Teachers’ Knowledge Development During Toolkit-Supported Lesson Study Preliminary Findings

1. Teachers’ Knowledge Development During Toolkit-Supported Lesson Study Preliminary Findings Rebecca Perry, Catherine Lewis, Shelley Friedkin, & Elizabeth Baker Mills College Oakland, California http://www.lessonresearch.net

2. This material is based upon work supported by the National Science Foundation under Grant No. DRL-0633945 and DRL-0723340. 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 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 4. REFLECT Share data What was learned about students learning, lesson design, this content? What are implications for this lesson and instruction more broadly? 3. DO RESEARCH LESSON Conduct research lesson Collect data

4. How does lesson study improve instruction? • Visible • Features of Lesson Study • Planning • Curriculum Study • Research Lesson • Data Collection • Discussion • Revision • Etc. ? Instructional Improvement

5. How Does Lesson Study Improve Instruction? Pathways Teachers’ Knowledge -of Content -of Instruction -of Student Thinking Teachers’ Personal Disposition -Identity -Sense of Efficacy -Attention to Student Thinking - Beliefs about Students - Inquiry Stance on Practice Learning Community -Changes in Norms -Changes in Participation Opportunities - Changes in tools • Visible • Features of Lesson Study • Planning • Curriculum Study • Research Lesson • Data Collection • Discussion • Revision • Etc. Instructional Improvement

6. How Does Lesson Study Improve Instruction? Pathways Teachers’ Knowledge -of Content -of Instruction -of Student Thinking Teachers’ Personal Disposition -Identity -Sense of Efficacy -Attention to Student Thinking - Beliefs about Students - Inquiry Stance on Practice Learning Community -Changes in Norms -Changes in Participation Opportunities - Changes in tools • Visible • Features of Lesson Study • Planning • Curriculum Study • Research Lesson • Data Collection • Discussion • Revision • Etc. Instructional Improvement

7. How Does Lesson Study Improve Instruction? Pathways Teachers’ Knowledge -of Content -of Instruction -of Student Thinking Teachers’ Personal Disposition -Identity -Sense of Efficacy -Attention to Student Thinking - Beliefs about Students - Inquiry Stance on Practice Learning Community -Changes in Norms -Changes in Participation Opportunities - Changes in tools • Visible • Features of Lesson Study • Planning • Curriculum Study • Research Lesson • Data Collection • Discussion • Revision • Etc. Instructional Improvement

8. Toolkit 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 4. REFLECT Share data What was learned about students learning, lesson design, this content? What are implications for this lesson and instruction more broadly? 3. DO RESEARCH LESSON Conduct research lesson Collect data

9. Why Toolkits? • Kyouzai kenkyuu (“curriculum study”) is important part of lesson study • U.S. textbooks may not support “curriculum study” of the mathematics, student thinking • Much U.S. mathematics education research is not well-reflected in teachers’ manual or textbook

10. Toolkit Topics • Proportional Reasoning • Area of Polygons

11. Toolkit Contents • Mathematical Tasks & Student Work • Curriculum Materials • Research Articles & Summaries • Lesson Videos • Reflection Forms & Questions

12. Mathematical Tasks (Ex: NAEP)

14. Curriculum Materials

15. Research (Examples) • Driscoll, Mark, Nikula, Kelemanik, DiMatteo & Egan (2007) - The Fostering Geometric Thinking Toolkit: A Guide for Staff Development, Heinemann (Area). • Lamon (2006) - Teaching Fractions and Ratios For Understanding, Erlbaum (PR).

16. Lesson Videos (Example) Can You Find the Area? Akihiko Takahashi, U.S. Classroom

17. Reflection Forms and Questions (examples) • Concept map: Sequence of understandings that students develop • Daily meeting reflection • Reflection on lesson study cycle

19. Data Sources • Teacher assessment (pre and post) • Reflection forms • Lesson study artifacts • Video data of lesson study meetings & research lesson for 4 “intensive study” groups

20. Sample

21. Outcomes: Mathematical Knowledge for Teaching

22. Outcomes: Knowledge Mathematics Knowledge for Teaching (Hill & Ball; Univ. of Chicago School Mathematics Project)

23. Standardized Teacher Assessment Items

26. Prop Reasoning Item At the currency exchange, Jean-Pierre can get three Euros for every four Dollars he trades in. Jean-Pierre wonders if this is a proportional situation. Is it? Why or why not? Make a table, graph, and equation to show Jean-Pierre the relationship of Euros and Dollars. What aspects of the table, graph, and equation might help Jean-Pierre notice whether the relationship is proportional?

27. Change in Teachers’ Use of Prop. Reasoning Codes - Pre to Posttest

31. Teachers’ Reflections Learning Connections Complicate Coding 10% Coded Content/ Student Understanding of Content, e.g.: “Since I’m still developing my knowledge and understanding of proportion and ratio, I was surprised to learn the importance of fractions, algebra, patterns, multiplication and addition, tables, and graphs in solving problems involving ratio and proportional reasoning.” [ID 369]

32. Outcomes: Personal Dispositions

33. Teachers’ Interest/ Enjoyment in Learning Mathematics Scale • I enjoy teaching mathematics. • I like solving mathematics problems. • I actively look for opportunities to learn more mathematics. • I would like to learn more about area of polygons. • I am interested in the mathematics taught at many grade levels. • I would like to learn more about ratio, proportion, and rate..

35. Teachers’ Expectations for Student Achievement Scale • No matter how hard I try, some students will not be able to learn aspects of my subject matter (reversed). • My expectations about how much students should learn are not as high as they used to be (reversed). • Students who work hard and do well deserve more of my time than those who do not (reversed). • The attitudes and habits students bring to my classes greatly reduce their chances for academic success (reversed). • There is really very little I can do to ensure that most of my students achieve at a high level (reversed). • Most of the students I teach are not capable of learning material I should be teaching them (reversed).

38. Outcomes: Learning Community

39. Teachers’ Collegial Learning Effectiveness • I have learned a lot about student thinking by working with colleagues. • I have learned a great deal about mathematics teaching from colleagues. • I find it useful to solve mathematics problems with colleagues. • Working with colleagues on mathematical tasks is often unpleasant (rev.)

41. Summary: What have we learned? • Teachers’ Knowledge • No significant impact on standardized assessment items of MKT • Impact on open-ended assessment items and self-reported knowledge of topics • Teachers’ Personal Dispositions • Some evidence of increased enjoyment and expectations • Teacher Learning Community • Increase in self-reported collegial learning effectiveness

42. Final Thoughts • Standardized MKT assessment items may not be a good fit for lesson study, since a group’s focus cannot be specified in advance • Need for research to follow groups over multiple cycles, to see whether changes self-reported collegial learning effectiveness and personal dispositions have future impact • Our simple linear model does not capture any loops within the model – for example, how collegial learning effectiveness affects knowledge or vice versa.

43. Thank you! Email address: rperry@mills.edu clewis@mills.edu Website address: lessonresearch.net