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Out of the Labyrinth: Setting Mathematics Free 1st Edition

4.4 out of 5 stars 5 customer reviews
ISBN-13: 978-0195147445
ISBN-10: 0195147448
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Editorial Reviews

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"This book offers an engaging and practical guide for parents and educators, and a delight for anyone interested in sharing the pleasures of mathematics."--Lunar and Planetary Information Bulletin


"Out of the Labyrinth will delight readers with its engaging exploration of mathematics. It will allow students, parents, teachers, and others to wrestle with the accessible mysteries of math- and discover their inner math genius."--Lunar and Planetary Information Bulletin


"Out of the Labyrinth rejoices in the serious play of mathematics and explains how to think about math as a truly common pursuit... This beautiful book - full of fun and full of the wisdom of a lifetime of teaching - is so deftly done that by the time the Kaplans tell us that "math is our other native language," we believe them utterly." -- Barry Mazur, Gerhard Gade University Professor, Harvard University


"I found the book to be a provocative guide to the beauty and glory of mathematics with many excellent suggestions on how to communicate this to others, written by two masters of the art. I enjoyed the sections the most where I agreed with them the least. It challenged every prejudice I had developed about the subject." -- Benedict Gross, Leverett Professor of Mathematics and Dean of Harvard College


About the Author


Robert and Ellen Kaplan have taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. They are the founders of The Math Circle, a program for the exploration and enjoyment of mathematics, which is opening branches across America and Great Britain. Robert Kaplan is the author of the best-selling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages, and together they wrote The Art of the Infinite. Ellen Kaplan is also co-author of Chances Are: Adventures in Probability.
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Product Details

  • Hardcover: 256 pages
  • Publisher: Oxford University Press; 1 edition (January 22, 2007)
  • Language: English
  • ISBN-10: 0195147448
  • ISBN-13: 978-0195147445
  • Product Dimensions: 9.3 x 1.2 x 6.3 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #428,314 in Books (See Top 100 in Books)

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Format: Hardcover
WARNING: This book does not provide cookie-cutter curricula, problem sets and answers. Rather, this book presents a philosophy and approach to unleash curiosity and self-exploration of complex math in students from ages 4 through adult. Full of wit and wisdom and a joy to read, even for interested parents outside of the teaching field.

Written by two highly acclaimed opinion leaders in mathematics education, the book presents a convincing argument for incorporating the art of guided explorations and self-discovery into math curricula. Along the way, they also describe the classroom, organizational and practical issues they faced in founding their non-profit Math Circle in the Harvard University environs.

Mathematics is our lost native language, state the authors. Math talent is a myth, but the drudgery of most early math education fails to instill the confidence and sense of play which invites further exploration. The subtle Art of teaching is woven throughout the book as the lifelong teachers lend examples for creating an intimate model for guiding young students in their own discovery of complex math. Their approach consists of posing foundational questions to group of students -- Are there numbers between numbers? What is Area? -- then guiding a discussion down many paths "propelled by the fun of the chase."

This approach may sound straightforward, but the art requires a spirit of exploration and familiarity with mathematics on the part of the teachers, highlighting some of the challenges. The authors describe after-school and in-school models for incorporating the approach, as well as observations and class notes to lend color.
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Format: Hardcover
It began with the sort of grouse session that all teachers of mathematics from Euclid on would recognize. "Why is mathematics so poorly taught? *We* know how rich and mind-expanding mathematics can be--why don't our students?" But then, instead of the typical sniffs and harrumphs, the conversation took an unusual turn: Robert and Ellen Kaplan resolved to found The Math Circle, an after-school program that, in their words, "teaches the enjoyment of mathematics."

The Math Circle's starting premises are that mathematics is accessible to all, not the preserve of a talented few; that mathematics thrives in a setting of collegiality, engrossment, brio, and good will; and that the best way to learn mathematics is to create it oneself, by experimentation and the free play of ideas. What can follow from these simple but audacious axioms astounds the imagination. Students not only master but discover (invent?) pieces of sophisticated mathematical reasoning, with only minimal guidance from the group leader, who functions as neither authority nor drillmaster, but as moderator and scribe. Having visited The Math Circle, I can testify that the Kaplans' approach works splendidly. In one demonstration, I saw first graders unlock the summation formula for arithmetic series in forty-five minutes. (They hit on Gauss's pairing trick, as well as several more idiosyncratic strategies.) These were ordinary students, many of whom were shaky at the outset on addition, to say nothing of multiplication--yet the problem so drew them in, the development made so much sense to them, that by the end of the session, they all were calculating with ease. What an improvement on sum charts and times tables!

How do the Kaplans do it?
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Format: Hardcover
The Kaplans teach the enjoyment of mathematics to anyone willing to explore it with them. That is what their Math Circle, which they describe in this book, seems to be all about.

They set out here to explain an approach they have developed to passing on their love of mathematics. They hope and expect more teachers will be interested to offer a similar service and that they will find their approach helpful. The book is entertaining, even inspiring, certainly plausible, and full of the humorous and serious observations of these two evidently very experienced mathematical scholars and educators. For any mathematician who is ready to pick up an invitation to pass on the enjoyment of the subject, I suppose the test of the Kaplan approach will be in the doing. In extremely brief summary, a Math Circle leader carries no kit but rather a good knowledge of mathematics, a suitable collection of teasing openers, and an ability to moderate a seminar of budding mathematicians, usually but not always young. ("You know what?", said one adult student. "I'm going to die a genius!")

The Kaplans point out that not every potential student will necessarily feel interested in turning into a mathematician for a few magical hours every week. Anyone, they believe, can do what mathematicians do, but they are wary of taking students merely on the basis of parental desire or enthusiasm. They describe what they are offering as, in an important respect, a kind of communal and collegial play of the intellect. It sounds pretty friendly. I have a pleasant picture of wizards from the local Math Circle offering to escort the willing by paths of puzzlement to gardens of mathematical delight.

The Math Circle appears to have been evolving for well over a decade.
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