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 CollegeOakland, Californiarperry@mills.edu

http://www.lessonresearch.net

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

Post-LessonActivities

Research Lesson

Planning

Lesson StudyLesson Study

Planning

Lesson StudyLesson Study

Collaborative Discuss long-term & content goals Study available units & lessons on a

particular topic Revise an existing lesson

Research Lesson

Planning

Lesson StudyLesson Study

Designed to bring to life a particulargoal/ vision of education

1 teacher teaches; others observe/ collect data

Recorded - video, audio, student work, observation notes

Research Lesson

Planning

LessonLesson StudyStudyPost-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-LessonActivities

Knowledge Creation ProcessKnowledge Creation Process

Phase-specific collaborative 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 Important Knowledge for TeachingTeaching

(NRC, 2001)

Stage I - Characterizing InstructionStage 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 Stage II - Impact of Planning on Instructionon 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 PlanningIdeas 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 PlanningIdeas From Planning

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

Height Heightin buttons in paper

clipsMr. Short 4 6Mr. Tall 10 X

Mr. Short 4 10Mr. Tall 12 X

(Cramer, Post, & Currier, 1993)

Ideas From PlanningIdeas From Planning These methods differ from the standard cross-

multiply and divide algorithm

(McDougall Littell, 2004)

Ideas From PlanningIdeas From Planning

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

Stage III - Post-Lesson Stage III - Post-Lesson ReflectionReflection

Transcribed debriefing, planning sessions, coded as in stage II

Interviewed teachers and collected concept maps

Gathered artifacts re: continued reflection

Ideas from Post-Lesson Ideas from Post-Lesson ActivitiesActivities

Double number line can summarize methods

Ideas from Post-Lesson Ideas from Post-Lesson ActivitiesActivities

Double number line can summarize methods

Ideas from Post-Lesson Ideas from Post-Lesson ActivitiesActivities

Double number line can summarize methods

`

Implications for Professional Implications for Professional DevelopmentDevelopment

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 ResearchImplications 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