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Mathsemantics: Making Numbers Talk Sense [Paperback]

Edward MacNeal
4.7 out of 5 stars  See all reviews (7 customer reviews)

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Book Description

March 1 1995
Entertaining, anecdotal, and immensely practical, this book demonstrates that math can't be divorced from meaning, that numbers have inherent semantic content that makes them much easier to handle. A sensible and novel solution to the math block that afflicts our society today.

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From Publishers Weekly

What is the sum of two apples and three oranges? (Answer: five fruit). Round off .098 to the nearest whole number. (Answer: zero). These math problems, and the inability of many people to solve them, reflect semantic presumptions embedded in our language, according to MacNeal, a business consultant to the airline industry. In this anecdotal, sporadically illuminating book, he deflates dubious statistics, exposes pitfalls in surveys, punches holes in accountants' reports and offers advice to math teachers. MacNeal pinpoints mathematical or logical errors commonly made by travelers, market analysts, students and others--errors that he believes may be due to the adult's retention of the child's tendency to confuse words with the things that words represent. Appendices include problems as well as recruitment quizzes for secretaries, clerical workers and lawyers.
Copyright 1994 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

From Library Journal

Books like John Paulos's Innumeracy ( LJ 5/1/89) have demonstrated that many people don't understand numbers. MacNeal asks "why not?" and comes up with fascinating and helpful insights. He believes the problem is not so much an inability to do calculations as a semantic problem of naming the things you count. Thus, adding two apples and five oranges you get seven pieces of fruit, refuting the claim that "you can't add apples and oranges." Evidence from Jean Piaget's studies of children's language and from a math quiz that was given to job applicants at MacNeal's consulting business show how semantic mistakes lead to numerical errors (and also why people have so much difficulty solving story problems). This sounds very academic, but it's written in a friendly, personal style and offers eye-opening, practical advice on how to communicate numerically. A good antidote to innumeracy.
- Amy Brunvand, Fort Lewis Coll. Lib., Durango, Col.
Copyright 1994 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

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Most helpful customer reviews
5.0 out of 5 stars Educational and Entertaining. July 15 2001
By Phil
Format:Paperback
MacNeal makes a strong case that a proper understanding of mathematics requires thinking skills that our schools have not yet even identified. The author fills this book with examples of basic mistakes that "educated" people often make when using or even talking about numbers.
MacNeal argues convincingly that using mathematics properly goes far beyond being able to manipulate numbers. Mathematics is a language that helps us understand the real world. Divorcing this language from spoken languages, such as English, fails to teach students how to use and think about issues that relate to mathematics. (And that certainly includes a multitude of topics!)
"Mathsemantics" also provides a practical method of learning to make estimates. The author provides many examples of how to use information that we do have to make reasonable estimates regarding information that is unavaialable to us.
If I were a high school or college instructor...of almost any subject...I would (easily) find a way to make "Mathsemantics" required, relevant reading. This book provides so much more value than most of the "best-selling" books that you will read and hear about.
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Format:Hardcover
Review: Edward MacNeal Mathsemantics: Making Numbers Talk Sense Penguin; 1994 ISBN 0 14 023486 1 (24 chapters, Tests, References and Index!; 310 pages)
[From Prime Number (Mathematical Assocation of Victoria, Brunswick, Victoria, Australia) vol. 11, no. 2, 1996, p. 13)
Mathsemantics, like John Allen Paulos's stimulating Innumeracy (Penguin, 1988, about dealing comfortably with fundamental notions of number and chance), is easy to read, challenging, fascinating, and might change the way you teach and the way you think about teaching. Edward MacNeal discusses the connection between mathematics and the purpose and meaning of mathematics. According to MacNeal, many students experience difficulty because of confusion between formal mathematics and what the mathematics means, between the written symbols and the translated prose and the ideas they both represent. These examples of similar words have dramatically different mathematical meanings: "5 less than 10" is 5, while "5 less 10" is -5; "6 divided by 2" is 3, whereas "6 divided into 2" is one-third, yet "6 divided into 2 equal parts" is in fact 3 (pp 89 - 90). To resolve such confusion we need "mathsemantics" to make mathematics meaningful, and show how language can work mathematically.
MacNeal's discussion arises from the results of test questions uses to screen adult job-applicants on the basis of their ability to use mathematics and to think about what they are doing.
MacNeal describes three vivid lessons. When he was about six years old, his accountant father challenged MacNeal and his brother to write whole numbers in sequence: 1, 2, 3, 4, ..., offering a dollar for each number that had only a 1 following by zeros.
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By A Customer
Format:Hardcover
This book is a treat for anyone interested in math, words, analysis, and problem solving. Analysis is an art, and the author shows how numbers and words can present or hide the problem.
The author builds the book around a set of problems he collected or invented over 20 years to help him hire people to work in his business. The problems turn out to be arenas where common sense does battle with dumb rules ("you can't add apples and oranges") and the art of definition (a passenger, a trip, a ticket, a traveler, and an airplane seat are different entities).
This is also a funny book! The problems are interesting and concrete. The book is structured, too, so the reader easily gets a chance to hack away at the problem, and also see how other folks have done solving the problem over the last 20 years. (The explantions some folks give to explain their answers are sometimes screamingly funny, but always interesting.)
This book is a fun read. It would also make a great companion text in a high school or college math or analysis course.
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5.0 out of 5 stars Common Sense on an Uncommon Topic Oct. 29 2003
Format:Hardcover
The author is "an expert" - someone who knows something and can explain it to and/or use it for those who can't - or just don't - on their own.
I am a high school math teacher and community college and high school computer teacher. MacNeal THRILLED me with his insight into something that may be part of the problem with education the way we do it. Look for his connection of Piaget's work on the development of children's and adults' abilities through necessary stages with the Chinese language and with the teaching of math.
I have had more successes with some of my students because of MacNeal and his book.
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