. – Expose student thinking. – Help students see and drill into “big Ideas” For good questions to work: –Students must be able to listen and speak fearlessly. –Students must be provided appropriate scaffolding and challenge.

30. The coach can help teachers: identify the Big Math ideas in the lessons they plan to teach. develop questions that focus students on making sense of the math. craft questions that help students make connections. create questions that probe for student understanding.

31. Opening up Questions Conventional question: You saved $6 on a pair of jeans during a 15% off sale. How much did you pay? vs. You saved $6 on a pair of jeans during a sale. What might the percent off have been? How much might you have paid?

32. Or… You saved some money on a jeans sale. Choose an amount you saved: $5, $7.50 or $8.20. Choose a discount percent. What would you pay?

33. Or… Conventional question: What is 5 2 + 6 2 + 3 3 ? vs. Represent 88 as the sum of powers.

34. Possibilities 1 2 + 1 2 + …. + 1 2 (88 of them) 2 2 + 2 2 + … + 2 2 (22 of them) 5 2 + 5 2 + 5 2 + 2 2 + 2 2 + 2 2 + 1 2 5 2 + 6 2 + 3 3 34

35. Similarities and Differences How are quadratic equations like linear ones? How are they different? How is calculating 20% of 60 like calculating the number that 60 is 20% of? How is it different? How is dividing rational numbers like dividing integers? How is it different? 35

36. Some “opening up strategies” Start with the answer instead of the question. Ask for similarities and differences. Leave the values in the problem somewhat open. 36

37. How could you open these questions up? Add: 3/8 + 2/5.A line goes through (2,6) and has a slope of -3. What is the equation? Graph y = 2(3x - 4) 2 + 8.Add the first 40 terms of 3, 7, 11, 15, 19,…

38. Using Parallel Tasks Offer 2-3 similar tasks that meet different students’ needs, but make sense to discuss together.

39. Parallel Questions Task A: 1/3 of a number is 24. What is the number? Task B: 2/5 of a number is 24. What is the number? Task C: 40% of a number is 24. What is the number? How do you know the number is more than 24? Is the number more than double 24? How did you figure out your number?

40. Parallel Questions Task 1: Find two numbers where: - the sum of both numbers divided by 4 is 3. - twice the difference of the two numbers is -36. Task 2: Solve: (x + y) / 4 = 3 and 2(x – y) = -36 How did you use the first piece of information? The second piece? How did you know the numbers could not both be negative?

41. The Processes Problem solving Reasoning and proving Reflecting Selecting tools and strategies Connecting Representing Communicating 41

42. Coach’s Role Helping teachers realize they must identify the math that matters Helping teachers practice developing questions that focus on students making sense of the math Helping teachers practice developing questions that focus on building connections- how new math ideas are related to and built on older ones 42