Teaching Multiplication with Lesson Study : : Japanese and Ibero-American Theories for International Mathematics Education.
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| Place / Publishing House: | Cham : : Springer International Publishing AG,, 2020. ©2021. |
| Year of Publication: | 2020 |
| Edition: | 1st ed. |
| Language: | English |
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| Physical Description: | 1 online resource (302 pages) |
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Table of Contents:
- Teaching Multiplication with Lesson Study
- Foreword
- Preface
- References
- Acknowledgements
- Contents
- Contributors
- About the Editors
- Chapter 1: Introduction: Japanese Theories and Overview of the Chapters in This Book
- 1.1 Origin of This Book
- 1.2 Overview of Japanese Theories for Designing Lessons
- 1.2.1 Mathematical Thinking and Activity: Aims and Objectives
- 1.2.2 Terminology and Sequences: Extension and Integration
- 1.2.3 Problem-Solving Approach: Not Only a Teaching Method
- 1.2.4 Change Approaches for Developing Students and Teachers
- 1.3 Overview of Chapters in Part I: The Japanese Approach
- 1.4 Overview of Chapters in Part II, Focusing on Ibero-American Countries
- References
- Part I: Japanese Approach for Multiplication: Comparison with other Countries, and Theoretical, Historical, and Empirical Analysis for Lesson Study
- Chapter 2: Multiplication of Whole Numbers in the Curriculum: Singapore, Japan, Portugal, the USA, Mexico, Brazil, and Chile
- 2.1 Comparison of Curricular Standards' Descriptions for Introducing Multiplication in Different Countries
- 2.2 Comparison of the Assigned Grade Levels for Multiplication
- 2.2.1 Range of Digits
- 2.2.2 The Meaning of Multiplication
- 2.2.3 The Definition of Multiplication
- 2.2.4 Multiplication Tables
- 2.2.5 Use of Algorithm or Column Method for Multiplication
- 2.2.6 Comparing the Results with Previous Research
- 2.3 Questions for Later Chapters
- References
- Chapter 3: Problematics for Conceptualization of Multiplication
- 3.1 Definitions of Multiplication and Their Meanings in Situations in School Mathematics
- 3.1.1 The Concept of Multiplication in Pure Mathematics in Relation to School Mathematics
- 3.1.2 Multiplicative Situations, Expression, and Translations
- 3.1.2.1 Origin of Written Situations.
- 3.1.2.2 In Situations of Geometry with Proportionality
- 3.1.2.3 In Situations with Quantities and Definition by Measurement
- 3.1.2.4 Contradictions between Repeated Addition and Situations with Quantities
- 3.1.2.5 Using the Situation of Multiplication Only for the Attribute of the Object
- 3.1.2.6 In the Situation of Area, As for Extension to Decimals and Fractions
- 3.1.2.7 In the Situation of Tree Diagrams
- 3.1.2.8 Seeing the Tree Diagram as an Operator
- 3.1.2.9 Activity of Elementary School and Cartesian Product
- 3.1.2.10 In Situations of Splitting as for Partitive Division
- 3.1.2.11 Another Usage: Splitting in Relation to the Distributive Law
- 3.1.2.12 Limitations of Every Model for Multiplication
- 3.1.2.13 Conceptual Fields for Multiplication
- 3.2 Problems with Multiplication that Originate from Languages
- 3.3 European Languages and Their Historical Usages
- 3.3.1 The Transition in Chile
- 3.4 Final Remarks
- References
- Chapter 4: Introduction of Multiplication and Its Extension: How Does Japanese Introduce and Extend?
- 4.1 The Introduction of Multiplication Using the Japanese Approach
- 4.1.1 The Way to Initiate the Situation for Multiplication Before Repeated Addition in the Japanese Approach
- 4.1.1.1 Repeated Addition and Challenges to Difficulty
- 4.1.1.2 Use of the Multiplicand and Multiplier for Students to Think of Division Situations by and for Themselves
- 4.1.1.3 Commutativity and Order in Expression
- 4.1.1.4 Differences in the Multiplier and Multiplicand in an Array and a Block Diagram
- 4.1.1.5 Revisiting Which Notation Is Better and Why
- 4.2 Preparation for Multiplication in the Japanese Curriculum and Textbooks
- 4.2.1 Preparation for Introduction of Multiplication in the First Grade
- 4.2.1.1 Composition and Decomposition of Cardinal Numbers for Binary Operations.
- 4.2.1.2 Counting by Twos or by Fives as the Base for the New Unit to Count
- 4.2.1.3 Polynomial Notation
- 4.2.1.4 Production of Tentative/Arbitrary Units
- 4.3 Proportionality for Extension of Multiplication
- 4.3.1 Introduction of Proportional Number Lines and Their Adaptation for Extension
- 4.3.2 Extension of Multiplication by Using Proportional Number Lines
- 4.3.3 Partitive and Quotative Divisions Using Multiplication
- 4.3.4 Relationships Among the Rule of Three, Multiplication, and Division
- 4.3.5 From Division to Ratios and Rates Using the Multiplicative Format
- 4.4 Various Meanings of Fractions Embedding the Meanings of Division Situations
- 4.5 Further Challenges to Distinguish Additive and Multiplicative Structures
- 4.5.1 Redefinition of Proportionality at Junior High School
- 4.6 Final Remarks
- References
- Chapter 5: Japanese Lesson Study for Introduction of Multiplication
- 5.1 Lesson Study for the Introduction of Multiplication
- 5.1.1 Lesson Study on the Meaning of Multiplication, by Mr. Natsusaka
- 5.1.1.1 Description and Plan of the Lesson Being Investigated
- 5.1.1.2 A Public Lesson (Open Class) by Mr. Natsusaka
- 5.1.1.3 Post-Open Class Discussion
- 5.1.2 Lesson Plan on Applying the Meaning of Multiplication After Learning the Multiplication Table, by Mr. Tsubota
- 5.2 Evidence to See Any Number as a Counting Unit
- 5.3 Comparison of the Japanese and Chilean Approaches
- 5.4 Final Remarks
- References
- Chapter 6: Teaching the Multiplication Table and Its Properties for Learning How to Learn
- 6.1 Revisiting the Japanese Educational Principle
- 6.2 A Survey of Appropriate Grades to Introduce the Multiplication Table
- 6.3 The Multiplication Table in Japanese Textbooks for Learning How to Learn
- 6.3.1 Developing Multiplication Tables for the Rows of 2, 5, 3, and 4.
- 6.3.2 Transferring the Responsibility for Construction and Memorization of the Multiplication Table
- 6.3.3 Extension of the Multiplication Tables of 6-9 and 1
- 6.3.4 Properties of the Multiplication Table for Discovering the World of Multiplication with a Sense of Wonder
- 6.4 Memorizing the Multiplication Table as a Cultural Practice
- 6.4.1 Using the Cards
- 6.4.2 Using Area-Array Cards
- 6.4.3 Using a Notebook and Journal Writing at Home
- 6.5 The Sense of Wonder in the Multiplication Table
- 6.5.1 Focusing on Beautiful Patterns with a Sense of Wonder and Appreciation
- 6.5.2 Preparing a Problematic: "Why"
- 6.5.3 How to Begin the Class?
- 6.6 Final Remarks
- References
- Chapter 7: The Teaching of Multidigit Multiplication in the Japanese Approach
- 7.1 Diversity of Column, Algorithm, and Vertical Form Methods for Multiplication
- 7.1.1 Historical Illustration of Diversity
- 7.1.2 Revisiting the Confusion Between the Multiplier and Multiplicand, and the Need to Differentiate Them
- 7.1.3 Terminology for Teaching Column Multiplication
- 7.2 Lesson Study for Introducing Multiplication in Vertical Form
- 7.2.1 Lesson Study Video Introducing Vertical Form
- 7.2.2 Mr. Muramoto's Objectives for This Class
- 7.2.3 Description of Actual Lesson Episodes
- 7.2.4 Criteria for Formative Assessment in the Lesson Plan
- 7.3 Annex for Sect. 7.2: Excerpts of the Lesson Plan by Mr. Muramoto, Illustrating Why and How a Japanese Teacher Prepares School-Based Lesson Study
- 7.3.1 Maruyama Elementary School Mathematics Group Vision and Mathematics Lesson Study Group's Goals
- 7.3.1.1 Actual Setting of the Students in Maruyama
- 7.3.1.2 Research Theme for Lesson Study
- 7.3.1.3 Focal Points for Kyozaikenkyu (Preparation of Teaching Materials According to the Objective/Research on the Subject Matter) for Implementation of the Research Theme.
- 7.3.1.4 Thinking About Assessments That Help Students to Be More Precise in Their Problem-Solving Processes
- 7.3.2 Support for Other Teachers in School to Improve Students' Learning
- 7.3.2.1 Necessary Communication with Other Teachers
- 7.3.3 To Promote Human Character Formation with Strong Hearts and Minds, Students Who Acquire This Kind of Competency Can Participate in the Classroom in the Following Ways
- 7.3.3.1 Planning Consistent Development of Proficiency in Logical Thinking
- 7.3.4 Survey of Students for Preparation and Challenges
- 7.3.5 Exploring Topics That Students Learn in the Third Grade
- 7.3.6 Challenging Issues for the Lesson Study Group with Viewpoints
- 7.3.6.1 Viewpoint 1: Teaching Material to Connect Unknown Content with Learned content
- 7.3.6.2 Viewpoint 2: Knowing the Significance of Own Ideas Through Comparison with Others' Understanding
- 7.3.6.3 Viewpoint 3: Prepare the Task Sequence with Formative Assessments
- 7.3.7 Unit and Lesson Plans
- 7.4 Multidigit Multiplication in Vertical Form: Task Sequence for Extension and Integration in the Case of Gakko Tosho
- 7.4.1 Task Sequence for Extension
- 7.4.1.1 Task 1: Extension by Students
- 7.4.1.2 Task 2: 4 × 30
- 7.4.1.3 Task 3: 21 × 13
- 7.4.1.4 Tasks 4 and 5: With Carrying and with 0
- 7.5 Final Remarks
- References
- Part II: Ibero and Ibero-American Contributions for the Teaching of Multiplication
- Chapter 8: An Ethnomathematical Perspective on the Question of the Idea of Multiplication and Learning to Multiply: The Languages and Looks Involved
- 8.1 Introduction
- 8.2 Alternative Modes
- 8.2.1 Project Learning
- 8.2.2 Thinking of Multiplication Through Research Scripts
- 8.3 Multiplication: Tables with Polygons
- 8.4 Multiplication using Art and Technology
- 8.4.1 Multiplication Using the Calculator.
- 8.5 Some More Ideas About Learning and Teaching of Mathematical Knowledge.