What Do Lessons Tell Us About Teachers’ Learning From Lesson Study? Betsy King, Catherine Lewis, Aki Murata & Rebecc

1. What Do Lessons Tell Us About Teachers’ Learning From Lesson Study? Betsy King, Catherine Lewis, Aki Murata & Rebecca Perry Lesson Study Group at Mills College Oakland, California http://www.lessonresearch.net

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. Lesson Study Planning Phase Research Lesson Post-Lesson Activities

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

5. Lesson Study Planning Phase Research Lesson • 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

6. Lesson Study Planning Phase Research Lesson Post-Lesson Activities • Formally debrief lesson • Discuss how lesson brought goals to life • Revise and re-teach if desired

7. Case 1: Overview • 5-day summer workshop • 14 participants from 8 sites • Elementary and middle school teachers & administrators

8. What Happened • Initial planning group (“IPG,” 3 members) pre-planned series of 3 grade 5 lessons based on Investigations • Whole group (14 members) helped revise plans, collect data, discuss lessons • 1 IPG member “guest taught” the 3 lessons to a class of 5th graders over 3 days

9. Data • Video and transcriptions of 3 lessons, 3 debriefs, and 13 hours of planning meetings • Written reflections (twice daily) in response to prompts, e.g, what is mathematical discourse and how does it promote math learning? What are the important ideas in teaching volume? • Lesson plans • Follow-up emails with IPG

10. Identified “Learning Threads” Topics in mathematics and its teaching-learning that surfaced more than twice • Examples: • When and how to define mathematical vocabulary • Volume is not counted but measured: Moving students from counting to multiplicative view is important

11. More Examples of Learning Threads • Base times height provides a better basis for generalization to other prisms than does length times width times height • Need to focus on the mathematical purpose of the lesson, not just the activities • Blackboard can provide a written record of the lesson

12. When & How to Define Mathematical Vocabulary:Natural History of This Learning Thread

13. I: Prior to First Lesson • IPG added definitions and academic vocabulary activity to Investigations

14. IPG Additions • Teacher defines “volume” at outset • Teacher leads class to list descriptors of rectangular prisms and introduces term • “Length” “width” and “height” defined by teacher, linked to student informal vocabulary

15. Altered Lesson Plan Surfaced Differences in Thinking If use the term “rectangular prism”, must define it precisely. This can’t be done in 10 minutes; takes 2-3 lessons VS. Don’t want to spend too long defining it, but want to expose students to the term “rectangular prism”--if it’s said enough times students will get the idea

16. Examples of Pre-Lesson Views • “The fact that we call it a prism…It’s just like me calling you by your name….I don’t need to know where your name came from” • “If it were daily conversation, we could use “prism”, but since this is a mathematics lesson we need to use terms very very carefully…all the terms…should be defined

17. “Front-load” Vocabulary for 2nd Language Learners “We’re dealing with a lot of second language students… So when we’re given the opportunity to use some academic language, I think it’s … best…to go ahead and use it. If we were to called this a box or a shape…we are missing out on an opportunity to use the academic language and call this a rectangular prism so that they hear that word, are associating it with this particular shape.”

18. Lesson 1: A Compromise • Instructor did not define or use “rectangular prism” or “volume” • But spent much lesson time on activities designed to: • Elicit descriptors of rectangular prisms • Elicit students’ informal terms for height, width, and length and map to these 3 terms

19. Lesson 1 Debrief • Only 5/27 students wrote about 3 dimensions • Members concerned that lesson did not move students toward understanding of 3 dimensions and volume • Different ideas about why: • Inadequate vocabulary development • No classroom foundation for discourse • Nature of task (3 dimensions not needed)

20. Reflections After Lesson 1 “Consistency necessary with new vocabulary. Confusing for students/teacher to use same word to describe different thing.” “Do students need to be able to clearly define length, width, and height to find volume and understand the concept?”

21. Final Reflections:Elements You Will Incorporate in Practice “I’m going to focus on being more conscious of when, how I introduce vocabulary” “The difference between learning vocabulary vs. learning the concept/the meaning”

22. 3 Months Post-Workshop IPG revises unit and teaches in own venue Problem revised so all 3 dimensions need to be discussed Students who write about 3 dimensions -Summer workshop: 18% -Revised unit: 52%

23. Changed View of “Front-loading” Vocabulary “This is primarily a reading strategy that was assumed to work in mathematics. Contrary to this, we have found that if we begin by teaching the mathematical concept with informal vocabulary first and after the concept is grasped we explicitly add the academic vocabulary that this works much better in terms of students being able to use the vocabulary and retention…” An IPG member’s summary of talk to math conference

24. A Different View “I still take issue with [Japanese colleague’s] resistance to the vocabulary development aspects of the lesson. I still feel very strongly about the need for EL students to review and see academic language as often as we can offer it to them” -Another IPG member, 7 months after workshop

25. Implications for Lesson Study • Discussion of written lesson plan surfaced differences in thinking • Changes occurred over time, not in the course of a single lesson cycle • “Model” curriculum provides rich starting point

26. Implications for Research • Participants learned different things -Some things could be specified in advance, others not.

27. Implications for Research 2. Teachers continued to experiment after workshop Does PD foster structures, motivation, habits of mind for continued learning from practice?

28. Implications for Research 3. The Nature of “Research-Based Practice” Definitions and vocabulary development added because of research on 2nd language learners Need practice-based opportunities to test and qualify “proven” research findings

29. Please Evaluate Resources Table 2: History of Learning Thread Discussion Excerpts