Orchestrating Productive Mathematics Discussions:

1. Orchestrating Productive Mathematics Discussions: Analyzing, Selecting, and Sequencing Student Work

2. Warm Up A class needs five leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your answer. • Try to do this problem in as many ways as you can, both correctly and incorrectly. What might a student do? • If done, share your work with a neighbor. Consider together: What if there were 20 caterpillars? 100 caterpillars? N caterpillars? (Adapted from a NAEP task)

3. Module Learning Objectives We will continue the exploration of orchestrating productive mathematical discussions as we: • Build on the work we have done with tasks. • Analyze student work samples for alignment to lesson goals. • Discuss selecting and sequencing student solutions to highlight important mathematical ideas.

4. Mathematical Discourse What is discourse? What behaviors are these standards promoting in learners? SMP 1, 3, 6 MTP 3, 4, 6, 8

5. Mathematical Discourse • Mathematical discourse is a key part of keeping “doing mathematics” tasks at a high level. • Goals include: • Encouraging student construction of mathematical ideas. • Making students’ thinking public so it can be guided in mathematically sound directions. • Learning mathematical discourse practices.

6. 5 Practices for Orchestrating Productive Mathematics Discussions • Anticipating • Monitoring • Selecting • Sequencing • Connecting (Smith & Stein, 2011) Discuss each aspect of the model. Why would we want to use this model?

7. Why Do We Use the 5 Practices Model? • To make student-centered instruction more manageable by moderating the degree of improvisation required by teachers • To give teachers more control over the content that is discussed and teaching moves • To give teachers more time to diagnose students’ thinking • To allow teachers to plan questions and other instructional moves to probe student thinking • To provide a reliable process for teachers to take math lessons and class discussions to a deeper level

8. Leaves & Caterpillars Task A class needs five leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your answer. • Try to do this problem in as many ways as you can, both correctly and incorrectly. What might a student do? • If done, share your work with a neighbor. Consider together: What if there were 20 caterpillars? 100 caterpillars? N caterpillars? (Adapted from a NAEP task)

9. Leaves & Caterpillars Task A class needs five leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your answer. • Try to do this problem in as many ways as you can. • What if there were 20 caterpillars? 100 caterpillars? N caterpillars? Would this task be considered a cognitively demanding task? Why or why not?

10. Leaves & Caterpillars: The Case of David Crane Read the vignette and consider these questions: • What aspects of the vignette do you see as promising? • What aspects of implementation would you consider doing differently?

11. Selecting Student Work to Feature for Discussion — Adapted from Mary Kay Stein and Margaret Schwan Smith. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teacher of Mathematics.

12. Planning for Selecting — Adapted from Mary Kay Stein and Margaret Schwan Smith. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teacher of Mathematics.

13. Something to Consider When deciding whether to take up a student's idea in a whole group discussion: • Does it move us forward to our ultimate goal? • Is the class as a whole at a place to digest or make sense of it? • Do I have time to unpack it well right now or do I need to use it in a new lesson? ?

14. What About Wrong Answers? Do we select wrong answers to share during discussions? When do we select wrong answers to discuss? • Always? • Sometimes? • Never? My Favorite No

15. Sequencing Student Responses During the Discussion — Adapted from Mary Kay Stein and Margaret Schwan Smith. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teacher of Mathematics.

16. How Do I Sequence Work Samples? • Begin with the strategy used by the majority of students before moving to those strategies that only a few students used • Begin with a strategy that is more concrete, then move to strategies that are more abstract • Present strategies that address common misconceptions • Have related or contrasting strategies presented one right after the other — Adapted from Mary Kay Stein and Margaret Schwan Smith. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teacher of Mathematics.

17. Planning for Sequencing

18. Possible Sequencing Possible sequencing of the Leaves & Caterpillars Task: • Martin (picture) • Jamal (table) • Janine (picture/written explanation) • Jason (written explanation)

19. Connecting Student Responses During the Discussion

20. Planning for Sequencing

21. Possible Connecting What connections could be made among the responses?

22. Possible Connecting Compare Janine’s and Jamal’s work. Where is Janine’s unit rate in Jamal’s table? Compare Jason’s work with Martin’s and Jamal’s work. Where is the scale factor of 6?

23. Process Check • What strategies can you use to ensure that ALL students engage in mathematical discourse in your classroom? • What can you do to leverage incorrect or incomplete reasoning or solutions to strengthen the learning of all students? • Based on your learning for this section, what action step(s) might you take in order to foster mathematical student discourse in your classroom?

24. Mathematical Discourse • Mathematical discourse is a key part of keeping “doing mathematics” tasks at a high level. • Goals include: • Encouraging student construction of mathematical ideas. • Making students’ thinking public so it can be guided in mathematically sound directions. • Learning mathematical discourse practices.

25. Moves to Guide Discussion and Ensure Accountability • Revoicing a statement or question • Restating what someone says • Asking students to apply their own reasoning to someone else’s reasoning • Prompting students for further participation • Using wait time

26. Moving Beyond “Showing and Telling” • Choose cognitively demanding tasks. • Understand the importance and challenge of facilitating a discussion. • Plan using the 5 practices model in order to facilitate discussions more effectively.

27. Let’s Look at Some Student Work Think back to the task we did in our PD Module: Analyzing and Sequencing Tasks,Mr. Nelson’s Art Supplies. • How did you approach the task? • How did you anticipate that students would approach the task? • Let’s take a look at some student work for this task.

28. Task: Mr. Nelson’s Art Supplies Mr. Nelson is going shopping and spilled grape jelly on the supply list! Help find the missing information for each item on his list of art supplies. Show how to distribute the supplies he bought amongst two work tables.

29. Looking at Student Strategies As a table group, analyze the student work from the taskMr. Nelson’s Art Supplies. Place a post-it note on each response noting what the student understands or what the student is missing.

30. Sharing Our Thinking Select a response that surprised you and share your group’s discussion about that response. What evidence helps determine what the student understands?

31. Looking at Student Strategies • Pretend you are circulating around the classroom and you see the student work. • Select and sequence the responses. • Decide which students you would select to share their work. In what order? • Explain how the work you selected will frame the discussion in a way that fosters student understanding of the mathematical goal.

32. Sequence 1- Humberto, Jeffrey, Jillian, Makayla (Valeria) 2- Humberto, Camryn, Jillian 3- Zyon (first part), Camryn, Jillian 4- Camryn, Jillian, Zyon, Makayla 5- Humberto, Zyon, Jillian, Makayla What if I have questions about… ??

33. Progression Possibilities

34. Original photo from: lickr.com/photos/jose_kevo/2205309676/

35. Reflection • What aspects of planning and choosing tasks are relevant to preparing lessons that involve rich conversations about important mathematics? • What steps can we take when students share their work to ensure productive mathematical discussions in our classroom?

36. Reflection In this cycle of reflection, where do you find yourself as it relates to orchestrating productive mathematical discussions? Write two or three action steps you can take between now and September to take your classroom discussions to the next level. What resources do you need or what steps can you take to move to the next stage?

37. References National Council of Teachers of Mathematics. (2014). Principles to actions: ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics. Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematical discussions. Reston, VA: National Council of Teachers of Mathematics. Stein, M. K., Engle, R.A., Smith, M.S. & Hughes, E. K. (2008). Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell. Mathematical Thinking and Learning, 10, 4, 313-340.

38. Tools for Teachers Writing Teams Kindergarten • Dawne Coker, Lead • Lynne Allen • Leigh Belford • Carol Midgett First Grade • Martha Butler, Lead • Felisia Gulledge, Lead • Laura Baker • Danielle Long Second Grade • Tery Gunter, Lead • Carly Morton • Dianne Wells • Isaac Wells Third Grade • Leanne Daughtry, Lead • Robin Hiatt • Meg McKee • Kaneka Turner Fourth Grade • Ana Floyd, Lead • Lisa Garrison • Shelly Harris • Deanna Wiles Fifth Grade • Marta Garcia, Lead • Susan Copeland • Brandi Newell • Rebekah Lonon

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