1. Leveraging Student Representations and Discourse to Advance Learning through Progressions LEUSD Middle and High School September 23, 2015

2. How long is the song I Got You? Ryan Dent, LEUSD

3. What should kids be doing while they’re learning mathematics? Ryan Dent, LEUSD

5. According to the CA Math Framework… Ryan Dent, LEUSD

7. What do you notice? What do you wonder? Rachel Ryan Dent, LEUSD

8. Pre/Post Reflection What can I do to get every student to engage in the SMP’s? What challenges – that I can control - have been keeping me from doing so? Write down initial thoughts, and then you will revise at the end of the day. Ryan Dent, LEUSD

9. CLAIM When teachers use tasks that promote reasoning and problem-solving, use and connect multiple representations, and facilitate meaningful discourse through posing purposeful questions, students will engage in the SMP’s. Ryan Dent, LEUSD

11. Phil Daro on Principles to Actions https://www.youtube.com/watch?v=o2MgrECf9 Xo Ryan Dent, LEUSD

12. “They would have to learn to be tenacious, to probe their own and others’ ideas and interpretations, to doubt and be skeptical. And they would have to learn to combine intellectual aggressiveness and a willingness to take risks with a humility about the incompleteness and uncertainty of their own ideas.” Ryan Dent, LEUSD

13. Which one doesn’t belong? Ryan Dent, LEUSD

14. Which one doesn’t belong? Ryan Dent, LEUSD

15. While watching the video… Students What were the kids doing? What SMP’s were they engaged in? What big mathematical ideas showed up in what they did/said? How would the kids describe their role in “math”? Teacher What was he doing? What was the purpose of his questions? What big mathematical ideas did he draw out? How would the teacher describe his role? Ryan Dent, LEUSD

16. “Line of Best Fit” Lesson Scatter Plots Ryan Dent, LEUSD

19. Talking Points Round 3 Tally Agree/Disagree/Unsure Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas. An effective teacher makes the mathematics easy for students by guiding them step by step through problem-solving to ensure that they are not frustrated or confused. Mathematics learning should focus on developing understanding of concepts and procedures through problem- solving, reasoning and discourse. Ryan Dent, LEUSD

20. Representations Ryan Dent, LEUSD Contextual Physical Visual Symbolic Verbal

21. Ryan Dent, LEUSD

22. Talking Points Ryan Dent, LEUSD

23. Today’s Meet What is “depth of understanding?” Ryan Dent, LEUSD

24. What do you notice? Ryan Dent, LEUSD

25. How many blocks would be in the 7 th step? How many blocks would be in the 43 rd step? How many blocks would be in the n th step? Ryan Dent, LEUSD

26. Is this useful for anything? Ryan Dent, LEUSD

27. Could you use this student’s work to engage all kids in the SMP’s? Ryan Dent, LEUSD

28. What’s the difference? Ryan Dent, LEUSD

29. What is “depth of understanding?” Ryan Dent, LEUSD How does connecting student representations promote depth?

30. Pre/Post Reflection What can I do to get every student to engage in the SMP’s? Ryan Dent, LEUSD

31. Task http://youtu.be/5JCm5FY-dEY Ryan Dent, LEUSD

32. Orchestrating Productive Discussions Ryan Dent, LEUSD What you read What we did

33. What is “depth of understanding?” Ryan Dent, LEUSD How does connecting student representations promote depth?

34. Pre/Post Reflection What can I do to get every student to engage in the SMP’s? Ryan Dent, LEUSD

35. Hot Dogs and Buns Task http://robertkaplinsky.com/work/how-many- hot-dogs-and-buns-should-he-buy/ Ryan Dent, LEUSD

36. While watching the video… Students What were the kids doing? What SMP’s were they engaged in? What big mathematical ideas showed up in what they did/said? How would the kids describe their role in “math”? Teacher What was he doing? What was the purpose of his questions? What big mathematical ideas did he draw out? How would the teacher describe his role? Ryan Dent, LEUSD

37. Contextual Physical Visual Symbolic Verbal

38. Talking Points Round 3 Tally Agree/Disagree/Unsure Students’ understanding is deepened through discussion of similarities among representations that reveal underlying mathematical structures or essential features of mathematical ideas that persist regardless of the form. Using these different representations is like examining a concept through a variety of lenses, with each lens providing a different perspective that makes the concept richer and deeper. Multiple representations should be done and presented by the teacher so that students of a variety of learning styles will see the mathematics. Ryan Dent, LEUSD

39. Phil Daro says, “If I were teaching today…” Ryan Dent, LEUSD

40. Types of tasks Open-Ended Closed Open Middle

41. Rachel What do you notice? What do you wonder? video 1 (post) video 2 (pre) But first, think about a procedure that kids are expected to be proficient with before the end of this year. Ryan Dent, LEUSD

43. Would you rather…

44. Ryan Dent, LEUSD

45. Pre/Post Reflection What can I do to get every student to engage in the SMP’s? Ryan Dent, LEUSD

46. Tough Reflection Questions Compare the percent of time that students are talking in your classroom to the percent of time that you’re talking. Does that need to change? Of the time that you are talking, what percent of what you say is a statement? What percent of what you say is a question? Do your questions strive for what you want them to say, or to make their thinking visible? Who’s engaging in the SMP’s in your classroom…your students or you? Ryan Dent, LEUSD

47. What is my PLAN to get every student to engage in the SMP’s? Using Adobe Voice, create a compilation of the things you’ve heard, seen, captured, and/or experienced to illustrate a specific plan for what you are going to do to engage every student in the SMP’s. Think about the potential for using similar tools for students in your classroom. Ryan Dent, LEUSD

48. Explore the MTBOS 1.Spend some time exploring the MTBOS for a task that you could use in the next week to promote reasoning and problem-solving. http://bit.ly/1hIr6bP http://bit.ly/1hIr6bP 2.Identify a goal that would you would strive for in using that task that will keep you focused throughout the task. 3.Anticipate the strategies/representations students will use, and the sequence you will display them in Ryan Dent, LEUSD

49. I hope… You will launch rich, open-middle problems to kids to solve on their own. You will use their representations in a sequence for universal access. You will ask at least 3 times as many questions as you make statements. You will make kids’ thinking visible through discourse during at least 60% of your classroom time. Ryan Dent, LEUSD