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