MAA Books Beat: Stories at the Heart of Teaching

Written by Steve Kennedy, MAA Acquisitions Editor, Stories at the Heart of Teaching appears in the October/November 2014 issue of MAA FOCUS.


Steve Willoughby taught mathematics for 59 years at every level from elementary school to graduate school. He is a keen and perceptive observer and a witty and talented storyteller. And, man, after 59 years does he have some stories to tell in Textbooks, Testing, Training: How We Discourage Thinking. 

From a fourth-grade book on a page titled “Divided By 6”:

Twelve turkeys. Six turkeys in each cage. How many cages?

There was a picture on the page with the right number of cages so that exactly six turkeys could be, and were, placed into each with no leftover turkeys. The teachers’ guide directed that any student who wrote the answer without writing “12 ÷ 6 = 2” was to be marked wrong. Fortunately, because of the title at the top of the page and four years of intensive schooling, no child would have an urge to read the problem. There are two numbers. One is 6. Certainly 12 must be divided by 6 and the problem is solved to the satisfaction of all concerned without a single thought passing through the head of anyone involved or of any child making the heinous error of counting the cages depicted.

Did the authors really suppose that if somebody wanted to know how many cages there were, he would count the turkeys, count how many are in each cage, and, upon discovering the unlikely fact that the same number were in each cage, would divide the first number by the second?

Tom Sinclair Reviews Textbooks, Testing, Training: How We Discourage Thinking

Tom Sinclair reviewed Textbook, Testing, Training: How we Discourage Thinking by Stephen S. Willoughby as part of MAA Reviews.

"This short book recounts many specific true stories from my fifty-nine years of teaching that I believe cast some light on what is wrong with American education and perhaps some clues as to what might improve it." (p. 1)

This is an incisive yet readable critique of the American education system. Willoughby writes from the perspective of six decades of experience. He knows that the best way to persuade someone is to tell them a story. The author illustrates his points with anecdotes from his own experience and those of his colleagues.

Two things surprised me about this book. First, Willoughby's writing captures the teaching experience to perfection. I often found myself nodding with familiarity as I read. The second surprise is the humor. Willoughby writes with a dry, ironic sensibility that remains warm and inviting. Even when describing his frustrations he never descends into cynicism.

Willoughby breaks down the problem with our education system into three broad categories. Doing education right is a complex problem with a complex solution. He presents ways that we teachers can be part of that solution.

Read the full review here.

New eBook: Textbooks, Testing, Training: How We Discourage Thinking

Textbooks, Testing, Training: How We Discourage Thinking

by Stephen S. Willoughby

Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature.

— James Tattersall, Providence College

Steven S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him, some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Steve has strong, cogent and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Steve's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book.

Order your copy today in the MAA eBooks Store.

(PDF: $11.00,  POD: $18.00)

Annie Selden Reviews Distilling Ideas

Annie Selden reviews Distilling Ideas: An Introduction to Mathematical Thinking by Brian P. Katz and Michael Starbird as part of MAA Reviews. 

The authors of this book, as they explain in their first chapter, are taking readers/students on a journey — one that will “add new, powerful inquiry skills” to a student’s repertoire: abstraction, exploration, conjecture, justification, application, and extension. The book is clearly intended for inquiry-based mathematics courses. It is replete with explorations to undertake, definitions to explore, and theorems to prove, but there are no sample proofs or answers.

The book has five chapters, with the middle three chapters on graphs, groups, and ε-δ calculus constituting the bulk of the book. To me, it is clear that any one of these middle chapters by itself has the potential to be used for an entire one-semester course. There is really enough material in the ε-δ calculus chapter for an introductory junior level real analysis course. Similarly, the group theory chapter gets to Sylow’s Theorem and has more in it than most students could cover in one-semester when doing all the work themselves.

Read the full review here. 

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Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education.