1. How Do We Judge Whether Lesson Study is Working? How Do We Prove It To Others?

2. This material is based upon work supported by the National Science Foundation under Grant No. 0207259. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

3. Traveler, there is no road. The road is created as we walk it together. Antonio Machado

4. Goals Advance our understanding of lesson study and its evaluation Examine potential measures of lesson study progress Identify measures for our own work Formulate a networking plan (if desired)

5. sources

6. Planning Phase Lesson Study Collaborative planning Discuss goals for students & content Study available units & lessons Build from an existing lesson

7. Research Lesson Planning Phase Lesson Study 1 teacher teaches; others observe/ collect data Designed to bring to life a particular goal/ vision of education Record lesson - video, audio, student work, observation notes

8. Post-Lesson Activities Research Lesson Planning Phase Lesson Study Formally debrief lesson Share data Draw implications for lesson and teaching- learning more broadly Revise and re-teach if desired

9. Lesson Study 1. STUDY Consider long term goals for student learning and development Study curriculum and standards 2. PLAN Select or revise research lesson Do task Anticipate student responses Plan data collection and lesson 3. DO RESEARCH LESSON Conduct research lesson Collect data 4. REFLECT Share data What was learned about students learning, lesson design, this content? What are implications for this lesson and instruction more broadly?

10. ? Instructional Improvement Visible Features of Lesson Study Consider Goals Study Curriculum and Standards Plan and Conduct Research Lesson Collect Data Debrief Lesson Use Debrief to Inform Instruction How does lesson study improve instruction?

11. Visible Features of Lesson Study  Plan  Teach  Observe  Discuss  Etc. Key Pathway  Lesson Plans Improve Instructional Improvement A Common Early Conception of Lesson Study

12. Visible Features of Lesson Study Consider Goals Study Curriculum and Standards Plan and Conduct Research Lesson Collect Data Debrief Lesson Use Debrief to Inform Instruction What Else? How Does Lesson Study Improve Instruction? Cause Changes In: Teachers -Knowledge of subject matter and its teaching -General knowledge of instruction -Ability to observe students -Connection of daily instruction to long-term goals -Motivation/willingness to improve -Capacity to learn together, collegial networks Curriculum -Better lessons -Choice of better curricula System -Changes in policy -Changes in learning structures Result in Changes in Teaching-Learning Specific Examples: Teaching -Offer high-level task Learning -Student journals reveal thinking re: proportional reasoning

13. Can patterns help us find an easy way to answer the question: How many seats fit around a row of triangle tables?

14. Lesson Study What Happens Over Lesson Study Cycles? Builds: - Knowledge - Motivation to Improve Collective Work

15. Lesson Study 1. STUDY Consider long term goals for student learning and development Study curriculum and standards 2. PLAN Select or revise research lesson Do task Anticipate student responses Plan data collection and lesson 3. DO RESEARCH LESSON Conduct research lesson Collect data 4. REFLECT Share data What was learned about students learning, lesson design, this content? What are implications for this lesson and instruction more broadly?

16. Measures Related to Instruction Specific to topic: Yoshida: counting by ones vs. chunking R. Perry: ideas about proportional reasoning General to subject area: MK Stein: Mathematical task level General to teaching-learning: Student discourse

17. Low-Stakes, High-Yield Assessment Measures that reveal student thinking in ways that help you build learning “Use of assessments in an ongoing and repeated manner to monitor the qualities of teaching and learning, where the goal is solely formative and no high stakes are connected to the effort. My claim is that the two go together; the higher the stakes attached to the assessment, the less likely it is to yield useful diagnostic or formative information to the guide the practice. Most of the energy of educational assessment specialists has gone into "high stakes, low yield" assessments, given at the end of the year or program, designed for a single administration, and with results far too late to guide program modification or student work.” Lee Shulman, Carnegie Endowment for the Advancement of Teaching

18. ( NCTM, 2002)

19. Ideas From Planning Unit rate (value of a ratio) relates equivalent fractions; Relates to measurement; Uses division; Units (e.g., of 1) can be grouped to form larger units (e.g., of 5) Teachers don’t typically think in units, but in “simplest form” (Lo, Watanabe, & Cai, 2004)

20. Ideas From Planning These methods differ from the standard cross-multiply and divide algorithm (McDougall Littell, 2004)

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22. Ideas from Post-Lesson Activities Double number line can summarize methods

23. Evaluation of Proportional Reasoning How many of the research-identified important ideas about proportional reasoning came up in teachers’ planning? How many came up during the lesson?

24. Mathematical Task Level 1.Non-Mathematical 2.Memorization 3.Procedures Without Connections 4.Procedures With Connections 5.Doing Mathematics Stein, M.K., Smith, M.S., Henningsen, M., & Silver, E.A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press. Smith, M.S., & Stein, M.K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-3

25. Levels of Math-Talk Community Shift Over 0-3: Classroom community grows to support -student reasoning & contribution -focus on mathematical thinking, not only answers Shifts in 4 dimensions: -Questioning -Explaining Mathematical Thinking -Source of Mathematical Ideas -Responsibility for Learning Hufferd-Ackles, Fuson, Sherin JRME Mar 2004 35: 2, 81-116

26. Motivation to Continue to Improve Instruction Do teachers find their work useful? Are they motivated to continue it? Why or why not? Do teachers feel commitment and connection to group members? Do they feel responsibility to help others improve?

27. Changes in Norms, Identity, Learning Structures Changes in: Beliefs about children & teaching Identity: see self as researcher, as learner e.g., “kindergarten teachers should know algebra”) Schedules & structures (e.g.,meetings)

28. Example: Capacity to Learn Ex from www.stanford.edu/group/CRCwww.stanford.edu/group/CRC The teachers in this school Feel responsible to help each other do their best Share ideas and teaching practices

29. Example: Beliefs about Students Ex from www.stanford.edu/group/CRCwww.stanford.edu/group/CRC By trying different teaching methods I can significantly affect my students’ achievement level My expectations for my students’ learning have been increasing

30. Planning Phase Lesson Study Is the group building Knowledge? -Drawing on excellent resources -Solving, discussing mathematical tasks, predicting student thinking -Connecting prior & new ideas, exploring conflicts Motivation to Keep Improving Practice? -Ownership of work, connection to own questions & student needs -Commitment, connection to colleagues

31. Research Lesson & Debrief Planning Phase Lesson Study Is group building Knowledge? Observational Skills Research Stance Grasp of Student Thinking Motivation to Keep Improving Practice? Perceived Usefulness of Learning from Colleagues, Students, Outside Resources Sense of Commitment, Connection

32. Post-Lesson Activities Research Lesson Planning Phase Lesson Study Is the group building Knowledge? -Continued Application to Practice -Continued Information-Seeking - New Questions Motivation to Keep Improving Practice? - Perceived Usefulness of What Was Learned - Valuing/Feeling Valued by Colleagues

33. Protocol for Sharing Plans Listen SILENTLY to evaluation presentation (5 minutes) Write SILENTLY (5 minutes) -Most important things that will be learned from this evaluation -What might be added/changed