Out of the Labyrinth: Setting Mathematics Free 1st Edition by Robert Kaplan (PDF)

Description

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.

User’s Reviews

Editorial Reviews: About the Author Ellen Kaplan has taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. With her husband, Robert, she wrote The Art of the Infinite. Ellen 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 from Amazon users which were colected at the time this book was published on the website:

⭐This book changed my life-no kidding. It was interesting and fun and really made me think about math differently, especially about teaching and approaching math as a puzzle to enjoy.]

⭐The Kaplans write hugely entertaining and enlightening books on math.

⭐I highly recommend this book. I admit I haven’t personally implemented all of their ideas into the classroom, but their philosophy that mathematics (and perhaps any subject for that matter) is best learned through discovery of the concepts, with process rather than the completion of a checklist of covered facts the goal, struck a chord with me. They back up this philosophy with many anecdotes; the book has a very personal tone to it. As the Kaplans state in the book, the quote that best summarizes their philosophy is: “What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.” (G. C. Lichtenberg, 18th century German scientist)As a math graduate student (admittedly, not at an upper echelon school) and teaching assistant, I could relate much of what they said to my own learning and teaching experiences. Particularly in grad school, I have found that most of my authentic mathematics learning has taken place when I have played around with concepts, challenging myself to understand how mathematical structures work from their roots, rather than being told by an instructor that such and such is true. At its best, direct instruction simply states and proves and does not motivate and/or allow for exploration of the ideas to arrive at the conclusions. At its worst (not in graduate school, where proof is king), it merely states. But discovery learning, in my opinion, is better than even the best direct instruction can be. Throughout much of the book, the Kaplans don’t address certain difficulties such as rigid curriculum and time restrictions that I thought would make their ideas unimplementable into a typical classroom setting. But they point out in the last chapter that even under these conditions, the Math Circle approach can work. In the first two or three weeks of such a course, the class may be behind the syllabus, but because students will have internalized the “why” rather than the “what” of the concepts during this time, the instructor can pick up the pace after that, and students will be more engaged with the course.Another important component of the Kaplans’ approach is its collegial nature. Many times society views academics as a competition. This prevents students from combining their individual ideas into a stronger collective knowledge. It also discourages the more timid from participating in discussion, for fear of appearing ignorant. (This latter fact applies to me growing up. The reality that I’ve found is that there is no shame in not knowing something and bringing forth one’s ignorance helps others strengthen their knowledge by having to explain it, or reveals that they were taking certain things for granted without having justified them in their mind. Or, just as often, it reveals that many other people have the same gaps of knowledge or understanding and are also afraid to admit it.) It should be noted that this collegial setting does not inhibit the development of the individual; each person feels free to express their own take on the problem at hand.I will definitely be trying to implement the Math Circle philosophy into my future teaching.

⭐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.UPDATE: Recently the Kaplans lectured to leading teachers and educators at conferences by the American Mathematical Society and Mathematical Association of America. Let’s hope this momentum continues among the important institutions laying the educational infrastructure.FULL DISCLOSURE: I have two boys, aged 8 and 6, who have attended the Kaplans’ Math Circle classes for the last two years. My wife and I were careful to make sure that our boys were excited enough about the classes to trade off among other activities they love like soccer, art and gladiator battles. The boys re-register each semester and we are continually impressed with the Math Circle’s ability to create an environment where the children explore more complex math than I ever thought possible. Math as Play. I’m a convert.

⭐This has the same attributes of a mystery novel, you just have to get to the next page, very informative and lots of fun.

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