| Foreword to the American Edition |
|
vii | |
| Introduction |
|
1 | (14) |
|
|
|
1 | (1) |
|
Why a circle? Why a journal? |
|
|
2 | (2) |
|
Should journals be edited? |
|
|
4 | (1) |
|
A novice's reflections on pre-school math |
|
|
5 | (3) |
|
|
|
8 | (1) |
|
A Short History of Our Circle |
|
|
9 | (3) |
|
|
|
12 | (1) |
|
|
|
13 | (2) |
|
Chapter 1 The First Session: Narrative and Reflections |
|
|
15 | (20) |
|
|
|
15 | (9) |
|
Piaget's phenomena: reality or illusion? |
|
|
24 | (4) |
|
Why read psychology books? |
|
|
28 | (4) |
|
|
|
32 | (3) |
|
Chapter 2 The Boys' Math Circle, Year One |
|
|
35 | (34) |
|
Session 21 The Mobius band |
|
|
35 | (2) |
|
Session 22 What is bigger, the whole or its part? |
|
|
37 | (4) |
|
Session 23 The Tower of Hanoi |
|
|
41 | (4) |
|
Session 24 A bit of topology |
|
|
45 | (2) |
|
Session 25 The boy in the elevator |
|
|
47 | (1) |
|
Session 26 Intersecting classes |
|
|
48 | (2) |
|
Session 27 Pegboard quadrilaterals |
|
|
50 | (2) |
|
Session 28 We start probability theory |
|
|
52 | (2) |
|
|
|
54 | (2) |
|
|
|
56 | (4) |
|
Session 31 Probability theory, again |
|
|
60 | (2) |
|
|
|
62 | (7) |
|
|
|
63 | (4) |
|
|
|
67 | (2) |
|
Chapter 3 Children and (5 2): The Story of One Problem |
|
|
69 | (14) |
|
|
|
70 | (1) |
|
|
|
71 | (3) |
|
|
|
74 | (2) |
|
|
|
76 | (3) |
|
|
|
79 | (4) |
|
Chapter 4 The Boys' Math Circle, Year Two |
|
|
83 | (54) |
|
Session 33 Geometric similarity |
|
|
83 | (3) |
|
Session 34 An uneventful session |
|
|
86 | (1) |
|
Session 34 Almost calculating probabilities |
|
|
87 | (3) |
|
Session 36 A game of three dice |
|
|
90 | (2) |
|
Session 37 How many rectangles? |
|
|
92 | (2) |
|
Session 38 Losing my grip |
|
|
94 | (2) |
|
|
|
96 | (9) |
|
A short excursion into the past |
|
|
97 | (3) |
|
The programming language Kid |
|
|
100 | (5) |
|
Session 40 First encounter with Dienes blocks |
|
|
105 | (2) |
|
Session 41 More of the same (robots and Dienes blocks) |
|
|
107 | (2) |
|
|
|
109 | (2) |
|
Session 43 On certain properties of addition |
|
|
111 | (4) |
|
|
|
115 | (2) |
|
Session 45 Generalized chains |
|
|
117 | (2) |
|
Session 46 Isomorphic problems |
|
|
119 | (1) |
|
Session 47 The end of the story about (5 2) |
|
|
120 | (2) |
|
Session 48 True and false statements |
|
|
122 | (3) |
|
A bit of programming, just with Dima |
|
|
123 | (2) |
|
Session 49 Thinking about symbols |
|
|
125 | (3) |
|
Session 50 A double anniversary |
|
|
128 | (1) |
|
Session 51 Which path is longer? |
|
|
129 | (2) |
|
Session 52 Breaking a code |
|
|
131 | (1) |
|
Session 53 A genealogical tree |
|
|
132 | (2) |
|
Session 54 The end of the school year |
|
|
134 | (3) |
|
Chapter 5 Notation, abstraction, mathematics, and language |
|
|
137 | (12) |
|
|
|
137 | (2) |
|
|
|
139 | (2) |
|
Each person has more than one type of intelligence |
|
|
141 | (3) |
|
Teaching mathematics as a native tongue |
|
|
144 | (5) |
|
Chapter 6 The Boys' Math Circle, Year Three |
|
|
149 | (46) |
|
Session 55 Logical problems |
|
|
149 | (3) |
|
Session 56 Construction foreman |
|
|
152 | (2) |
|
Session 57 Who is booter, Gobr or Stoon? |
|
|
154 | (4) |
|
|
|
158 | (6) |
|
|
|
160 | (4) |
|
Session 59 What does the other person see? |
|
|
164 | (3) |
|
|
|
167 | (2) |
|
Session 61 How do you add invisible numbers? |
|
|
169 | (3) |
|
Session 62 Which room is larger? |
|
|
172 | (1) |
|
Session 63 Reason versus chance |
|
|
173 | (3) |
|
Session 64 We battle against the odds, again |
|
|
176 | (4) |
|
|
|
180 | (3) |
|
|
|
183 | (1) |
|
|
|
184 | (11) |
|
Miscellaneous jokes, conversations, and puzzles |
|
|
185 | (10) |
|
Chapter 7 The Boys' Math Circle, Final Six Months |
|
|
195 | (22) |
|
Session 68 Calendar conundrum |
|
|
195 | (2) |
|
|
|
197 | (3) |
|
Session 70 More programming |
|
|
200 | (3) |
|
Session 71 Classroom puzzles... almost |
|
|
203 | (2) |
|
|
|
205 | (3) |
|
Session 73 Odd numbers and squares |
|
|
208 | (2) |
|
Session 74 The geometry of numbers |
|
|
210 | (2) |
|
|
|
212 | (2) |
|
Session 76 All things must end, sometime |
|
|
214 | (3) |
|
Chapter 8 At Home and in School |
|
|
217 | (22) |
|
Mathematical discussions, with sad digressions about school |
|
|
217 | (17) |
|
|
|
234 | (5) |
|
Chapter 9 The Girls' Math Circle, Year One |
|
|
239 | (34) |
|
|
|
239 | (7) |
|
Session 1 Piaget's phenomena, again |
|
|
246 | (5) |
|
Session 2 Princes and princesses |
|
|
251 | (2) |
|
Session 3 How many differences? |
|
|
253 | (3) |
|
Session 4 Building from diagrams |
|
|
256 | (3) |
|
|
|
259 | (2) |
|
Session 6 The boy's morning |
|
|
261 | (1) |
|
Session 7 Play trumps science |
|
|
262 | (2) |
|
Session 8 Between two mirrors |
|
|
264 | (2) |
|
Session 9 In the courtyard |
|
|
266 | (4) |
|
Session 10 Bi-colored cubes |
|
|
270 | (1) |
|
|
|
271 | (2) |
|
Chapter 10 The Girls' Math Circle, Year Two |
|
|
273 | (22) |
|
Session 12 Something's amiss with probability theory |
|
|
273 | (2) |
|
Session 13 Intersecting classes again |
|
|
275 | (2) |
|
Session 14 The Tower of Hanoi |
|
|
277 | (1) |
|
Session 15 Towers of equal height |
|
|
278 | (2) |
|
|
|
280 | (1) |
|
|
|
281 | (1) |
|
Session 18 Faces, vertices, and edges of a cube |
|
|
282 | (4) |
|
Session 19 The wolf, the goat, and the cabbage |
|
|
286 | (4) |
|
Session 20 A chain with one difference |
|
|
290 | (5) |
| Epilogue |
|
295 | (4) |
| Index of Math, Pedagogy, and Psychology |
|
299 | |
