Transcript Document

Teachers’ Knowledge Development
During Toolkit-Supported
Lesson Study
Preliminary Findings
Rebecca Perry, Catherine Lewis,
Shelley Friedkin, & Elizabeth Baker
Mills College
Oakland, California
http://www.lessonresearch.net
This material is based upon work supported by the National
Science Foundation under Grant No. DRL-0633945 and DRL0723340. 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
4. REFLECT
Select or revise research
lesson
Share data
What was learned about
students learning, lesson
design, this content?
What are implications for this
lesson and instruction more
broadly?
2. PLAN
Do task
Anticipate student responses
Plan data collection and lesson
3. DO RESEARCH
LESSON
Conduct research lesson
Collect data
How does lesson study improve instruction?
Visible
Features of
Lesson Study
•Planning
•Curriculum Study
•Research Lesson
•Data Collection
•Discussion
•Revision
•Etc.
?
Instructional
Improvement
How Does Lesson Study Improve Instruction?
Visible
Features of
Lesson Study
•Planning
•Curriculum Study
•Research Lesson
•Data Collection
•Discussion
•Revision
•Etc.
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
Instructional
Improvement
How Does Lesson Study Improve Instruction?
Visible
Features of
Lesson Study
•Planning
•Curriculum Study
•Research Lesson
•Data Collection
•Discussion
•Revision
•Etc.
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
Instructional
Improvement
How Does Lesson Study Improve Instruction?
Visible
Features of
Lesson Study
•Planning
•Curriculum Study
•Research Lesson
•Data Collection
•Discussion
•Revision
•Etc.
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
Instructional
Improvement
Toolkit
Lesson Study
1. STUDY
Consider long term goals for
student learning and
development
Study curriculum and
standards
4. REFLECT
Select or revise research
lesson
Share data
What was learned about
students learning, lesson
design, this content?
What are implications for this
lesson and instruction more
broadly?
2. PLAN
Do task
Anticipate student responses
Plan data collection and lesson
3. DO RESEARCH
LESSON
Conduct research lesson
Collect data
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
Sample
Number of
Participants
Individual Teachers
Groups
Elementary Teacher
Middle Teacher
Current
High Teacher
Position
Not Teaching
Years
<5 Years
Teaching
5-14 Years
Experience
15+ Years
New to LS
Years Prior
Done 1 LS Cycle
Lesson Study Done LS for 1-2 Yrs
Experience
Done LS for 3+ Yrs
% With Math
Degree/
Credential
Assigned PR Assigned AP
Toolkit
Toolkit
44
37
8
8
21%
46%
59%
30%
14%
16%
7%
8%
18%
31%
50%
46%
32%
23%
36%
49%
16%
11%
16%
22%
32%
19%
48%
41%
Comparison
Teachers
28
6
41%
30%
11%
19%
26%
73%
11%
59%
15%
15%
11%
39%
Outcomes:
Mathematical
Knowledge for Teaching
Outcomes: Knowledge
Mathematics Knowledge for Teaching (Hill & Ball;
Univ. of Chicago School Mathematics Project)
Standardized Teacher
Assessment Items
#
# Question Individual
Stems
Items
Proportional
Reasoning Subtest
Area of Polygons
Subtest
11
7
Source (# Items
from Source)
24
LM T (2 4
10
LM T (5 ), U C SM
(4 ), N A E P (1
Standardized Scores on
Proportional Reasoning Subtest
0 .4 0
Standard Deviation Units
0 .3 0
0 .3 0
0 .3 2
0 .2 0
P retes t
P os ttes t
0 .1 0
0 .0 0
- 0 .1 0
- 0 .1 7
- 0 .2 0
P R T oolkit T eac hers (N =4 4 )
- 0 .1 7
C omparis on T eac hers (N =2 8 )
Standarized Scores on Area of
Polygons Subtest
0 .1
0 .0 4
0 .0 5
Standard Deviation Units
0
- 0 .0 5
- 0 .0 2
- 0 .1
P retes t
P os ttes t
- 0 .1 5
- 0 .2
- 0 .2 5
- 0 .2 6
- 0 .3
- 0 .3 1
- 0 .3 5
A P T oolkit T eac hers (N =3 7 )
C omparis on T eac hers (N =2 8 )
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 Comparison
Teachers
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
60%
50%
% Increase
40%
A P T oolkit T eac hers (N =2 1 )
A ll C omparis on T eac hers (N =4 4 )
30%
20%
10%
0%
A rea C alc ulation
C onnec tion to O ther T opic s
M eaning of A rea; M eaning
of M eas urement
I have strong knowledge of ratio,
proportion, and rate.
4 .5
3 .9 1
4
3 .5
3 .4 8
3 .2 9
3 .4 3
Scale Rating
3
2 .5
P retes t
P os ttes t
2
1 .5
1
0 .5
0
P R T oolkit T eac hers (N =4 3 )*
C omparis on T eac hers (N =2 8 )
I have strong knowledge of area of
polygons.
4 .5
3 .9 7
4
3 .3 9
3 .5
3 .3 9
3 .0 6
Scale Rating
3
2 .5
P retes t
P os ttes t
2
1 .5
1
0 .5
0
A P T oolkit T eac hers (N =3 7 )*
C omparis on T eac hers (N =2 8 )
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
Teachers’ Interest/ Enjoyment in
Learning Mathematics Scale
• 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
26
2 5 .8 1
2 5 .5
Scale Rating
2 5 .1 8
25
P retes t
P os ttes t
2 4 .6 4
2 4 .5
2 4 .2 9
24
2 3 .5
T oolkit T eac hers (N =7 7 )
C omparis on T eac hers (N =2 8 )
Teachers’ Expectations for Student
Achievement Scale
• 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
2 4 .5
2 4 .3 9
2 4 .0 4
Scale Rating
24
2 3 .5
2 3 .2 4
P retes t
P os ttes t
2 3 .0 4
23
2 2 .5
22
T oolkit T eac hers (N =8 0 )
C omparis on T eac hers (N =2 8 )
By Trying a Different Teaching Method, I
Can Significantly Affect a Student's
Achievement.
5
4 .5
4 .4 7
4 .2 3
4 .4 6
4 .2 9
Scale Rating
4
3 .5
P retes t
P os ttes t
3
2 .5
2
1 .5
1
T oolkit T eac hers (N =8 1 )*
C omparis on T eac hers (N =2 8 )
Outcomes:
Learning Community
Teachers’ Collegial Learning
Effectiveness
• 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
1 8 .0 0
1 7 .4 2
1 7 .5 0
1 7 .0 0
Scale Rating
1 6 .5 0
1 6 .0 0
1 5 .9 0
1 5 .7 4
1 5 .5 0
1 5 .3 3
1 5 .0 0
1 4 .5 0
1 4 .0 0
T oolkit T eac hers (N =8 1 )*
C omparis on T eac hers (N =2 7 )
P retes t
P os ttes t
Summary: What have we learned?
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
Final Thoughts
• 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.
Thank you!
Email address:
[email protected]
[email protected]
Website address:
lessonresearch.net