Research Lessons

1
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
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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?

3
Toolkit-Supported Lesson Study Preliminary
Findings Rebecca Perry Catherine
Lewis Mills College Oakland, California http//www
.lessonresearch.net rperry_at_mills.edu,
clewis_at_mills.edu
4

• 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.

5
Agenda

• Overview of lesson study, research
• Preliminary overall findings
• Findings from Chelsea group

6
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
4. REFLECT Share data What was learned about
students learning, lesson design, this
content? What are implications for this lesson
and instruction more broadly?
3. DO RESEARCH LESSON Conduct research
lesson Collect data
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How does lesson study improve instruction?

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

?
Instructional Improvement
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How Does Lesson Study Improve Instruction?
Pathways

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

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
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Toolkit
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
4. REFLECT Share data What was learned about
students learning, lesson design, this
content? What are implications for this lesson
and instruction more broadly?
3. DO RESEARCH LESSON Conduct research
lesson Collect data
10

• 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

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Toolkit Topics

• Proportional Reasoning
• Area of Polygons

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Toolkit Contents

• Mathematical Tasks Student Work
• Curriculum Materials
• Research Articles Summaries
• Lesson Videos
• Reflection Forms Questions

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Mathematical Tasks (Ex NAEP)
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Curriculum Materials
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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.

17
Lesson Videos (Example)
Can You Find the Area? Akihiko Takahashi, U.S.
Classroom
18
Reflection Forms and Questions (examples)

• Concept Map Sequence of Understandings that
  Students Develop
• Daily Meeting Reflection
• Reflection on Lesson Study Cycle

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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

21
Sample
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Outcomes Mathematical Knowledge for Teaching
23
Standardized Teacher Assessment Items
24
Outcomes Knowledge Mathematics Knowledge for
Teaching (Hill Ball Univ. of Chicago School
Mathematics Project)
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Outcomes Personal Dispositions
29
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.

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(No Transcript)
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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).

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(No Transcript)
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(No Transcript)
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Outcomes Learning Community
35
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.)

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(No Transcript)
37
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
4. REFLECT Share data What was learned about
students learning, lesson design, this
content? What are implications for this lesson
and instruction more broadly?
3. DO RESEARCH LESSON Conduct research
lesson Collect data
38
Time on Toolkit-Supported Lesson Study-Chelsea
39
Toolkit-Supported Lesson Study
1. STUDY Consider long term goals for student
learning and development Study curriculum and
standards
40
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--gt conceptual
  understanding
• Sequence of lessons to reach content goals (e.g.,
  teach formula last)

41

• 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.

42
Toolkit-Supported Lesson Study
2. PLAN Select or revise research lesson Do
task Anticipate student responses Plan data
collection and lesson
43
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

44

• 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.

45
Toolkit-Supported Lesson Study
4. REFLECT Share data What was learned about
students learning, lesson design, this
content? What are implications for this lesson
and instruction more broadly?
3. DO RESEARCH LESSON Conduct research
lesson Collect data
46
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

47
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

48
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 groups 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

49
Thank you!
Email address
rperry_at_mills.edu clewis_at_mills.edu
Website address
lessonresearch.net