Math Talk Deepens Student Mathematical Understanding with Carla Kozak

1. Math Talk Deepens Student Mathematical Understandingwith Carla Kozak Developed by ERLC/ARPDC as a result of a grant from Alberta Education to support implementation

2. Where do you work? Using the text tool, type your name and the name of school district where you work?

3. Agenda GOAL: Today’s session will focus on why communication in mathematics is integral to building students’ understanding and how teachers can encourage worthwhile math talk among their students. • What is Math Talk? What does it look like? • Why is communication important? • How can teachers encourage worthwhile Math Talk? • Where are those rich mathematical tasks?

4. Definition of Discourse NCTM (1991) - a way of representing, thinking, talking, agreeing and disagreeing. Ball (1991) adds that discourse is the how [process] student knowledge is constructed and exchanged in the classroom.

5. Just like Me What does communicating mathematically look like in your math class? Think about your students and respond with: Yes, this is just like my classroom OR No, this is not like my classroom

6. Just like Me My students work in pairs and small groups.

7. Just like Me My students know that everyone’s idea is accepted and discussed.

8. Just like Me My students use manipulatives to support the math concepts they are learning.

9. Just like Me My students draw pictures to show their thinking.

10. Just like Me My students use words or numbers to explain their thinking.

11. Just like Me My students share more than one way to solve a problem.

12. Just like Me My students explain and model personal strategies for solving problems and learn from each other.

13. Show me how you solved it! “Communication elevates math to a thinking skill rather than a rote skill. It allows us to move beyond just doing the math and push students to understand, to explore, and to explain math ideas.” (O’Connell & O’Connor, 2007)

14. Math Talk Watch the short clip and please click on the when you have finished viewing the video. http://teachertube.com/viewVideo.php?video_id=129790

15. Does Megan have a strong understanding of number sense? Respond with a or

16. 1000 – 899 = ? Solve this problem.

17. How does this demonstrate students’ understanding of NUMBER? 110 10 10 - 8 9 9 0 9 9 1 0 1

18. Tom Lehrer- New Math342- 173= ? Watch the short clip and please click on the when you have finished viewing the video. http://www.youtube.com/watchv=SXx2VVSWDMo&feature=related

19. Enter most elementary classrooms in Canada today and you will find a room filled with the sounds of learning - students talking.

20. Preparing the Future Students must be able to: • reason about quantitative information, • possess number sense, • check for the reasonableness of solutions, • communicate (both orally and in writing) their solutions to problems.

21. Principles and Standards for School Mathematics(NCTM, 2000) All students to should be able to: • organize and consolidate their mathematical thinking through communication, • communicate their mathematical thinking coherently and clearly to peers, teachers, and others,

22. Principles and Standards for School Mathematics(NCTM, 2000) All students to should be able to: • analyze and evaluate the mathematical thinking and strategies of others, and • use the language of mathematics to express mathematical ideas precisely.

23. Alberta K-9 Mathematics Program of Studies (Alberta Education, 2007) Communication is one of the seven mathematical processes that permeate the teaching and learning of mathematics; “communication is important in clarifying, reinforcing and modifying ideas, attitudes and beliefs about mathematics”.

24. “Using math talk in your classroom requires a different lesson format than the lesson in which the teacher demonstrates a technique or skill and follows up with student practice.” (Sullivan and Lilburn, 2002) How do you see this working in your math class?

25. “The teacher needs to be “receptive to all students’ responses, the teacher must acknowledge the validity of the various responses while making clear any limitations, drawing out contradictions or misconceptions, and building class discussion from partial answers. ” (Sullivan and Lilburn, 2002)

26. Four Things for Teachers to Consider • Create safe, supportive environment, • Provide engaging mathematical tasks, • Manage Math Talk, and • Ask good questions.

27. 1. Create safe, supportive environment

28. How do you create a safe, supportive environment for your students? Click on the text box and type a phrase.

29. All ideas accepted whether right or wrong. • Student ideas will be respected and not be judged negatively by the teacher or their peers. • All student contributions are worthwhile and valued. • Students are not afraid to take risks or to make mistakes. • Mistakes are seen as opportunities to learn • Students learn that other classmates may hold different views and that everyone has the opportunity to argue their case or re-assess their thinking.

30. Create safe, supportive environment Together, the teacher and students build “a safe intellectual environment, one where it is alright to be wrong, to challenge another, to correct another, and, more important, to correct oneself” (Leinhardt & Steele, 2005).

31. 2. Provide engaging mathematical tasks • Interesting problems that ‘go somewhere’ mathematically can often be catalysts for rich Math Talk. • Students need to “formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.” (NCTM, 2000)

32. 60-45= 61-46= 59-44= 62-47= 107-39= 201-79= 1001-899=

33. +5 +10 60-45= 61-46= 59-44= 62-47= 107-39= 201-79= 1001-899= 45 50 60

34. +5 +10 60-45= 61-46= 59-44= 62-47= 107-39= 201-79= 1001-899= 45 50 60 +10 +5 46 56 61

35. 3. Manage Math Talk • Provide opportunities to talk during the lesson. • Consider a variety of ways to organize students to encourage sharing- pairs, small groups or whole class discussions. • Listen to students’ responses in order to guide the conversations.

36. 4. Ask good questions By asking good questions, teachers engage students in meaningful dialogue, “…not just any kind of student talk is expected to be productive for supporting or challenging students’ thinking.” (Franke et al., 2007)

37. Ask good questions • Different types of questions: • probing (What do you mean by…), • justifying (Can you solve it another way?), • factual (How many were there?) • Use levels in Blooms Taxonomy to ask more higher level questions.

38. “The more teachers know about students’ thinking, the more effectively they can adapt their own instructional practices to uncover and address students’ misconceptions and the gaps in their knowledgeand understanding, and so support student learning” (Webb et.al., 2008).

39. Resources See attached list

40. Final Thoughts Using the text tool, write a word or two that stood out for you from today’s session.

41. Thank you Contact me at Carla.Kozak@epsb.ca