Calculus by and for Young People (Ages 7, Yes 7 and Up) [Spiral-bound]

Donald Cohen (Author)

Book Description

ISBN-10: 096216741X | ISBN-13: 978-0962167416 | Publication Date: March 1989 | Edition: Revised

This book is a description of how young people, Don and some mathematicians, solved problems which involve infinite series, infinite sequences, functions, graphs, algebra, +, - important mathematical ideas. At the same time they do a lot of arithmetic, and use pineapples, the tower puzzle, with science to math activities, and the use of other hands-on materials.

Editorial Reviews

Review

".. But the main attractiveness (of Don's book) is due to an explicit philosophy that children are capable of behaving as mathematicians. ..Somehow we reach an almost formal treatment of integration and differentiation without an integral sign or a dy/dx. But on the way we have been presented with a variety of very accessible problems. .."

-- reviewed by David Fielker in the Sept. '92 Mathematics Teaching (England)

"..many fresh and revealing insights.. a very handy resource.." -- July '93 Undergraduate Mathematics Education Trends, a newsletter of the MAA and AMS

"Trying to divide six cookies fairly among seven people? Third-grader Brad had the right idea: cut each one in half, share out as many as you can; again halve the pieces not shared until there are pieces enough to share, and continue. He quit at sixteenths, amidst lots of crumbs. But he could see that everyone got 1/2 + 1/4 + 0/8 + 1/16 + 1/32 + 0/64 +...of a cookie. The sum is not hard to express in terms of more familiar series, once you notice that the missing portion of unity is itself a geometric series for 1/ (1- (1/8)). Iteration is more powerful and more intuitive than dividing a round cookie into seven equal parts.

This spiral-bound book the size of your hand reports with infectious enthusiasm the work of many beginners in one fine teacher's class over the decades, some of them highly gifted kids and some of them grown-ups with no particular mathematical bent. All were on their way to an understanding of slope and integral, natural logarithm and exponential. En route a good many famous problems were encountered, among them the proof of the snaillike divergence of the harmonic series (its first million terms add up to about 14.4, a sum given here to a dozen decimals), the Fibonacci sequence in pineapples and that glorious relation among, e, i, pi, 0 and 1.

The crossings between recreational mathematics, modern calculators and the track of such pioneers as Newton and Euler make this breezy and personal account, more notebook than book, good fun for the mathematically inclined young person and helpful for any adults who seek freer and solid arithmetic teaching". -- Phylis and Philip Morrison, Scientific American, Dec. 1988

From the Publisher

TOC: Chapter 1: 7 Year-Olds do Chapter 2: Brad's: Share 6 Cookies With 7 People Chapter 3: Ian's Proof : Infinity = -1 Chapter 4: The Snowflake curve--Its Area and perimeter Chapter 5: The Harmonic Series Chapter 6: On Thin Spaghetti and Nocturnal Animals (functions and graphs) Chapter 7: The Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean Chapter 8: Solving Equations and Iteration Chapter 9: The Binomial Expansion and Infinite Series Chapter 10: Pi and Square Roots Chapter 11: Compound Interest to e and i Chapter 12: The Two Problems of the Calculus Chapter 13: Area Under Curves--The Integral Chapter 14: Slopes and The Derivative Bibliography

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Product Details

• Spiral-bound: 179 pages
• Publisher: Don Cohen; Revised edition (March 1989)
• Language: English
• ISBN-10: 096216741X
• ISBN-13: 978-0962167416
• Product Dimensions: 5.3 x 3.8 x 0.5 inches
• Shipping Weight: 5.6 ounces
• Average Customer Review: 3.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,839,253 in Books (See Top 100 in Books)

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30 of 31 people found the following review helpful:

5.0 out of 5 stars Calculus isn't beyond the reach of the average kid!, August 4, 2001

By 

Kimbo "Kimbo" - See all my reviews

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This review is from: Calculus by and for Young People (Ages 7, Yes 7 and Up) (Spiral-bound)

This is an outstanding book because it takes the mumbo-jumbo out of traditionally taught calculus and makes the ideas accessible to ANYONE, not just to math whizzes. The technical vocabulary and symbolic notation can always be learned later. This book introduces the important ideas of calculus with simple, natural language and, most helpful of all, illuminating graphics, so the beauty (yes, beauty) and fun of calculus comes through. I would recommend this book to anyone who is teaching children, and also to math phobics. (I am the former, and was the latter for many years.) This book is FUN, and it makes calculus FUN!

53 of 61 people found the following review helpful:

2.0 out of 5 stars This book is too small for the price, May 18, 1999

By A Customer

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This review is from: Calculus by and for Young People (Ages 7, Yes 7 and Up) (Spiral-bound)

Before you buy this book be aware that it measures [approximately] less than 3x5". However, Donald Cohen has some great ideas. It is true that you can easily introduce younger students to the type of thinking that will be necessary in precalculus and up. I think it is worth it to get the workbook, which covers most of the material presented in this book. But don't buy both.

4 of 4 people found the following review helpful:

4.0 out of 5 stars Examples of insightful solutions to math problems produced by very young children, February 26, 2008

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Calculus by and for Young People (Ages 7, Yes 7 and Up) (Spiral-bound)

This collection of calculus problems is not well organized in the sense that the order of presentation starts with the fundamentals that support work in calculus. The problems deal with infinite series, the Koch Snowflake curve, Fibonacci numbers and the golden mean, continued fractions, compound interest, area under curves and derivatives. By themselves, the problems covered are not unique or even that hard.
What distinguishes this book is that the author presents solution methods generated by children as young as 7. The solutions are not "lucky guesses"; they are the consequence of significant mathematical insight. Cohen is the co-founder of "The Math Program" an initiative where teachers are available to give private math lessons to young children. This book can be considered a report describing their success.
Mathematics is an area where insight is often superior to grinding work. In this book Cohen describes many instances where a young child had a leap of insight that led to the successful solution to a problem. It should be a reminder to math teachers that not all students think the same way and sometimes a nonstandard solution demonstrates significant mathematical ability.