The “Sandwich” Approach to Professional Development: Knowledge Creation Though Lesson Study

Rebecca Perry, Catherine Lewis, Aki Murata, Lesson Study Group Members Lesson Study Group at Mills College Oakland, California [email protected]

http://www.lessonresearch.net

This research is supported by the National Science Foundation under Grant No. REC-0207259.

Planning

Lesson Study

Research Lesson Post-Lesson Activities

Planning

Lesson Study

 Collaborative  Discuss long-term & content goals  Study available units & lessons on a particular topic  Revise an existing lesson

Planning

Lesson Study

Research Lesson

 Designed to bring to life a particular goal/ vision of education  1 teacher teaches; others observe/ collect data  Recorded - video, audio, student work, observation notes

Planning

Lesson Study

Research Lesson Post-Lesson Activities

 Formally debrief  Discuss how lesson brought goals to life  Reflect on learning  Revise and re-teach, if desired

Knowledge Creation Process Planning Phase Research Lesson

Phase-specific collaborative activities

Post-Lesson Activities

* Other professional experiences Human & material resources * Knowledge created by: a) encountering new ideas, b) making connections/ contrasting ideas with existing knowledge, c) self monitoring learning (e.g., asking questions or seeking clarification), and d) drawing on motivation and efficacy.

Important Knowledge for Teaching ( NRC, 2001)

Stage I - Characterizing Instruction

 Videotaped, transcribed lesson  Coded for math content, instructional strategies to identify themes  Reviewed individual written student work with video support to capture mathematical thinking

( NCTM, 2002)

Stage II - Impact of Planning on Instruction

  Transcribed planning sessions, coded for:  Instructional elements (content, instruction, s. thinking)  Evidence of knowledge creation (new idea, compare/ contrast idea, question/ clarify)  Supports Identified themes overlapping with lesson and traced evolution of ideas  Today detailing evolution of

unit rate

concept

Ideas From Planning (Lo, Watanabe, & Cai, 2004)

 Unit rate (value of a ratio) relates equivalent fractions;  Relates to measurement;  Requires division;  Units (e.g., of 1) can be grouped to form larger units (e.g., of 5)

Ideas From Planning Mr. Short Mr. Tall Mr. Short Mr. Tall 4 10 4 12

Height in buttons Height in paper clips

6

X

10

X

(Cramer, Post, & Currier, 1993)

“Unit rate” (multiplicative) and “factor of change” (additive) methods are alternative ways of solving proportional reasoning problems.

Ideas From Planning

 These methods differ from the standard cross multiply and divide algorithm

(McDougall Littell, 2004)

Ideas From Planning

 Students’ solutions to caterpillar problem demonstrated the use of different rates (1:2.5, 2:5, 4:10).

Stage III - Post-Lesson Reflection

 Transcribed debriefing, planning sessions, coded as in stage II  Interviewed teachers and collected concept maps  Gathered artifacts re: continued reflection

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Ideas from Post-Lesson Activities

Double number line can summarize methods

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Ideas from Post-Lesson Activities

Double number line can summarize methods



Ideas from Post-Lesson Activities

Double number line can summarize methods

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Implications for Professional Development

Organize in “sandwich” configurations   Draw on materials that specify important mathematical ideas Consult with “knowledgeable others”  Actively engage teachers in mathematics  Compare adult and student thinking

Implications for Research

 More research to clearly define mathematical concepts (borrowing from other countries)  Collect/use student work (pre-post) as window into teacher thinking  Collect/ use reflection tools like concept maps or journals