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.

MAA Review of Beyond the Quadratic Formula

Mark Hunacek reviews Beyond the Quadratic Formula by Ron Irving as part of MAA Reviews.

"Combining mathematics and history, this text tells, in a way accessible to beginning students, the interesting story of how formulas came to be discovered for the roots of third and fourth degree polynomials, and why nobody will discover corresponding formulas for fifth (or higher) degree polynomials.

Specifically, the book begins with an introductory chapter on polynomials (treated informally as formal expressions rather than rigorously defined), and is followed by a chapter on quadratic equations, in which the familiar quadratic formula is derived from several different points of view. The study of cubic equations begins in the next chapter, which discusses Cardano’s formula. One of the more amusing aspects of Cardano’s formula is that even nice, simple numbers can wind up being represented by horrendous sums of cube roots of expressions involving square roots; lots of examples are provided in the book. "

Read the full review here.

To purchase the book, visit the MAA Store or the MAA eBooks Store.

MAA Review of Learning Modern Algebra

Mark Hunacek reviews Learning Modern Algebra by Al Cuoco and Joseph J. Rotman as part of MAA Reviews. This is an interesting, well-written book, in search of an appropriate course in which it could be used as a text. From the title, one would think that it was intended primarily as a text for an introductory abstract algebra course, but using it that way would require a fairly radical overhaul of the traditional syllabus of such a course. This is intentional: the authors make clear in the Preface to the book that they believe that this traditional syllabus (namely number theory, followed by groups and then rings) to be not only “totally inadequate for future teachers of high school mathematics” but also “unsatisfying for other mathematics students” as well. They propose that abstract algebra should be taught in two semesters: number theory and rings in the first, groups and linear algebra in the second. Even for such a course, however, this book would likely not be appropriate for both semesters; it covers a lot of number theory and ring theory, but very little group theory and linear algebra. (More about the specific contents later.) The primary intended audience of the book is future high school teachers. The authors take great pains to relate the material covered here to subjects that are taught in high school mathematics classes. And not just high school algebra classes: there is, for example, a fairly lengthy and quite detailed section on straightedge and compass constructions, including statements and (at least partial, and often full) proofs of many sophisticated results regarding impossible constructions. Read the full review here. To order your copy today, visit the MAA Store or the MAA eBooks Store.

Debbie Gochenaur Reviews Uncommon Mathematical Excursions

Debbie Gochenaur reviews Uncommon Mathematical Excursions: Polynomia and Related Realms by Dan Kalman as part of MAA Reviews. Offering an assortment of topics in the algebra, geometry, and calculus curricula, this book is intended as an enrichment for those familiar with these topics at the upper-secondary or introductory college math level. While the book may be geared especially for teachers who have taught their courses enough times to be thoroughly comfortable with the content, advanced students, as well as scientists and mathematicians in general, may find topics within this book intriguing. It has the potential to appeal to a broad audience. The book is meant to guide the readers in exploring ideas that are related to his/her core mathematical knowledge. The book is divided into three parts — The Province of Polynomia, Maxiministan, and The Calculusian Republic. Kalman ensures that the reader can make connections to known undergraduate mathematics and advanced secondary topics in the algebra, geometry, and calculus domains; he works to help the reader make extensions and perhaps understand more clearly the depth of mathematics in these seemingly elementary topics. Overall, the reader may be surprised by aspects of a particular topic that will lead to a greater understanding and appreciation for the mathematics. Read the full review here. Purchase your copy in the MAA Store.