1.
What is the product of Lesson Study? Japanese Mathematics Textbook and Theory of Teaching
Masami Isoda, PhD
Professor, University of Tsukuba, Japan.
Project Overseer, APEC Lesson Study Project
Honorary PhD, Khon Kaen University, Thailand (2011)
Honorary Professor, Universidad San Ignatio de Loyora, Peru (2014)

2. What are the products of LS?
PCK?
Lesson Plan?
Teaching methods?
Theory of Education for Teachers
Participating Teachers
Theories of Education
Lesson
study
Teacher
Children
Subject M.
Theory of Mathematic

3. What is your lesson from video?
What do you want to feel in?

4. How can you teach it? Trough the PSA!!
Problem Solving Approach: Teaching Approach to develop skills for learning, developing, communicating mathematics
Problem Solving Approach does not mean to teach solutions.
It includes knowing representation of mathematics, value of mathematics, and knowing the developing ways of mathematics.
How can you teach representation of mathematics, its values and its ways?
Problem Posing
Independent Solving
Comparison and Discussion
Summary and Integration
Two keys of Lesson Study for Problem Solving Approach
Good Teaching Sequence which enable students to use what they leaned before.
Well Managed Teaching A. which teach learning how to learn.
How can you teach it?
Trough the PSA!!

5. As a constructivist, if following are explained by children, how do you think?
Which are appropriate to explain the area formula of trapezoid? a b c
Half of math-educator preferred c because c is good to deduce the formula by the formula of rectangular.
They preferred injection ways of teaching even if….
In Japan, the teachers who can use the textbook ….
All, a, b and c, are appropriate because …
a and b are appropriate because….
All appropriate and compare a and b with c …

6. Teaching Approach itself improved by challengers.
The lesson study community to make an effort to develop the children who learn…
Problem
Personal Level a b c vs
Dialectic
Problem Solving
Approach
Open Approach a b c
School Level LS
Injection

7. Feature and Effect of Japanese textbook for lesson study: Comparison of U.S & Japanese Texts
Compared
2 US elementary math series
Investigations (2007)
Harcourt California (2002)
2 Japanese elementary math series
Tokyo Shoseki (Hironaka & Sugiyama)
Gakkou Tosho (Hitotsumatsu et al.)
Tsukuba, Japan, February 19, 2011
Catherine Lewis,Mills College, Oakland, CA

8. Compared with US textbooks, Japanese textbooks use a limited numbers of representation for teaching fraction but consistently care about the features of Fraction
By Catherine Lewis (2011)

9. Change in Teachers’ Fraction Knowledge (N=213)
‘Lesson Study using Fraction Resource Kit developed by Japanese Mathematics textbook in English, shows significant difference when it is compared with the results of Lesson Study activities without specific subject or ordinary lecture style teacher training.
We can improve teachers content knowledge if we support their learning with good resource kit.’
By Catherine Lewis (2011)

10. Principles as for the theory of Problem Solving Approach
Principle 1. Problem Solving Approach is preferred for teaching how to learn: developing children who learn mathematics for/by themselves.
Principle 2. For developing children, teachers plan the lesson that children enable to learn the value, and how to develop mathematics as well as mathematical idea and skills.
Principle 3. Teachers prepare tasks which are the cause of problems for children. Solving the problem is a major aim, the tasks is not.
Principle 4. Teachers manage the teaching based on the planned assessment depending on the teaching phases: Problem Posing, Independent Solving, Discussion and Comparison, and Summary and Integration.
Principle 5. Curriculum is well developed on the sequence of mathematical extension and integration within the Zone of Proximal Development for children.
Mathematicians who know mathematical activity usually construct math.
Children are observers or mathematicians?

11. Powered by dbook Problem Posing : what we learned before.
Four phases for teaching approach:
Problem Posing : what we learned before.
Independent Solving: Patients, representation
Comparison and Discussion: Knowing and developing ideas
Summary and Integration: Value, Leaning how to learn
English Translation of Japanese Textbooks.
Powered by dbook

12. Please complete the black board plan
Why we have to compare?
Task is given by teacher
Various Solutions and Comparison
<Fill in 2 >
<Fill in 4 >
How much
Area?
Let ‘s use!
<Fill in 7>
<Fill in 3 >
<Fill in 5 >
<Fill in 8>
<Fill in 1 >
<Fill in 6>
Problem/atic is posed from children, if possible
Resume the result of comparison and selection based on generality
Why we need problematic?

13. Please Explain the Principles with the Example
Principle 1. Problem Solving Approach is preferred for developing children who learn mathematics for/by themselves.
Principle 2. For developing children, teachers plan the lesson that children enable to learn the value, and how to develop mathematics as well as mathematical idea and skills.
Principle 3. Teachers prepare tasks which are the cause of problems for children. Solving the problem is a major aim, the tasks is not.
Principle 4. Teachers manage the teaching based on the planned assessment depending on the teaching phases: Problem Posing, Independent Solving, Discussion and Comparison, and Summary and Integration.
Principle 5. Curriculum is well developed on the sequence of mathematical extension and integration within the Zone of Proximal Development for children.
Which one is difficult to explain?

14. Let’s learn from good collaborative lesson studies
Hondulas by JICA (Isoda 2007)
Thailand (Inprasihta 2005)
How teacher changed.

15. Comparison and Discussion
El Enfoque de Resolucion de Problemas
Checking List for Prob. Solving Approach in Japan. in Ozone Elementary School
Problem Posing
Self-Evaluation
1. The lesson sets tasks that can be solved in a variety of different ways by applying previously learned knowledge, and presents the content to be learned.
2. The lesson planned with tasks (problem given by teacher) and problems (problematic from students), and promotes problem (problematic) awareness.
3. The teacher expected methods and solutions before.
Independent Solving
1. The children can recall and apply what they have already learned.
2. The children’s ideas are predicted before.
3. Inappropriate solutions are predicted, and advice and hints are prepared for them before.
4. The teacher, walking around, observes and helps children to insure that children use mathematical representation to solve the problems.
5. Notebook are written and taken in a manner such that they will be helpful for presentation as well.
Comparison and Discussion
1. Steps (Validity, Compare, Similarity and Generalization or Selection) are planned for comparative discussion.
2. The ideas to be taken up are presented in an order that is planned before.
3. The method for writing presentation sheets is planned in advance and directions are provided.
4. In addition to develop the ability to explain, children are also fostered with the ability to listen and the ability to question.
5. When ideas are brought together (generalized), it is important to experience them by themselves.
6. The reorganization or integration of ideas proceeds smoothly from the presentation and communication of children.
Summary
1. Activities are incorporated that let children experience for themselves the merits of the ideas and procedures that are generalized.
2. The summary matches the aims and problems (problematic) of this lesson.
3. It is recognized that both correct and incorrect answers (to the task) have something good in the foundation of their ideas.
4. Children are made to experience the joy and wonder of learning.
Lesson Planning Checklist
Lesson Plan Checklist
Blackboard Planning Checklist
Children's Checklist for listening, explaining and notebook writing. etc.
Isoda, M. Olfos. R. (2009). El Enfoque de Resolucion de Problemas. Chile: Ediciones Universtarias de Valparaiso

16. Through the self-evaluation each other in whole school LS
The power of School Level Lesson Study Approach for improvement of the quality of whole education through mathematics
図2.　地域平均と大曽根小学校学力比較
数学的な考え方問題群(100点換算)における平均の差
数値は地域平均点とのポイント差
Figure 5. Ozone Elementary School’s Academic Abilities Compared to the Regional Average
Figure 6. Ozone Elementary School’s Academic Abilities Compared to the Regional Average
6th Graders
5th Graders
4th Graders
Year before Implementation
1st Year
2nd Year
Difference from average in mathematical thinking problem set (converted to 100 points)
Numerical values are point differences from regional average points
6th Grade Mathematic
6th Grade Japanese
6th Grade 4 Subjects
5th Grade Mathematics
5th Grade Japanese
5th Grade 4 Subjects
before
2nd year

17. Through the self-evaluation each other in whole school LS
Through understanding the Prob. Sol. Approach:
Promised Approach if whole teachers challenge
自力解決の指導
比較検討の指導
まとめの指導
Figure 7. Improvements in Teacher Instruction as Measured with the Lesson Planning Checklist
Problem Posing
Comparison and Discussion
Independent Solving Instruction
Summary
Achieved
Not Achieved
Start Time
After 1.5 Years

18. The checking list developed by Ozone Elementary School with Isoda (2009)

21. Reference Mathematical Thinking :How to Develop it in the Classroom
By (author): Masami Isoda (University of Tsukuba, Japan), Shigeo Katagiri (Society of Elementary Mathematics Education, Japan)
World Scientific 2012
Lesson Study: Challenges in Mathematics Education (Series on Mathematics Education)
Maitree Inprasitha, Masami Isoda, Patsy Wang-Iverson, Ban-har Yeap, World Scientific 2015
Masami Isoda(2015). Dialectic on the Problem Solving Approach: Illustrating Hermeneutic as the Ground Theory for Lesson Study in Mathematics Education., S.J. Cho (ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education, Springer