What Counts as Evidence of Learning from Practice? Collaborative Critique of Lesson Study Research Methods Teacher Learning in Elementary School Lesson Study Catherine C. Lewis, Rebecca R. Perry, Aki Murata Mills College, Oakland CA Teacher Learning in Middle/High School Lesson Study Brian T. Lord & Jane Gorman, Education Development Center Discussant/Chairs Deborah L. Ball, Jennifer M. Lewis

What Constitutes Evidence of Teachers’ Learning from Lesson Study? Three Elementary School Examples Catherine Lewis Rebecca Perry Aki Murata Lesson Study Group at Mills College Oakland, California Paper available at lessonresearch.net

This material is based upon work supported by the National Science Foundation under Grant No 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.

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 student 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, the lesson design, instruction? What are implications for improvement of this lesson and instruction more broadly?

Change in Framework Learning: 1. Acquiring Knowledge 2. Connecting Knowledge (Reorganizing, Pruning) 3. Monitoring Progress Based on Knowledge Integration Environment (Linn, Eylon, & Davis, 2004)

Figure 3: Reasons to Gather Evidence Build lesson study knowledge base and theory Summative impact studies Test design- based improvements STEP ONESTEP TWO

Please Respond on Form How important is the knowledge pursued by the teachers? Will the knowledge be generative or fleeting?

Understanding Student Thinking about “Solving in Different Ways” Aki Murata Mills College

Mindy’s Experience in the Lesson Study Group Primary-grade Lesson Study Group (4 teachers, Grades 1, 2, and Special Ed) Third Year Being a Part of District’s Lesson Study Effort Math Topic: Combining with Unknown Change Monthly Lesson Study Meetings (Oct Feb 2004) In-class Student Assessment Anticipated Student Thinking Modified Existing Lesson Research Lesson Taught in February, Revised and Re-taught again in March

Shift in Mindy’s Thinking about “Solving in Different Ways” “What Different Ways can We Solve a Problem?” “Pictures, Numbers, and Words!” [Oct] Lesson Plan Goals and Anticipated Responses Mix Student Thinking Processes and Ways of Showing [Oct - Feb] Mindy Came to Realize: –A Student Can Show One Thinking Process in Multiple Ways –Teacher Observation and Questions Necessary to Identify Student Thinking Processes [Feb] Mindy Sets Goal to Pay Closer Attention to Student Thinking as They Work on Problems [Mar]

Counting-up Strategy Shown in Different Ways (Example 7 + __ = 10) Using drawings: 1. Student draws 7 circles 2. He/she counts up to 10 (8, 9, 10) as he/she draws more circles, 3. He/she counts the second part again from 1 (1, 2, 3) to get the answer 3. Using cubes: 1.Student builds a tower with 7 cubes, 2. He/she counts up to 10 as he/she adds more cubes (8, 9, 10), 3. He/she counts the second part again from 1 (1, 2, 3) to get the answer 3.

Different Strategies, Both Using Cubes (Example 7 + __ = 10) Counting Up: 1.Student builds a tower with 7 cubes, 2. He/she counts up to 10 as he/she adds more cubes (8, 9, 10), 3. He/she counts the second part again from 1 (1, 2, 3) to get the answer 3. Decomposing: 1.Student builds a tower with 10 cubes, 2.He/she takes the part of 7 away from the tower, 3.He/she counts the remainder of the tower to get the answer 3.

Features of Lesson Study that Supported Mindy’s Learning Opportunities to think deeply about student thinking Contextual/structural support –Multiple reflection opportunities (planning meetings, research lessons, debriefing) –Collaborative setting to exchange ideas Tools and material support –Actual student data (pre-lesson & in-lesson) –Existing lesson plan –Data collection tool provided by a collaborating educator

Please Respond on Form How important is the knowledge pursued by the teachers? Will the knowledge be generative or fleeting?

Learning about Line Symmetry Rebecca Perry Mills College

How Many Lines of Symmetry Do these Designs Have?

Background on the Study Five grade 3-6 teachers from 3 Bay Area districts. Case study period: 3 days during 2003 summer workshop; (Follow-up throughout and after workshop). Topic: line symmetry for 4 th graders. Data: videotaped and transcribed lesson study work, written artifacts, communication.

Progression of Ideas about Line Symmetry Young children… can explore [symmetry]…by using mirrors, paper folding, and tracing. Later, their knowledge… should become more formal and systematic. In grades 9-12 students draw on an understanding of symmetry to use matrices and function notation to express transformation. [NCTM Principles and Standards, 2000]

Teachers’ Definition of Line Symmetry Day 1: –“A line that divides a figure into two halves such that the halves are mirror images of each other.” [NCTM Navigations] –“If it’s the same on one side [of a mirror reflection] then it’s the same on the other side.” Day 3 and 7 months after workshop: –“Points at opposite locations across a line.” –“The parameters have to be defined (at least in the teacher’s mind)… color and/ or shape can affect symmetry.”

Ways of Demonstrating Line Symmetry Day 1: –“What helps me is…folding it. I think I was the only person yesterday who needed to fold it, to double check myself.” Day 3: –Visualize, using cues Not even number (matched pairs) Shape of design Color Position/ orientation –Fold/ use a mirror to prove

Features of Lesson Study that Supported Teachers’ Learning Discussion of (Students’ and Teachers’) Thinking Based on: –Symmetrical/ Assymetrical Designs and Lesson Materials –Existing Lesson Plans and Curricula –Group’s Cross-Grade Knowledge and Prior Teaching Experience –Input from 2 Outside Math Specialists –Observations of Students’ Reactions to the Lesson

Example 3: Lesson Study Cycle From summer algebra-lesson study workshop Elementary teachers (cross-school group) Cycle of 2 research lessons, 2 days apart, in “borrowed” classrooms at year-round school

Can patterns help us find an easy way to answer the question: How many seats fit around a row of triangle tables?

What did teachers learn? There are several different types of patterns in this problem (numeric, algebraic, physical) and connections among the patterns Students may see the numeric pattern without seeing the algebraic or physical patterns Students may learn something in the course of organizing data for themselves that they do not learn by organizing it in a table provided to them

What features of lesson study supported teachers’ learning? Existing curriculum Careful observation of students Sharing of student observation data 2 (conflicting) measures of student learning Re-teaching of research lesson Audience comments Reflection after 2 teachings

Please Respond on Form How important is the knowledge pursued by the teachers? Will the knowledge be generative or fleeting?