This document provides an overview of a PDST team meeting in December 2017 about lesson study and structured problem solving. The key points discussed include:
1. An introduction to lesson study and structured problem solving as models for teacher professional development and classroom practice.
2. Details of PDST's lesson study programs from 2008-2018 which involved thousands of teachers in lesson study communities of practice.
3. The structure of a lesson study cycle and how it is used to collaboratively plan, teach, observe and refine mathematics lessons with a focus on problem solving.
4. The structure of a mathematics lesson using structured problem solving, with sections for presenting the problem, individual work time, presenting solutions and discussion.
8. 8
PDST Team Meeting
December 2017
Video Study
Sample Lesson Number Key Insight or question
3-country study: representative
sample of 8th grade (2nd year)
mathematics lessons in USA,
Germany & Japan
231 lessons Is there such a phenomenon as “cultural
script” to describe lessons at national level?
9. 9
PDSTTeamMeeting
December2017
The Japanese approach to mathematics teaching
“The teacher can provide students with opportunities to
understand these basic ideas, and support their learning so
that the students become independent learners. When we
watched a Japanese Lesson, for example, we noticed that the
teacher presents a problem to the students without first
demonstrating how to solve the problem.”
Stigler and Hiebert, 1999, The Teaching Gap
Structured Problem
Solving
A model of classroom practice
10. 10
PDST Team Meeting
December 2017
Sugiyama2008
Level 1
Level 2
Level 3
The teacher can provide students with opportunities to
understand these basic ideas, and support their
learning so that the students become independent
learners.
The teacher can explain the meanings and reasons of
the important basic ideas of mathematics in order for
students to understand them
The teacher can tell students the important basic ideas
of mathematics such as facts, concepts, and
procedures.
Three Levels of Expertise in Mathematics Teaching
Structured Problem
Solving
A model of classroom practice
12. 12
PDST Team Meeting
December 2017
“Although researchers have been emphasising problem solving, we
still do not see many mathematics classes using problem solving as
an integral part of mathematics teaching and learning.”
Changing Classroom Practice
(Stigler and Hiebert, Closing the Teaching Gap, 2009)
2009
1995
1985
13. PDSTTeamMeeting
December2017 Changing classroom practice
“Listening to experts during special professional development
days does not translate into improved teaching. Effective
teacher learning must be built into teachers’ daily and weekly
schedules. Schools must become the places where teachers,
not just students, learn.”
(Stigler and Heibert, Closing the Teaching Gap, 2009)
14. PDSTTeamMeeting
December2017
Lesson Study - a vehicle for change
Lesson Study has been used for 30+ years to develop teachers’
craft in teaching through structured problem solving.
Lesson Study has been used by teachers in Japan for CPD for 100+
years.
Lesson Study
A model of CPD
15. PDSTTeamMeeting
December2017
Benefits of Lesson Study
Research shows...
Evidence of statistically significant impact on
teaching and learning
Four benefits include:
“Greater teacher collaboration, a sharper focus
among teachers on students’ learning,
development of teacher knowledge, practice and
professionalism and improved quality of classroom
teaching and pupil learning outcomes”.
Gersten et al (2014)
Lewis et al (2006)
Cajkler et al (2014)
17. PDSTTeamMeeting
December2017
Research Theme
Identify the issue to
overcome
Meitheal Machnaimh
groundwork for
designing the lesson
Develop lesson proposal
Live research structured
problem solving lesson
Post-lesson discussion to
solidify ideas for
addressing the research
theme.
Summarise the learning
and identify the next
step
Supported by
Knowledgeable Other
Final comments by Knowledgeable
Other to summarise and guide
future research
Teachers collaborate to
tackle a problem in
teaching and learning.
What happens during Lesson Study?
Planning
Reflecting
The Lesson Study
Cycle
18. PDST National Meeting
December 2017
The Research Theme
Aligned with
• School improvement
• SSE dimensions, domains and standards
19. PDST National Meeting
December 2017
Planning
4. The Research Lesson
Lesson Goals
The Problem
Lesson Flow
Student Responses
Ceardaíocht
Boardwork
3. The unit
Unit Goals
Relationship to Syllabus
Unit Plan
2. Research
Whole school
teaching
Research findings
1.
Mathematical
Topic
What problem
exists?
20. PDST National Meeting
December 2017
Meitheal Machnaimh (kyozai kenkyu)
• Choose a problem to facilitate goals of the lesson
• Develop Pedagogical Content Knowledge
Planning
21. PDST National Meeting
December 2017
• Taught by one member of research group
and observed by others
• Pre-determined set of data gathered
• Strict protocols are observed
The Research Lesson
22. PDST National Meeting
December 2017
Reflecting
• Post-lesson discussion
oWere the goals of the lesson and the research theme met?
oWhat specific problems did students have?
oHow would you revise the lesson?
• Finalise lesson proposal
25. PDSTNationalMeeting
December2017 A Structured Problem-Solving Lesson
Note: Timings are approximate reflective of a 45 minute class period
Presenting the
problem
hatsumon
Review previous lesson.
Teacher carefully
introduces the
problem.
Encourage the use of
prior knowledge.
10 minutes
Student problem
solving
kikanshido
Students work
individually or in group.
Students write solution
methods and
explanations, using
diagrams, calculations
and mathematical
sentences.
Teacher encourages
and notes solutions.
10 minutes
Presenting the
solutions &
Ceardaíocht
neriage
Students present their
solution at the board in
a pre-decided order.
Teacher facilitates
students understanding
other solutions.
Whole class discussion
on similarities and
differences.
“Kneading” of solutions
to achieve lesson goals.
20 minutes
Highlighting and
summarising
matome
Summarising and
reflecting on solutions
and learning.
Extension task.
5 minutes
26. PDST National Meeting
December 2017
Presenting the ProblemPresenting the problem
Individual
problem solving
Understanding the
problem
Having insight into
the solution
Individual problem
solving
Activitiesiour
Capturing the problem
situation mathematically
Thinking insightfully and
having one’s own ideas
Expressing one’s own
ideas
E
Understand the problem
clearly and correctly
Looking for the
differences between
problems they have
previously learned
Recalling prior knowledge
Trying to solve the problem
using knowledge
previously learned
Expressing their own ideas
in a way everyone can
T
id
c
S
b
Presenting the problem
Individual
problem solving
Understanding the
problem
Having insight into
the solution
Individual problem
solving
Activitiesiour
Capturing the problem
situation mathematically
Thinking insightfully and
having one’s own ideas
Expressing one’s own
ideas
E
Understand the problem
clearly and correctly
Looking for the
differences between
problems they have
previously learned
Recalling prior knowledge
Trying to solve the problem
using knowledge
previously learned
Expressing their own ideas
in a way everyone can
T
id
c
S
b
• Review prior learning
• Present the problem
• Check that students understand the problem
27. PDST National Meeting
December 2017
Student Individual WorkIndividual
problem solving
Presenting solutions and Cear
Individual problem
solving
Presenting student
solutions
Understanding
solutions
Expressing one’s own
ideas
Explaining their ideas Understanding others’
ideas
Trying to solve the problem
using knowledge
previously learned
Expressing their own ideas
in a way everyone can
understand
Trying to explain their
ideas in a way everyone
can understand
Speaking in front of the
board with their face and
body looking toward the
Listening to others
presenting their solutions
and understand it
(read body language
nodding etc..)
• The teacher
oencourages multiple approaches
oassesses and recording students’ learning
ohelps students develop their thinking through questioning
oplans for Ceardaíocht
28. PDST National Meeting
December 2017
Presenting Solutions and Ceardaíochtg
Presenting solutions and Ceardaíocht
Presenting student
solutions
Understanding
solutions Ceardaíocht
Explaining their ideas Understanding others’
ideas
Comparing and contrasting
solutions, deciding which
is ‘best’
m
s
Trying to explain their
ideas in a way everyone
can understand
Speaking in front of the
board with their face and
body looking toward the
Listening to others
presenting their solutions
and understand it
(read body language
nodding etc..)
Looking for differences
and similarities between
their ideas and their peers
Thinking of what is the
best, most efficient way of
handling the problem
• Students present solutions in a pre-determined order
• Teacher develops whole class understanding through
o questioning
o facilitating discussion between students
o using misconceptions as learning opportunities
• Teacher ‘kneads’ solutions to move whole class towards the lesson goals
30. PDST National Meeting
December 2017
Summarising & Reflecting
• Teacher summarises key points of the lesson
o Focus is on concept / Don’t focus on procedures
• Students reflect on their learning
o What did you learn today?
o What did you have trouble understanding?
o What questions do you have?
• Extension task is provided
nting solutions and Ceardaíocht Summing up
nt Understanding
solutions Ceardaíocht
Summary of the
lesson
uctured problem-solving lesson
Understanding others’
ideas
Comparing and contrasting
solutions, deciding which
is ‘best’
Reflecting on the lesson
31. PDST Team Meeting
December 2017
1. Given that Lesson Study is an established model
of CPD, what are the opportunities it presents for
you and the work of your team?
2. How could the lesson structure, as used in
structured problem solving, be facilitated in your
area?
Q1. Q2.
33. 33
PDSTTeamMeeting
December2017
Participating in Lesson Study
Reflection &
Sharing research
Teaching &
observing the
Live Research
Lesson & Post-
Lesson
Discussion
Planning &
Drafting the
Research Lesson
Proposal
Induction
Training
October March
5 x 2.5 hours 2 hours 2.5 hours3 days
34. 34
PDST Team Meeting
December 2017
Lesson Study Participation
2014
2015
2016
2017
2018
10 associates
100 teachers
45 schools
Education-Centre based
Online Forum
Maths Counts 2016
2016-20172017-2018
33 associates
250 teachers
100 schools
Education Centres & schools
Online Forum
Maths Counts 2017
44 associates
400 teachers
140 schools
School based
Online Forum
Maths Counts 2018
Nationwide Launch
50 teachers
20 schools
Education-Centre based
Maths Counts 2015
36. 36
PDST Team Meeting
December 2017
Observations
Teachers need sustained
support to develop the skills
needed for a structured
problem solving lesson
A lot of informal learning
happens while teachers
collaborate to design a lesson
Teachers learn a lot simply
from being in another
teacher’s classroom
Teachers are very polite and
are slow to critique a lesson
Many teachers recognise the
positive effects Lesson Study
has had on their approach to
teaching in general
Some teachers find the Lesson
Study model of CPD
challenging
37. PDST Team Meeting
December 2017
Structured Problem Solving Workshop
Presenting the
problem
Student problem
solving
Presenting the
solutions &
Ceardaíocht
Highlighting and
summarising
Topic:
Understanding
the area of basic
2D shapes
Level:
5th & 6th Class
1st Year
What you’ll get:
Live Lesson
Lesson Proposal
Lesson Analysis