Out of the Labyrinth: Setting Mathematics Free

by Robert M. Kaplan, Ellen Kaplan

Who hasn't feared the math Minotaur in its labyrinth of abstractions? The subject can seem convoluted and forbidding. Yet to do mathematics is to wrestle with “accessible mysteries”-and Out of the Labyrinth shows how exhilarating the challenge can be. Robert and Ellen Kaplan are founders of the Math Circle, a pioneering learning program begun at Harvard in 1994 and now spreading around the world. In their classrooms students ages six to sixty have discovered mathematics as the highest form of intellectual play, while exploring topics that range from Roman numerals to quantum mechanics.



The Kaplans reveal the secrets of their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Stocked with puzzles, colorful anecdotes, and insights from the authors' own teaching experience, Out of the Labyrinth is both an engaging and practical guide for parents and educators, and a treasure chest of mathematical discoveries. For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion.

Genres: Mathematics, Education, Nonfiction, Science, Teaching, Stem

256 pages, Hardcover

First published January 1, 2007

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. 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 and Bozo Sapiens: Why to Err is Human, co-written with her son Michael Kaplan.

Reviews

[Russ · Rating 3 out of 5]

I'm all in favor of the basic premise of this book: that teaching kids how to discover math on their own is more likely to make math interesting and is a better way to teach them to think. I also enjoyed the examples from the classes and the ways they got students to get into certain ideas, even though many of the ideas were over my head. It's the long, middle section of the book that I found less compelling. The authors found the need to explain their theory of how the brain works and their idea that everyone has an "architectural instinct." I found myself saying, "Let's just stick to math and leave psychology and other fields to experts in those fields." Still, it's an interesting book; I'd just skim the central chapters.

[Jeff · Rating 4 out of 5]

The Kaplans have written a great rationale and explanation of their Math Circle approach to teaching mathematics. They articulate a vision for mathematics education founded in small groups of students (5 to 15) working collaboratively on intriguing math problems. They have an inquiry based approach that engenders the transferable habits of mind necessary for mathematicians to solve any problem rather than teaching algorithmic approaches that help students solve only particular kinds of problems. Math Circles gives students opportunities to experience working and learning mathematics as collegial rather than competitive, and focused on serious content and discovery rather than instruction.

In general, Out of the Labyrinth: Setting Mathematics Free describes all of this beautifully with a deep foundation in the whys and hows of Math Circles. However, as in The Art of the Infinite, the Kaplans writing can be dense with both literary references and quick explanations of fairly complex math which required me to slow down and reread (not always a bad thing). That said Out of the Labyrinth is a much more accessible book, with many more sections of straightforward explanatory prose, and this serves their purposes in that this book needs to be more widely read.

[Ian · Rating 3 out of 5]

This book had some interesting ideas about teaching mathematics through small group exploration of particular mathematical problems. However, it was marred by the opaque language, through which the authors seemed hell-bent on demonstrating their 'cleverness'. The mathematics was straight-forward, the English on the other hand was tortuous and Baroque and a lot of the time, I had to re-read paragraphs to see what it was the authors were getting at - only to find that the meaning didn't justify the effort expended. At times I wondered how the authors managed to communicate at all with small children. It was only in the final chapter where they gave examples of journals that they managed to communicate with simplicity and clarity, which made it all the clearer that the language of the earlier chapters was a pose.

I would recommend that maths teachers give this book a miss and instead read one of the books about problem-posing which is an approach explained with far greater clarity and less desire to impress.

[Jim Razinha · Rating 3 out of 5]

This book intends to make math more accessible, which I understand to be the point of the Math Circle program created by the authors. Unfortunately, that accessibility is obscured by a cumbersome narrative. The authors seem to have taken a cue from the "Never utilize a diminutive utterance when a polysyllabic synonym will suffice" mantra. Incongruously, in this book, when they are presented, simple concepts are inflated and more challenging concepts are oversimplified. They aren't presented all that much though.

The authors say in the first chapter that the book describes (among other things) how they removed the barriers to enjoying mathematics...but I don't think they succeeded. The illustrative problems are well done, but the trappings are the majority of the book and are unwieldy. The attempts to remove barriers to enjoying mathematics unfortunately include barriers to enjoying reading about the removal of barriers.

[Matteo · Rating 3 out of 5]

it's as elitist a book as i can remember: it's full of words that i have to look up, that could easily be replaced by simpler words. It contains some useful insights into the teaching of math, an interesting hint at the sexism and racism that permeated academic mathematics in the US a couple of decades ago (no word on the current status) and an unwarranted attack on ethnomathematics.

thank goodness i bought it used.

[Gretchen · Rating 1 out of 5]

Was reading this in hopes of getting concrete advice about how to replicate the authors' Math Circle model in my own community. Found it relatively unhelpful on that score. The most useful pieces for me were the verbatims from meetings of their Math Circles. I found those fascinating and helpful in getting a sense of how they operate. Unfortunately, there were too few of those. I was hoping for something that read like a set of lesson plans more than anything else.

[Jessica · Rating 1 out of 5]

I did not like this book at all. It was boring, self-promoting, and totally ridiculous in parts. The whole premise was that there is no such thing as talent. While I agree that everyone can learn to do math, I am firmly of the opinion that it will never come easily to some people, and it comes naturally to some people. Anyway, the book annoyed me.

[Susan · Rating 5 out of 5]

Great book! A must-read for anyone involved in math clubs or math circles, and for parents of kids who love math. And for people who design the math curriculum in the schools... and for all math teachers.

[Pcallist · Rating 4 out of 5]

Very interesting,about teaching math but applicable to the curious and parents

[Al Doyle · Rating 5 out of 5]

Great read, challenging yet informative.

[Arron · Rating 4 out of 5]

[Extensive focus on procedures] stunts thought by demoting math to the level of incantatory magic [...]. At its extreme, it takes the edge off the mind's finest capacity: to size up the unknown.