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

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 |

300 | |