Out of the Labyrinth: Setting Mathematics Free

Robert Kaplan, Ellen Kaplan9780195147445, 0195147448

Who hasn’t feared the math Minotaur in its labyrinth of abstractions? Now, in Out of the Labyrinth, Robert and Ellen Kaplan – the founders of The Math Circle, the popular learning program begun at Harvard in 1994 – reveal the secrets behind their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics.Written with the same wit and clarity that made Robert Kaplan’s The Nothing That Is an international bestseller, Out of the Labyrinth offers an engaging and practical guide for parents and educators, and a delight for anyone interested in sharing the pleasures of mathematics. The Kaplans begin by describing the state of modern math education – the lockstep acquisition of “skills,” “number facts,” and “mad minute” calculations. Instead, they argue, math should be taught as the highest form of intellectual play, an endeavor to be explored and enjoyed by children (or adults) of any age. One by one, they dismantle the many barriers to appreciating mathematics, from the self-defeating belief that mathematical talent is inborn, to the off-putting language of mathematics, to the question of why anyone should care. They show, for instance, that mathematical ability is not a matter of inborn genius, but of doggedness and attention. Even Einstein admitted that “I know perfectly well that I myself have no special talents. It was curiosity, obsession, and sheer perseverance that brought me to my ideas.Enhanced throughout with puzzles, practical equations, and colorful anecdotes from their own classrooms, Out of the Labyrinth will delight readers with its engaging exploration of mathematics. It will allow students, parents, teachers, andothers to wrestle with the accessible mysteries of math – and discover their inner math genius.

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Table of contents :
Contents……Page 8
Acknowledgments……Page 10
CHAPTER ONE: A Glimpse Inside……Page 14
CHAPTER TWO: Cod Liver Oil……Page 18
CHAPTER THREE: The Myth of Talent……Page 28
Stubbornness……Page 38
Orneriness……Page 41
A High Threshold of Frustration……Page 44
The Jump-Cut Mind……Page 46
Putting on Hold……Page 48
2. Taking Apart……Page 50
Method vs. Approach……Page 52
Atomizing……Page 53
Attention Without Tension……Page 59
Precision……Page 62
Rotating the Diamond……Page 65
Breaking Apart……Page 68
Pursuing the Possible……Page 70
Play……Page 72
Stubbornness Revisited……Page 75
The Riddle of the Pygmy Shrew……Page 76
Analogy……Page 79
Holding Hypotheses Like Birds……Page 83
Experimental Fervor……Page 87
The Architectural Instinct……Page 89
The Conductor……Page 91
Language: Symbols……Page 94
Language: Equations……Page 101
Language: Third Person Remote……Page 106
The Buddha, the Bodhisattva, and the Bo……Page 109
Climbing a Tall Building……Page 113
Alienation……Page 116
Diamond Hard……Page 119
Who Cares?……Page 123
CHAPTER SIX: How Math Has Been Taught……Page 130
Behind the Phenomena……Page 135
The Teaching Wars……Page 138
Cookbooks, Song-Lines, and Games……Page 141
Ancestral Voices Calling for Reform……Page 145
Anticurriculum……Page 150
The Curate’s Egg……Page 151
Russian Math Circles……Page 153
CHAPTER SEVEN: How Mathematicians Actually Work……Page 158
CHAPTER EIGHT: The Math Circle……Page 172
Ends……Page 173
The Students……Page 178
The Leaders……Page 182
The Math……Page 189
Connecting……Page 193
Intuition Grows……Page 194
A Proof Takes Shape……Page 198
Looking Leads to Seeing……Page 201
Competition……Page 202
Courses……Page 212
Sample Outline of a Middle Course: Interesting Points in Triangles……Page 214
Perilous Turnings and Pivotal Moments……Page 217
From a Journal……Page 222
What’s the Way Forward?……Page 236
To Take with You……Page 240
Appendix: Thoughts of a Young Teacher……Page 242
A Note on Our Pronouns……Page 246
A……Page 248
C……Page 249
E……Page 250
G……Page 251
K……Page 252
M……Page 253
P……Page 254
S……Page 255
T……Page 256
Z……Page 257