teachers’ knowledge development during toolkit-supported lesson study preliminary findings rebecca...

Teachers’ Knowledge Development During Toolkit-Supported

Lesson Study

Preliminary Findings

Rebecca Perry, Catherine Lewis, Shelley Friedkin, & Elizabeth Baker

Mills CollegeOakland, California

http://www.lessonresearch.net

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.

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

3. DO RESEARCH LESSON

Conduct research lesson

Collect data

4. REFLECT

Share data

What was learned about students learning, lesson

design, this content?

What are implications for this lesson and instruction more

broadly?

? InstructionalImprovement

VisibleFeatures of Lesson Study

•Planning•Curriculum Study•Research Lesson•Data Collection•Discussion•Revision•Etc.

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

InstructionalImprovement

VisibleFeatures of Lesson Study

•Planning•Curriculum Study•Research Lesson•Data Collection•Discussion•Revision•Etc.

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

InstructionalImprovement

VisibleFeatures of Lesson Study

•Planning•Curriculum Study•Research Lesson•Data Collection•Discussion•Revision•Etc.

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

InstructionalImprovement

VisibleFeatures of Lesson Study

•Planning•Curriculum Study•Research Lesson•Data Collection•Discussion•Revision•Etc.

How Does Lesson Study Improve Instruction?

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

3. DO RESEARCH LESSON

Conduct research lesson

Collect data

4. REFLECT

Share data

What was learned about students learning, lesson

design, this content?

What are implications for this lesson and instruction more

broadly?

ToolkitToolkit

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

Toolkit Topics

• Proportional Reasoning

• Area of Polygons

Toolkit Contents

• Mathematical Tasks & Student Work

• Curriculum Materials

• Research Articles & Summaries

• Lesson Videos

• Reflection Forms & Questions

Mathematical Tasks (Ex: NAEP)

Curriculum Materials

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).

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

Reflection Forms and Questions (examples)

• Concept map: Sequence of

understandings that students develop

• Daily meeting reflection

• Reflection on lesson study cycle

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

SampleAssigned PR

ToolkitAssigned AP

ToolkitComparison

TeachersIndividual Teachers 44 37 28Groups 8 8 6Elementary Teacher 21% 46% 41%Middle Teacher 59% 30% 30%High Teacher 14% 16% 11%Not Teaching 7% 8% 19%<5 Years 18% 31% 26%5-14 Years 50% 46% 73%15+ Years 32% 23% 11%New to LS 36% 49% 59%Done 1 LS Cycle 16% 11% 15%Done LS for 1-2 Yrs 16% 22% 15%Done LS for 3+ Yrs 32% 19% 11%

% With Math Degree/ Credential 48% 41% 39%

Number of Participants

Years Prior Lesson Study Experience

Years Teaching Experience

Current Position

Outcomes: Mathematical

Knowledge for Teaching

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

Standardized Teacher Assessment Items

# Question Stems

# Individual

ItemsSource (# Items

from Source)Proportional Reasoning Subtest 11 24 LMT (24)

Area of Polygons Subtest 7 10

LMT (5), UCSMP (4), NAEP (1)

Standardized Scores on Proportional Reasoning Subtest

0.30

-0.17

0.32

-0.17-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

PR Toolkit Teachers (N=44) Comparison Teachers (N=28)

Standard Deviation Units

Pretest

Posttest

Standarized Scores on Area of Polygons Subtest

-0.02

-0.26

0.04

-0.31

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

AP Toolkit Teachers (N=37) Comparison Teachers (N=28)

Standard Deviation Units

Pretest

Posttest

Prop Reasoning Item

At the currency exchange, Jean-Pierre can get three Euros for every four Dollars he trades in.

a) Jean-Pierre wonders if this is a proportional situation. Is it? Why or why not?

b) Make a table, graph, and equation to show Jean-Pierre the relationship of Euros and Dollars.

c) What aspects of the table, graph, and equation might help Jean-Pierre notice whether the relationship is proportional?

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

PR Toolkit Teachers

Comparison Teachers

x and y multiplied by same number -constant rate/ ratio + +multiplicative relationship +unit rate (isolated Euros or Dollar value with equation) -equivalent ratios (shows equivalent ratios in table) + +y=mx form of equation +linear relationship/ straight line + -line goes through 0 +constant slope -equal cross products +

What Students Need to Understand about Area of Rectangles - Increase in Use of

Coding Category Pre- to Posttest

0%

10%

20%

30%

40%

50%

60%

Area Calculation Meaning of Area; Meaningof Measurement

Connection to Other Topics

% Increase

AP Toolkit Teachers (N=21)

All Comparison Teachers (N=44)

I have strong knowledge of ratio, proportion, and rate.

3.483.29

3.91

3.43

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

PR Toolkit Teachers (N=43)* Comparison Teachers (N=28)

Scale Rating

Pretest

Posttest

I have strong knowledge of area of polygons.

3.06

3.39

3.97

3.39

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

AP Toolkit Teachers (N=37)* Comparison Teachers (N=28)

Scale Rating

Pretest

Posttest

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]

Outcomes: Personal Dispositions

• 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..

Teachers’ Interest/ Enjoyment in Learning Mathematics Scale

Teachers' Interest/ Enjoyment in Learning Mathematics

25.18

24.64

25.81

24.29

23.5

24

24.5

25

25.5

26

Toolkit Teachers (N=77) Comparison Teachers (N=28)

Scale Rating

Pretest

Posttest

• 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).

Teachers’ Expectations for Student Achievement Scale

Teachers' Expectations for Student Achievement

23.04

24.39

23.24

24.04

22

22.5

23

23.5

24

24.5

Toolkit Teachers (N=80) Comparison Teachers (N=28)

Scale Rating

Pretest

Posttest

By Trying a Different Teaching Method, I Can Significantly Affect a Student's

Achievement.

4.23 4.294.47 4.46

1

1.5

2

2.5

3

3.5

4

4.5

5

Toolkit Teachers (N=81)* Comparison Teachers (N=28)

Scale Rating

Pretest

Posttest

Outcomes: Learning Community

• 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.)

Teachers’ Collegial Learning Effectiveness

Teachers' Collegial Learning Effectiveness

15.90

15.33

17.42

15.74

14.00

14.50

15.00

15.50

16.00

16.50

17.00

17.50

18.00

Toolkit Teachers (N=81)* Comparison Teachers (N=27)

Scale Rating

Pretest

Posttest

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

Summary: What have we learned?

• 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.

Final Thoughts

rperry@mills.edu

clewis@mills.edu

lessonresearch.net

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Thank you!