PDST National Meeting December 2017 Online Version 2

PDSTTeamMeeting
December2017
Overview
1. Introduction to Lesson Study and Structured Problem Solving
2. Group Activity
3. An Overview of PDST’s Lesson Study Programmes

PDSTTeamMeeting
December2017 Resources
www.projectmaths.ie/pdstdec17

PDST National Meeting
December 2017
The Maths Development Team
2008
2009
2010
2011
2012
2013
2014
2015
2016
Project Phase
National Roll-Out
Lesson Study
Phase 2Phase 1
10 Full-Day Workshops for
6,500 teachers
Seminar
School Visits
5 Content Courses
3 ICT courses
Teaching & Learning Plans
Teacher Handbooks
Student CD
Online Resources
Video Tutorials
www.projectmaths.ie
10 Full-Day Workshops
School Visits
www.projectmaths.ie
Teaching & Learning Plans
Teaching & Learning Resources
Induction Training
Lesson Study Meetings
Maths Counts
Lesson Study Handbook
Lesson Proposals
Lesson Study Posters
2017
2018

Lesson Study & Structured Problem
Solving

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PDSTTeamMeeting
December2017
Lesson Study
A model of CPD
Lesson Study vs. Structured Problem Solving
Structured Problem
Solving
A model of classroom practice

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PDST Team Meeting
December 2017
Let’s start at the beginning…

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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?

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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

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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

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PDSTTeamMeeting
December2017
84%
62%
26%
5%
94%
76%
38%
7%
93%
89%
67%
14%
Low Benchmark Intermediate
Benchmark
High Benchmark Advanced
Benchmark
Trends In Mathematics & Science Study
(TIMSS 2015)
International Average Ireland Japan
Their results are different too

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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

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)

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

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)

PDSTTeamMeeting
December2017
Identify research theme
and issue to overcome
Meitheal Machnaimh
groundwork for
designing the lesson
Develop lesson proposal
Live research structured
problem solving lesson
Post-lesson discussion to
reflect on how the lesson
addressed the research
theme and goals
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

December 2017
The Research Theme
Aligned with
• School improvement
• SSE dimensions, domains and standards

December 2017
The issue to overcome
• Teachers identify a problem in the teaching and learning of
mathematics

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?

December 2017
Meitheal Machnaimh (kyozai kenkyu)
• Choose a problem to facilitate goals of the lesson
• Develop Pedagogical Content Knowledge
Planning

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

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

December 2017
Share the Outcomes
• Lesson-Study Library
• Maths Counts
• Share Day

Teaching Through Structured
Problem Solving

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

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
ideas
E
Understand the problem
clearly and correctly
Looking for the
differences between
problems they have
previously learned
Recalling prior knowledge
using knowledge
previously learned
T
id
c
S
b
• Review prior learning
• Present the problem
• Check that students understand the problem

December 2017
Student Individual WorkIndividual
problem solving
Presenting solutions and Cear
Individual problem
solving
Presenting student
solutions
Understanding
solutions
ideas
Explaining their ideas Understanding others’
ideas
using knowledge
previously learned
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

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

December 2017
Presenting Solutions and Ceardaíocht
• Boardwork provides a record of the learning

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

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.

www.pdst.ie
Lesson Study Pilot
Primary Numeracy Team
Yvonne Slevin
Dennis Mulligan

www.pdst.ie
Methodology
“The relationship between a school and Advisor has
a direct impact on how the lesson study unfolds. On
this occasion I had already facilitated a whole staff
workshop and was therefore known to the
participants as a ‘knowledgeable other’.
This made it difficult to become an authentic co-
learner or facilitator.”
Advisor 9

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Facilitation
“Rotating facilitation of each session proved almost
impossible as the teachers lacked facilitation skills.
They were clearly not used to acting in this way
with colleagues.”
(Advisor, School 8)
“It made it easier to give
direction, structure and
focus to the planning
meetings and provided
valuable knowledge”
(Teacher, School 3)
“Excellent, provided the
anchor to the whole
project and offered great
support”
(Teacher, School 4)

www.pdst.ie
“to create more
independent
learners.”
Goals
“…excited and confident
learners who are willing to try
new things and value
mistakes.”
“…to become confident and
purposeful Mathematicians.”
“…inspired to articulate
their mathematical
understanding.”
“Identifying a goal took some time as
teachers appeared to be more familiar
with setting short term goals like those
in their fortnightly plans rather than
long term goals for their pupils”
(Advisor, School 5)
“This is really hard to do, as
it is hard to think what they
need to be good at when
they are leaving the school”
(Teacher, School 7).

www.pdst.ie
“Can the pupils find any
“rules” for working out
equivalent fractions?”
Research Questions
“Cén bealach is fear gasúir a
spreagadh chun oibriú as a stuaim féin
le fadhbanna a réiteach go
muiníneach agus go taitneamhnach?”
“How is pupils’ reasoning of adding
two digit numbers be supported by
the expanded column method?”
“How can we as teachers
enable the children to use
a problem solving
approach to fractions?”

www.pdst.ie
This was one of the most difficult parts of the process to facilitate.
The teachers continuously lost focus and there was a lot of going
around in circles. Constant reminding of goals by advisor”
(Advisor, School 2)
“I thought it was very useful as we all had different experiences,
methods of teaching, and also we’re used to using different
resources”
(Teacher, School 2)
“I was surprised about how long the planning of the lesson took
and how we needed to discuss all the detail of it”
(Teacher, School 7)
Planning Phase

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Lesson Observation
The observers were surprised with language that emerged such as “infinity”.
They also observed the struggle for all pupils. It was uncomfortable for the
observing teachers…They were observing for misconceptions, gaps in
knowledge, mistakes, any progress the pupils made and how to note any
reflections/thoughts/a-ha moments they had”
(Advisor, School 1)
On reflection, the observation
template had a very narrow focus
and I feel it would merit a session on
its own”
(Advisor, School 6)
“We had a clear template of specific
areas we were to observe
(interaction, problem solving,
communication etc.”
(Teacher, School 8)

www.pdst.ie
“Very powerful for the teachers particularly
after the second lesson. Teachers could see
lack of understanding around the idea of a
fraction/whole after first lesson. Also, noticed
the difficulty children had working in groups
and communicating their ideas”
(Advisor, School 2)
Reflection Phase

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Reflect and Review

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Teacher Feedback
Statement Strongly
Disagree
Disagree Neither Agree
or Disagree
Agree Strongly Agree
Lesson study
improved my
teaching of
mathematics
6% 11% 34% 48%
Lesson study
improved my content
knowledge of
mathematics
11% 14% 42% 31%
Lesson study is
beneficial for
collaboration with
colleagues
6% 20% 74%

www.pdst.ie
Teacher Feedback
“I think the lesson study project highlighted for me
the effectiveness of using manipulatives during
maths lessons – irrespective of class level and from
now on I intend to incorporate more hands on
practical maths activities in my maths teaching”
(Teacher, School 8)
“I’m more conscious of allowing
the children talk-time and making
the lesson less teacher-led.”
(Teacher, School 9)

www.pdst.ie
“Aithním thar rud ar bith
eile anois an bearna idir
an obair theibí agus an
obair phriaiticiúil.”
Teacher Feedback
“A great form of CPD, one can
really learn from colleagues,
different ideas and
approaches.” “I thought it was very
useful as we all had
different experiences and
methods of teaching…”
“I think it’s great for the
teachers to see it. It’s very
doable. I would definitely
do it again.”

www.pdst.ie
• Sense of ownership
• Promoting collaboration
• Meeting needs of school
• Utilising expertise from within
• Improved teaching and learning
• Deepening subject matter knowledge
Opportunities

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Challenges
• Time
• Leadership
• Supervision
• Sustainability
• Teacher competency

www.pdst.ie
• Substitute Cover
• Time for Re-teach
• Shared Learning Day
• Ensure support of principal and management
• Update Lesson Booklet to enhance
opportunities for facilitation skills
Modifications

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Reeling in the Year
Research & Training
Feb – March
Review & Reflect
June
Modifications
September
Begin Anew
November
Christmas NTM
2016
Lesson Study Cycle
March – May
Report
July
Training
October

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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

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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

PDSTTeamMeeting
December2017 Communities of Practice
MDT
Associates
Teachers

57
PDST Team Meeting
December 2017
Feedback

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

PDST Team Meeting
December 2017
O’Brien Centre for Science
UCD
Maths Counts 2018
Our 5th National Lesson Study Conference
2nd & 3rd March 2018

PDST National Meeting December 2017 Online Version 2

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