Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers

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American Mathematical Soc., 2011 - Mathematics - 300 pages

This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.

This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource.

In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

 

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Contents

Introduction
1
Narrative and Reflections
15
The Boys Math Circle Year
21
Chapter 3
70
Chapter 4
83
Chapter 5
137
Chapter 6
149
1
153
128
214
8
217
129
221
131
232
First graders
234
9
239
35
246
Princes and princesses
251

94
156
105
162
What does the other person see?
164
Reflection
167
How do you add invisible numbers?
169
109
170
Which room is larger?
172
Reason versus chance
173
We battle against the odds again
176
Homeomorphism
180
Topology
183
Four colors
184
Miscellaneous jokes conversations and puzzles
185
The Boys Math Circle Final Six Months
195
Oral puzzles
197
115
199
More programming
200
Classroom puzzles almost
203
Subprograms
205
119
206
Odd numbers and squares
208
The geometry of numbers
210
The Mayans
212
37
253
134
254
Building from diagrams
256
47
259
137
260
The boys morning
261
Play trumps science
262
Between two mirrors
264
In the courtyard
266
144
268
Bicolored cubes
270
Fives
271
The Girls Math Circle Year Two
273
Intersecting classes again
275
149
277
Towers of equal height
278
Turning 90
280
152
283
52
288
Epilogue
295
56
300
Copyright

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About the author (2011)

Alexander Zvonkin is at the Universit Bordeaux I, Talence, France

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