http://math-info.criced.tsukuba.ac.jp/ 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)

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

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

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!!

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 …

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

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 www.lessonresearch.net　Clewis@mills.edu

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)

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)

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?

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

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?

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?

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

Comparison and Discussion El Enfoque de Resolucion de Problemas Checking List for Prob. Solving Approach 2007-2008 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. 4 3 2 1 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

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

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

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

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