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

Post-Lesson Activities Research Lesson Planning Lesson Study

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

Research Lesson Planning Lesson Study 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

Research Lesson Planning Lesson Study Post-Lesson Activities Formally debrief Discuss how lesson brought goals to life Reflect on learning Revise and re-teach, if desired

Research Lesson Planning Phase Post-Lesson Activities Knowledge Creation Process Phase-specific collaborative activities Other professional experiencesHuman & 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 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) (Lo, Watanabe, & Cai, 2004)

Ideas From Planning “Unit rate” (multiplicative) and “factor of change” (additive) methods are alternative ways of solving proportional reasoning problems. Height in buttonsin paper clips Mr. Short 4 6 Mr. Tall 10 X Mr. Short 4 10 Mr. Tall 12 X (Cramer, Post, & Currier, 1993)

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

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

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