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El. knyga: Mathematical Thinking: How to Develop it in the Classroom [World Scientific e-book]

(Society Of Elementary Math Education, Japan), (Univ Of Tsukuba, Japan)
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Mathematical Thinking: How to Develop it in the ClassroomDidesnis paveikslėlis
Kitos knygos pagal šią temą:
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Partnerių interneto svetainė: http://www.worldscientific.com/worldscibooks/10.1142/8163#t=toc
Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties to develope it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.
Preface to the Series v
Preface to the Book vii
Acknowledgements xi
Introductory
Chapter: Problem Solving Approach to Develop Mathematical Thinking		 1(28)
Part I Mathematical Thinking: Theory of Teaching Mathematics to Develop Children Who Learn Mathematics for Themselves
29(100)
Chapter 1 Mathematical Thinking as the Aim of Education
31(6)
1.1 Developing Children Who Learn Mathematics for Themselves
31(1)
1.2 Mathematical Thinking as an Ability to Think and to Make Decisions
32(3)
1.3 The Hierarchy of Ability and Thinking
35(2)
Chapter 2 The Importance of Cultivating Mathematical Thinking
37(10)
2.1 The Importance of Teaching Mathematical Thinking
37(2)
2.2 Example: How Many Squares Are There?
39(8)
Chapter 3 The Mindset and Mathematical Thinking
47(6)
3.1 Mathematical Thinking
47(2)
3.2 Structure of Mathematical Thinking
49(4)
Chapter 4 Mathematical Methods
53(34)
4.1 Inductive Thinking
53(3)
4.2 Analogical Thinking
56(3)
4.3 Deductive Thinking
59(3)
4.4 Integrative Thinking
62(4)
4.5 Developmental Thinking
66(4)
4.6 Abstract Thinking (Abstraction)
70(4)
4.7 Thinking That Simplifies (Simplifying)
74(2)
4.8 Thinking That Generalizes (Generalization)
76(2)
4.9 Thinking That Specializes (Specialization)
78(3)
4.10 Thinking That Symbolizes (Symbolization)
81(2)
4.11 Thinking That Represents by Numbers, Quantities, and Figures (Quantification and Schematization)
83(4)
Chapter 5 Mathematical Ideas
87(24)
5.1 Idea of Sets
87(2)
5.2 Idea of Units
89(2)
5.3 Idea of Representation
91(4)
5.4 Idea of Operation
95(3)
5.5 Idea of Algorithms
98(2)
5.6 Idea of Approximations
100(2)
5.7 Idea of Fundamental Properties
102(2)
5.8 Functional Thinking
104(4)
5.9 Idea of Expressions
108(3)
Chapter 6 Mathematical Attitude
111(10)
6.1 Objectifying
111(2)
6.2 Reasonableness
113(2)
6.3 Clarity
115(2)
6.4 Sophistication
117(4)
Chapter 7 Questioning to Enhance Mathematical Thinking
121(8)
Appendix for the List of Questions for Mathematical Thinking
127(2)
Part II Developing Mathematical Thinking with Number Tables: How to Teach Mathematical Thinking from the Viewpoint of Assessment
129
Example 1 Sugoroku: Go Forward Ten Spaces If You Win, or One If You Lose
137(12)
(1) Type of Mathematical Thinking to Be Cultivated
137(1)
(2) Grade Taught
137(1)
(3) Preparation
137(1)
(4) Overview of the Lesson Process
137(1)
(5) Worksheet
138(1)
Let's play this game!
139(1)
(6) Lesson Process
140(8)
(7) Summarization on the Blackboard
148(1)
(8) Evaluation
148(1)
Example 2 Arrangements of Numbers on the Number Table
149(10)
(1) Type of Mathematical Thinking to Be Cultivated
149(1)
(2) Grade Taught
149(1)
(3) Preparation
149(1)
(4) Overview of the Lesson Process
149(1)
(5) Worksheet
150(1)
(6) Lesson Process
151(5)
(7) Summarization on the Blackboard
156(1)
(8) Evaluation
156(3)
Example 3 Extension of Number Arrangements
159(14)
(1) Type of Mathematical Thinking to Be Cultivated
159(1)
(2) Grade Taught
159(1)
(3) Preparation
159(1)
(4) Overview of the Lesson Process
159(1)
(5) Worksheet
160(3)
(6) Lesson Process
163(8)
(7) Summarization on the Blackboard
171(1)
(8) Evaluation
171(2)
Example 4 Number Arrangements: Sums of Two Numbers
173(12)
(1) Type of Mathematical Thinking to Be Cultivated
173(1)
(2) Grade Taught
173(1)
(3) Preparation
173(1)
(4) Overview of the Lesson Process
173(1)
(5) Worksheet
174(2)
(6) Lesson Process
176(7)
(7) Summarization on the Blackboard
183(1)
(8) Evaluation
183(2)
Example 5 When You Draw a Square on a Number Table, What Are the Sum of the Numbers at the Vertices, the Sum of the Numbers Along the Perimeter, and the Grand Total of All the Numbers?
185(18)
(1) Type of Mathematical Thinking to Be Cultivated
185(1)
(2) Grade Taught
185(1)
(3) Preparation
185(1)
(4) Overview of the Lesson Process
185(1)
(5) Worksheet
186(3)
(6) Lesson Process
189(10)
(7) Summarization on the Blackboard
199(1)
(8) Evaluation
200(1)
(9) Further Development
200(3)
Example 6 Where Do Two Numbers Add up to 99?
203(14)
(1) Types of Mathematical Thinking to Be Cultivated
203(1)
(2) Grade Taught
203(1)
(3) Preparation
203(1)
(4) Overview of the Lesson Process
203(1)
(5) Worksheet
204(2)
(6) Lesson Process
206(9)
(7) Summarization on the Blackboard
215(1)
(8) Evaluation
215(1)
(9) Further Development
216(1)
Example 7 The Arrangement of Multiples
217(14)
(1) Type of Mathematical Thinking to Be Cultivated
217(1)
(2) Grade Taught
217(1)
(3) Preparation
217(1)
(4) Overview of the Lesson Process
217(1)
(5) Worksheet
218(1)
(6) Lesson Process
219(11)
(7) Summarization on the Blackboard
230(1)
(8) Evaluation
230(1)
Example 8 How to Find Common Multiples
231(14)
(1) Type of Mathematical Thinking to Be Cultivated
231(1)
(2) Grade Taught
231(1)
(3) Preparation
231(1)
(4) Overview of the Lesson Process
231(1)
(5) Worksheet
232(1)
(6) Lesson Process
233(9)
(7) Summarization on the Blackboard
242(1)
(8) Evaluation
242(1)
(9) Further Development
242(3)
Example 9 The Arrangement of Numbers on an Extended Calendar
245(10)
(0) Introduction
245(1)
(1) Type of Mathematical Thinking to Be Cultivated
245(1)
(2) Grade Taught
245(1)
(3) Preparation
245(1)
(4) Overview of the Lesson Process
246(1)
(5) Worksheet
246(2)
(6) Lesson Process
248(5)
(7) Summarization on the Blackboard
253(1)
(8) Evaluation
253(2)
Example 10 Development of the Arrangement of Numbers in the Extended Calendar
255(14)
(0) Introduction
255(1)
(1) Type of Mathematical Thinking to be Cultivated
255(1)
(2) Grade Taught
255(1)
(3) Preparation
255(1)
(4) Overview of the Lesson Process
256(1)
(5) Worksheet
256(3)
(6) Lesson Process
259(8)
(7) Summarization on the Blackboard
267(1)
(8) Evaluation
267(2)
Example 11 Sums of Two Numbers in an Odd Number Table
269(14)
(0) Introduction
269(1)
(1) Type of Mathematical Thinking to Be Cultivated
269(1)
(2) Grade Taught
269(1)
(3) Preparation
270(1)
(4) Overview of the Lesson Process
270(1)
(5) Worksheet
270(2)
(6) Lesson Process
272(9)
(7) Summarization on the Blackboard
281(1)
(8) Evaluation
281(2)
Example 12 When You Draw a Square on an Odd Number Table, What Are the Sum of the Numbers at the Vertices and the Grand Total of All the Numbers?
283
(0) Introduction
283(1)
(1) Type of Mathematical Thinking to Be Cultivated
283(1)
(2) Grade Taught
283(1)
(3) Preparation
283(1)
(4) Overview of the Lesson Process
284(1)
(5) Worksheet
284(2)
(6) Lesson Process
286(10)
(7) Summarization on the Blackboard
296(1)
(8) Evaluation
296(1)
(9) Further Development
296
Shigeo Katagiri is known as one of most famous math-educators in Japan who established the national curriculum to develop mathematical thinking systematically in the classroom. Masami Isoda is a representative of APEC lesson study project, translator and editor of Prof. Katagiri's work into English on global lesson study movement with current perspective of mathematics education research.
Pastovi nuoroda: https://www.kriso.lt/db/9789814350853_pe.html