Contents -- Foreword -- Introduction: to the English Translation -- Introduction: translated from the Japanese version -- Chapter 1: Japanese Lesson Study in Mathematics -- Section 1: Japanese Education and Lesson Study: An Overview -- 1.1 "How is Lesson Study Implemented?" Takuya Baba Hiroshima University -- 1. The Process of Lesson Study -- 2. Class and Discussion Topics: A Case Study -- Types of Lesson Study Formats -- Section 2: A Brief History of Mathematics Lesson Study in Japan -- 2.1 "Where did Lesson Study Begin, and How Far Has It Come?" Masami Isoda University of Tsukuba -- 1. From Individualized Instruction to whole classroom instruction: Studying Teaching Methods -- 2. Dissemination of the Lesson Study Practices through the Elementary School Attached to the Tokyo Teachers' School. -- 3. Development and Dissemination of Teaching Methods Learned through Lesson Study -- 4. How Japanese Lesson Studies and Approaches are developed and known: A case of Open Approach -- Section 3: Official In-Service Teacher Training System -- 3.1 How is In-Service Teacher Training Conducted in Japan? Kazuyoshi Okubo Hokkaido University of Education -- 1. The In-Service Teacher Training System -- 2. Training Organized by the Government -- 3. In-School Training (Research) -- 4. Voluntary Training and Work-time Training -- 5. A Wider Perspective -- Section 4: Mathematics Curriculum and Way of Implementation -- 4.1 How Has Mathematics Education Changed in Japan? Eizo Nagasaki National Institute for Educational Policy Research of Japan -- 4.2 How Have the Goals of the Mathematics Curriculum Changed? Eizo Nagasaki National Institute for Educational Policy Research of Japan -- 4.3 How are Curriculum Standards Improved and Implemented? Yutaka Ohara Naruto University of Education -- 1. Improving Curriculum Standards -- 2. Curriculum System at Each School.

4.4 How is Each School's Mathematics Curriculum Formulated and Implemented? Shigeo Yoshikawa Ministry of Education, Culture, Sports, Science and Technology, Japan -- 1. Formulation of the School Curriculum -- 2. Preparation of an Annual Teaching Plan -- 3. Promoting Lesson Study and Determining Results -- 4.5 Teaching and Assessment Based on Teaching Guides Masao Tachibana Morioka City Board of Education (previous position: Ministry of Education, Culture, Sports, Science and Technology, Japan) -- 1. The Purpose of Assessment -- 2. Assessments that Improve the Teacher's Lessons -- 3. Assessment to Improve Student Learning -- 4.6 Textbooks and Teaching Guides Takeshi Miyakawa University of Tsukuba -- 4.7 What Kinds of Teaching Materials and Aids are Used in Japan? Hiroko Tsuji Hokkaido University of Education -- 4.8 What do Teachers and Teacher Trainees Think About Lesson Study? Tadayuki Kishimoto Toyama University -- 1. Teacher Trainee Attitudes toward Lesson Study -- 2. Teacher Attitudes toward Lesson Study -- Section 5: Comparisons of Features of Past International Comparative Studies -- 5.1 Why Have Japanese Lessons Paid Attracted Attention and What are its Features? Hanako Senuma National Institute for Educational Policy Research of Japan -- 1. Improving the Curriculum and Teaching Methods to Improve Academic Abilities -- 2. Pose Problems to Raise the Level of Mathematical Ideas and Switching Lessons Between Whole Classroom Work and Individual Work -- Section 6: Understanding Japanese Mathematics Lessons -- 6.1 How do Japanese Teachers Explain and Structuralize Their Lessons? Yoshinori Shimizu University of Tsukuba -- Japanese lessons as "structured problem solving" -- Teacher's Roles During the Lessons: Some Pedagogical Terms Shared by Teachers -- "Hatsumon" at the presentation of a problem -- "Kikan-shido" during problem solving by students.

"Neriage" in a whole-class discussion -- "Matome" as summing up -- Some practical ideas shared by Japanese teachers. Ensuring the Student's "Ownership" -- "Bansho": Effective Use of Chalkboard -- Teaching and Evaluation as Two Faces of the Same Coin -- The Importance of Evaluation as Incorporated with Teaching -- 6.2 How do Japanese Teachers Evaluate Their Students in Their Lessons? Hiroyuki Ninomiya Ehime University -- Image of the Japanese Classroom (The Teaching Gap, Stigler & Hiebert, 1999) -- The Objectives of Desk Instruction -- Integration of Teaching and Evaluation -- Chapter 2: Methods and Types of Study Lessons -- Section 1: Preparation for Lessons -- 1.1 Annual Teaching Plan as a Plan for Nurturing Students: How should Annual Teaching Plans be Created to Impart Useful Skills and Creative Ways of Thinking? Yasuhiro Hosomizu Attached Elementary School of University of Tsukuba -- 1. Connections should be "pasted" rather than "taped" -- 2. Divide subject units into small units for repetitive learning -- 1.2 Teaching Plans in which Questions Continuously Emerge: How to develop lessons in which students says, "Wow, it is really easy to calculate this way!" Yasuhiro Hosomizu Attached Elementary School of University of Tsukuba -- 1. Create opportunities where students can experience the excitement of thinking in mathematical terms -- 2. Developing creative mathematical activities -- 2.1. Mathematical activities to make students realize that patterns might exist -- 2.2. Mathematical activities for obtaining information that will help them recognize the patterns -- 2.3. Mathematical activities to encourage students to think about the reason why the patterns apply -- 2.4. Mathematical activities using a developmental approach.

1.3 Developing Creative Teaching Strategies Aimed at Imparting Diverse Ways of Thinking and Fostering Enjoyment of Learning Kozo Tsubota Attached Elementary School of University of Tsukuba -- 1. Purpose of the Lesson Plan -- 2. Teaching Strategies Aimed at Imparting Diverse Ways of Thinking and the Fun of Learning -- Explanation of lesson example -- 1. Unit: Solid Figures -- 2. Current Class Lesson: "Projected Diagram of a Cylinder" -- Section 2: Unique Japanese Lesson Development - Models and Examples -- 2.1 The Problem-Solving Oriented Teaching Methods and Examples Satoshi Natsusaka Attached Elementary School of University of Tsukuba -- 1. What is a problem-solving oriented lesson? -- 2. Examples of a problem - solving oriented lesson -- Third Grade -- Fourth Grade -- Fifth and Sixth Grades -- A partitive division problem -- A measurement division problem -- Developing a solution -- Progression through discussion -- A's Approach -- B's Approach -- Summarizing -- 3. Problems with problem-solving oriented lessons -- 2.2 Discussion-Oriented Teaching Methods and Examples: Discussion-Oriented Lessons for Improving Students' Expressive Skills Hiroshi Tanaka Attached Elementary School of University of Tsukuba -- 1. What is a "discussion-oriented" lesson? -- 2. "Discussion-oriented" lessons in practice -- 2.1 Unit: First Grade "Comparison of Length" -- 2.2 System of Curricular Content -- Direct Comparison: First Grade -- Indirect Comparison: First and Second Grade -- Comparison Using Arbitrary Units: First and Second Grade -- Comparison Using Universal Units: Second and Third Grade -- 2.3 First Grade: Learning Length: Specific Elements of Lesson Development -- Reference -- 2.3 Problem-Discovery Oriented Teaching Methods and Examples: What are Problem-Discovery Oriented Lessons? Yoshikazu Yamamoto Attached Elementary School of University of Tsukuba.

1. What is a Problem-Discovery Oriented Lesson? -- 2. Problem-Discovery Oriented Lessons in Practice -- 2.1 Unit: 6th Grade "Addition and Subtraction of Fractions" -- 2.2 Connecting Previous Lessons to the Current Lesson -- 2.3 Purpose: To cultivate perspectives on adding and subtracting fractions with different denominators through an activity that involves disassembling and assembling pattern blocks. -- 2.4 How Children Learn in this Lesson -- 1. Introduction -- 2. Problem Discovery 1 through an Activity (Subtracting fractions with different denominators) -- Chapter 3: Trends of Research Topics in Japan Society of Mathematical Education -- Section 1: Lesson Study in Elementary Schools -- 1.1 What are the Features of Lesson Study Projects Conducted in Elementary School Mathematics Departments? Tadayuki Kishimoto Toyama University Kozo Tsubota Attached Elementary School of University of Tsukuba -- Lesson Study Policies -- Problem-Solving Oriented Lessons -- 1.2 How Have the Goals of Mathematics Education Changed? Tadayuki Kishimoto Toyama University Kozo Tsubota Attached Elementary School of University of Tsukuba -- Post-War Revisions to the National Course of Study -- Curricular Shifts Between Grade Levels in the National Course of Study -- 1.3 How Have Research Trends at the Japan Society of Mathematical Education National Conference Changed? Tadayuki Kishimoto Toyama University Kozo Tsubota Attached Elementary School of University of Tsukuba -- Lesson Study Trends in Japan -- Recent Trends in Lesson Study -- Section 2: Lesson Study in Junior High Schools -- 2.1 The Current Status of Lesson Study in Junior High Schools Yutaka Oneda Attached Elementary School of University of Tsukuba -- 2.2 Changes in Curriculum and Class Hours in the New National Course of Study Yutaka Oneda Attached Elementary School of University of Tsukuba.

Changes in Curriculum and Class Hours.