Transcript Research Lessons

Using a Mathematical Toolkit to
Support Teachers’ Learning During
Lesson Study
NCTM Research Pre-session
Washington, DC, April, 2009
Rebecca Perry & Catherine Lewis
Mills College, Oakland, California
Patricia Burge & Jill Bombardier
Joseph Brown Middle School, Chelsea, Massachusetts
Discussion Questions
• How did presentations support or
invalidate conceptual framework?
• Other useful data on teacher learning?
• Implications
- …for other lesson study groups?
- …for other types of teacher PD?
- …for research on teachers’ learning?
Toolkit-Supported Lesson Study
Preliminary Findings
Rebecca Perry & Catherine Lewis
Mills College
Oakland, California
http://www.lessonresearch.net
[email protected], [email protected]
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.
Agenda
1. Overview of lesson study,
research
2. Preliminary overall findings
3. Findings from Chelsea group
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
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)
• Crowley (1987) - The van Hiele Model
of the Development of Geometric
Thought, NCTM Yearbook.
•Driscoll, Mark, Nikula, Kelemanik,
DiMatteo & Egan (2007) - The Fostering
Geometric Thinking Toolkit: A Guide for
Staff Development, Heinemann.
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
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
Outcomes: Knowledge
Mathematics Knowledge for Teaching (Hill & Ball;
Univ. of Chicago School Mathematics Project)
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 )
I have strong knowledge of area of
polygons.
5
4 .5
3 .9 7
4
3 .3 9
Scale Rating
3 .5
3 .3 9
3 .0 6
P retes t
P os ttes t
3
2 .5
2
1 .5
1
A P T oolkit T eac hers (N =3 7 )*
C omparis on T eac hers (N =2 8 )
60%
What Students Need to Understand About
Area of Rectangles - Increase in Use of
Coding Category
% Increase Pre- to Posttest
50%
40%
30%
A P T oolkit T eac hers
(N =2 1 )
20%
A ll C omparis on
T eac hers (N =4 4 )
10%
0%
A rea C alc ulation
M eaning of A rea; M eaning of C onnec tion to O ther T opic s
M eas urement
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.
Interest/ Enjoyment in Learning
Mathematics
2 5 .4
2 5 .2 2
2 5 .2
25
Scale Rating
2 4 .8
2 4 .6 9
2 4 .6 4
P retes t
P os ttes t
2 4 .6
2 4 .4
2 4 .2 9
2 4 .2
24
2 3 .8
A P T oolkit T eac hers (N =3 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
25
2 4 .3 9
2 4 .5
2 4 .0 4
24
Scale Rating
2 3 .5
P retes t
P os ttes t
23
2 2 .5
2 2 .4 1
2 2 .4 6
22
2 1 .5
21
A P T oolkit T eac hers (N =3 7 )
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 .4 1
4 .5
4 .4 6
4 .2 9
4 .0 8
Scale Rating
4
3 .5
P retes t
P os ttes t
3
2 .5
2
1 .5
1
A P T oolkit T eac hers (N =3 7 )
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.)
Collegial Learning Effectiveness
1 7 .5
1 7 .2 4
17
Scale Rating
1 6 .5
16
1 5 .7 4
1 5 .5
1 5 .3 2
1 5 .3 3
15
1 4 .5
14
A rea of P olygons T oolkit T eac hers (N =3 7 )*
C omparis on T eac hers (N =2 7 )
pretes t
pos ttes t
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
Time on Toolkit-Supported
Lesson Study-Chelsea
No.
Meetings
Logistics/norms
1
Study - "Kyouzai kenkyuu"
5
Plan - Lesson planning
5
Do - Research lesson
2
Reflect - Debriefing/ Reflection
3
Hours
0.7
6.5
9.0
2.0
3.7
22
Toolkit-Supported Lesson Study
1. STUDY
Consider long term goals for
student learning and
development
Study curriculum and standards
Learning from “Study” Phase
(Meetings 2-6)
•
•
•
•
How to collaborate, motivation to do so
Relationship of rectangle and triangle area
Multiple strategies for finding area
Pedagogy: allow students to experience content,
hear multiple solutions, struggle--> conceptual
understanding
• Sequence of lessons to reach content goals (e.g.,
teach formula last)
Many times I… [feel]… so limited as a teacher because I
have no control over what happens when my students are
not in school. … While I was analyzing the Japanese
textbooks …it hit me. The topics being discussed/taught
…[are] the same, even the approaches to teaching are
similar, but ...the teachers are talking less. It does not
matter where students are from or how “needy” certain
populations are, students need to come up with their own
solutions and discoveries in order to truly own a concept.
So my instinct to constantly be guiding instruction and
forcing students to find the “right answer” is not helping
them, it is hurting them.
Toolkit-Supported Lesson Study
2. PLAN
Select or revise research lesson
Do task
Anticipate student responses
Plan data collection and lesson
Learning from “Plan” Phase
(Meetings 7-11)
•
•
•
•
Collaboration hard, but worthwhile
Sequence of ideas for developing area unit
“Trust” students; set higher expectations
Questioning - with accurate math language - to
guide students
…The group struggled… with the question,
“How do we get students to say what we want
them to?” As teachers, we struggle with this
question on a daily basis… I am amazed that a
group of people with similar experiences and
teaching styles can bring such different ideas to
the table. I have learned a great deal through the
sharing… and comparing our experiences and
curriculum to the research materials.
Toolkit-Supported Lesson Study
4. REFLECT
3. DO
RESEARCH
LESSON
Conduct research
lesson
Collect data
Share data
What was learned
about students
learning, lesson
design, this content?
What are implications
for this lesson and
instruction more
broadly?
Learning from “Do” and “Reflect” Phases
(Research Lessons/ Debriefings)
•
•
•
•
Student solution methods/mistakes
Limits of student knowledge
Challenges of student & teacher materials
Unanticipated student responses and how they
might be handled by teacher
Summary: What have we learned?
Overall
• No significant impact on standardized assessment items of
MKT
• Impact on open-ended assessment items and self-reported
knowledge of topics
• Evidence of slight increase in enjoyment, efficacy
• Increase in self-reported collegial learning effectiveness
Chelsea
• Reflections suggest especially impacts on pedagogy and
collegial learning
Final Thoughts
• Each group experienced toolkit differently. Learning
related to specific group focus.
• Standardized MKT assessment items may not be a good
fit for lesson study, since group’s focus cannot be specified
in advance
• Open-ended/ qualitative data suggest linkages between
content, pedagogy, student thinking
• Research suggests LS creates potential for continual
learning
Thank you!
Email address:
[email protected]
[email protected]
Website address:
lessonresearch.net