1. Should we be thinking in new ways about locally-led professional learning? Randomized trial of lesson study with mathematical resource kits SREE, September 2011 Catherine Lewis & Rebecca Perry Mills College, Oakland, CA www.lessonresearch.net

2. This material is based upon research supported by the Department of Education Institute for Education Sciences, Grant No. R308A960003. Any opinions, findings, and conclusions or recommendations expressed in this website are those of the authors and do not necessarily reflect the views of the grantors.

3. Knowledge Development and Use through 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 student learning, lesson design, this content? What are implications for this lesson and instruction more broadly?

4. Pathways Teachers’ Knowledge - of Content - of Instruction - of Student Thinking - of Curriculum Teachers’ Beliefs, Dispositions - Attention to Student Thinking - Beliefs about Students - Inquiry Stance toward Practice - Identity - Sense of Efficacy Professional Community - Changes in Norms - Changes in Relationships - Changes in Learning Opportunities Materials & Tools -Tasks, lessons, etc. Instructional Improvement Visible Features of Lesson Study Planning Curriculum Study Research Lesson Data Collection Discussion Revision Etc. How Does Lesson Study Improve Instruction? Student Learning

5. Theoretical Context of Lesson Study Situated cognition (Learning in context of practice; e.g., Cobb et al, 2003) Shared, improvable instructional plan accumulates knowledge (Morris & Hiebert, 2011) Professional learning community fosters knowledge, beliefs and habits to improve instruction (McLaughlin & Talbert, 2001) Lesson observation yields “High-yield, low stakes data” (Shulman, 2007) and “Practical measurement” (Bryk, 2011)

6. Common Challenges in Understanding Fractions Seeing fraction as number (“I can’t put 2/3 on number line because it’s two different numbers”) Understanding the magnitude of the denominator (that 1/6 is smaller than 1/5) Knowing what is the whole (construct whole from a fraction) Seeing that fractions can be greater than one

7. Research Literature & Field Studies Suggested Affordances of Linear Measurement Context for Learning Fractions Davydov & Tsvetkovich (1991) Saxe et al., (2007, 2009) Dougherty (2008) Watanabe (1996, 2002, 2006, 2007)

8. Area of circle Area of rectangle Part of a set Linear measurement 1 meter

9. Comparison of US & Japanese Texts

11. Some Dramatic Differences Earlier Introduction of Fractions in US More representations in US (15) than Japan (4) Different Representations Only Japanese texts used linear measurement Only US texts used circle area (and many others)

12. Grade 1 Harcourt Brace (US)

13. Fraction Understanding Using Linear Measurement: Japanese Ex.

14. 1 meter How Can We Describe the Blue Mystery Piece in Terms of One Meter?

15. Seeing Fraction as Number Linear measurement context may help students transition to see fractions as numbers on number line, not just as pieces or as situation

16. How Linear Measurement Context Might Help Length helps students attend to magnitude of fractions (how much) rather than just count pieces (how many) 1 meter

17. Understanding Meaning of Denominator Only 1 dimension (length) varies, making it easier to see that ½ is bigger than ¼ 1 meter

18. Understanding the Whole Standard measurement unit gives clear, stable image of the “whole” 1 meter

19. Understanding 4/3 as 4 1/3’s Length may support multiplicative image that 3 times 1/3 meter is 1 meter and x times 1/n meter is x/n meter meter

20. Lesson Study Resource Kit 1.Mathematics tasks to solve and discuss (& related student work to analyze) 2.Curriculum inquiry: Japanese textbook, lesson video, teachers’ materials 3.Lesson study materials (template for lesson plan, protocol for discussion, etc.) 4.Suggested teacher-led inquiry process to explore and use resource kit

21. 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 student learning, lesson design, this content? What are implications for this lesson and instruction more broadly? Materials

22. Teachers try a problem: Find the length of the mystery strip

23. Conduct Lesson Study Cycle

24. Randomized Trial: 3 Conditions C1: Lesson study with fractions resource kit C2: Lesson study without fractions resource kit, focused on self-chosen topic other than fractions C3: Locally-chosen professional development (Roughly 5 month study period)

25. Sample 13 Groups per condition (4-9 teachers per group, locally formed) 213 Teachers  41% New to Lesson Study  78% Elementary Teachers 1059 Students (Grades 2-5)

26. Pre- and Post-Assessment Students’ Knowledge of Fractions 17-41 item student assessment (3 forms for grades 2-3, 4,5): items from published research studies, NAEP, California standards, curriculum materials Teachers’ Beliefs and Dispositions, e.g. effectiveness of collegial learning expectations for student achievement research relevance for practice Teachers’ Knowledge of Fractions 33-item teacher assessment, from Univ. of Michigan LMT (21 items); Univ. of Louisville; New Zealand, etc. (plus additional self-rating & open-ended measures)

27. Teachers’ Fraction Knowledge Item examples: 1. Anna says 7/3 is not possible as a fraction. a) Is 7/3 possible as a fraction? Yes No (Circle one.) b)What action, if any, do you take as a teacher to respond to Anna? [Source: New Zealand Maths, 2009] Robin has 2 1/3 yards of rope and needs 5/6 yards to make each jump rope. How many jump ropes can Robin make? Please show your work. [Source: adapted from Shifter, 1998]

28. Students’ Fraction Knowledge Item examples: - How many fourths make a whole? Answer:______ [Source: IES/NCES, 2007] - Which of the following fractions is the greatest? 1/9 1 /2 1/5 1/10 [Source: California Department of Education, 2005] - I drank 1 3/5 cups of juice yesterday and 1 4/5 cups today. How much juice did I drink altogether on both days? Please explain and show your work. [Source: Japanese teacher’s manual]

29. HLM Analyses: Lesson Study with Resource Kit Vs. Two Other Conditions Combined Significant Impact on Teachers’ and Students’ Fractions Knowledge Effect sizes for teachers’ knowledge:.19 for mostly LMT-based measure.26 for open-ended measure of understanding of whole.37 for self-rating of fractions knowledge

30. Teachers’ Knowledge of Fractions at Pre- and Post-Test (Z Score)

31. Change in Students’ Fractions Knowledge (Absolute Score, N=1059, Effect Size:.50)

32. HLM Analyses: Impact of LS with Resource Kit on Teachers’ Beliefs Significant Positive Impact (p<.05) on: -Perceived Effectiveness of Collegial Learning -Expectations for Student Achievement -Research Relevance for Practice Marginal Positive Impact (p<.10) on: - Using and Promoting Student Thinking No Impact on: - Professional Community (why different from collegial learning, above?) - Interest in Mathematics

33. Survey Item Examples Expectations for Student Achievement No matter how hard I try, some students will not be able to learn aspects of mathematics [reversed item] (7 items, alpha:.63 pretest,.64 posttest) Research Relevance for Practice Educational research often provides useful insights for teaching (4 items, alpha:.64 pretest,.66 posttest) Using and Promoting Student Thinking I have some good strategies for making students’ mathematical thinking visible (4 items, alpha:.63 pretest,.68 posttest)

34. Perceived Effectiveness of Collegial Learning in Mathematics (alpha:.62 pretest,.63 posttest) I have learned a lot about student thinking by working with colleagues Working on mathematics tasks with colleagues is often unpleasant (rev) I have good opportunities to learn about the mathematics taught at different grade levels I have learned a great deal about mathematics teaching from colleagues I find it useful to solve mathematics problems with colleagues Vs. Professional Community Scale e.g. Mathematics teachers in this school regularly observe each other teaching classes….

35. Perceived Quality of Professional Learning Teachers in both lesson study conditions rated their professional learning significantly more positively than teachers in the locally-chosen professional learning condition on scale of the following indicators:

36. Professional Learning Quality (11 items, alpha:.95 posttest) Built on my existing knowledge of teaching and learning Helped me consider how to apply what I learned… Gave me ideas I would like to share with colleagues Was intellectually engaging and important Helped me see how content ideas are connected… Encouraged my active participation Valued my opinion, experience, and contributions Supported my own professional inquiry and investigation… Encouraged me to share ideas and take intellectual risks Included intellectual rigor, constructive criticism… Encouraged me to become more of an educational leader in my school/ district

38. Summary “Low touch” lesson study supported by mathematical resources: – Increased teachers’ and students’ mathematical knowledge – Increased teachers’ beliefs in effectiveness of collegial learning, usefulness of research, efficacy to improve student learning Lesson study (with or without toolkit) was seen by teachers as higher quality professional development than locally chosen PD

39. Groups of teachers worked independently in distant sites, suggesting the potential of locally-led learning in which educators actively adapt program to local site (rather than centrally-prescribed fidelity) Marriage of teacher-led inquiry and research-based (“system-valued”) resources may build local ownership and quality simultaneously Conclusions

40. Teacher-led investigation may create demand for research-based knowledge. “The problem, then, lies not in the supply of new ideas, but in the demand for them. That is, the primary problem of scale is understanding the conditions under which people working in schools seek new knowledge and actively use it to change the fundamental processes of schooling.” – Richard Elmore Elmore, R. F. (1996). Getting to scale with good educational practice. Harvard Educational Review 66(1): 1-26 Conclusions

41. Shared, improvable “instructional products that guide classroom teaching” (Morris & Hiebert, 2011) may provide vehicle to build and share knowledge in the U.S., as they have in Japan But, there is no place that our curriculum is held accountable (as happens in public research lessons in Japan)

42. Pathways Teachers’ Knowledge - of Content - of Instruction - of Student Thinking - of Curriculum Teachers’ Beliefs, Dispositions - Attention to Student Thinking - Beliefs about Students - Inquiry Stance toward Practice - Identity - Sense of Efficacy Professional Community - Changes in Norms - Changes in Relationships - Changes in Learning Opportunities Materials & Tools -Tasks, lessons, etc. Instructional Improvement Visible Features of Lesson Study Planning Curriculum Study Research Lesson Data Collection Discussion Revision Etc. How Does Lesson Study Improve Instruction? Student Learning

43. Quotes from Participants “The information my lesson study colleagues gathered while observing the lesson was very eye-opening. I would never have realized how many misconceptions my students had about fractions by listening to them. They could say with ease the sign represented one fourth of a mile, but they could not explain what that meant. Having additional eyes and ears in the classroom during a lesson is extremely valuable to me as a teacher. …The collaboration that occurs before, during, and after a lesson is extremely valuable to me.” [Teacher #557]

44. 4. REFLECT 3. DO RESEARCH LESSON 1. STUDY 2. PLAN 4. REFLECT 3. DO RESEARCH LESSON 1. STUDY 2. PLAN TIME QUALITY Lesson Material & Tools Teacher Community 4. REFLECT 3. DO RESEARCH LESSON 1. STUDY 2. PLAN Teachers’ Knowledge & Dispositions

45. Quotes from Participants The lesson study has taught me: We must never assume that all students understand. It was observed several times that even our "good" students did not have full understanding….Lesson study is staff development in its purest form. Rich discussion occurs. Team members are allowed to be creative, curious, self- motivated participants. The team building was incredible.” [Teacher #562]

46. Thank you! Catherine Lewis clewis@mills.educlewis@mills.edu Rebecca Perry rperry@mills.edurperry@mills.edu Lesson Study Resources at: www.lessonresearch.net www.lessonresearch.net Fractions Resource Kit at: www.lessonresearch.net/FRACTIONTK/fractions_ toolkit.html

47. References Cited Cobb, P., McClain, K., de Silva Lamberg, T., & Dean, C. (2003). Situating teachers' instructional practices in the institutional setting of the school and district. Educational Researcher, 32(6), 13-24. McLaughlin, M. W., & Talbert, J. E. (2001). Professional communities and the work of high school teaching. Chicago: University of Chicago Press. Morris, A. K., & Hiebert, J. (2011). Creating shared instructional products: An alternative approach to improving teachinig. Educational Researcher, 40(1), 5- 21. Shulman, L. (2007). Counting and recounting: Assessment and the quest for accountability. Change: The Magazine of Higher Learning 39(1):20-25.