### Book review: Precalculus, 5e, by Barnett/Ziegler/Byleen

Over at Learning Curves, Rudbeckia Hirta had some thoughts about matching a textbook to a course. Our discussion there led me to write a review of the Terrible, Horrible, No Good, Very Bad precalculus text I’m using. (Incidentally, I’ve really warmed up to the finite math text I whined about earlier. It’s not perfect, but it’s clear, well-motivated, and *possible to work with*. Which is more than I can say about the precalc book:)

The product description boasts that “[t]he Barnett, Ziegler, Byleen College Algebra/Precalculus series is designed to be user friendly and to maximize student comprehension.” It should have been sent back to the editors before publication, because *Precalculus* is anything but.

Among the various and sundry flaws with this text:

- The fluctuating emphasis on word problems is bizarre: in the very first section (”Linear Equations and Applications”) the book launches into a barrage of word problems (geometry, number theory, quantity-rate-time, distance-rate-time, chemistry, and more), as though students have the basic skills and the experience to grapple with this huge mass of content. From there, it moves on to the more basic skills of solving linear inequalities, and factoring quadratics. There are some word problems, but gone is the all-applications-all-the-time approach in favour of developing underlying concepts. In addition, the book’s claim that “the worked examples are followed by matched problems that reinforce the concept that is being taught” is actually a flaw: students who learn from this text, learn to solve word problems by pattern-matching. Presented with a slightly different problem that draws upon skills they have picked up, they are lost.
- The ordering of the content is seemingly random. for example: in Chapter 1, students are presented with a slew of opportunities to express this quantity in terms of that one. Six sections later, in Chapter 2, they learn what a function is (ie, it’s an expression of one quantity in terms of another), and from there they have several opportunities to…express one quantity in terms of another. Some of the exercises in Chapter 2 are virtually identical in content to some of the exercises in Chapter 1 - for instance, students are asked to find break-even points of cost functions in both chapters. Most perplexing choice of ordering: students are taught to find equations of, and graph, circles in Section 2-1, one section before they’re taught to find equations of,and graph, straight lines. One section later we arrive at the “Functions” unit, followed by…”Graphing Functions”.
- This book would be around 200 pages shorter if it omitted all of the graphing calculator applications, which it should. There are questions asking students to describe the shape, or find the range, of a function by plotting it on a graphing calulator. As a pedagogical exercise, this is useless. It’s also counterproductive from the perspective of instructors faced with the unenviable task of teaching students to graph functions and find their ranges algebraically. Although the emphasis of a precalculus class should not be overly theoretical, students should come out of it with some notion of what sorts of operations are mathematically and logically sound. Finding the range of a function by plotting it on a calculator is not, while completing the square of a quadratic and analyzing it is. The book presents these two methods on equal footing.
- Speaking of graphing functions: the book pays some lip service to graphing functions by applying transformations - for instance, students should know what the graph of y=x^2 looks like, and from there they can apply transformations in order to graph y=-2(x-4)^2+3. But soon it abandons this approach, and graphing functions pointwise becomes the method of choice.
- The book description claims an emphasis on computational skills over theory. Indeed, it de-emphasizes theory to the point of presenting content as a series of disjoint rules. The “here’s a word problem, here’s the formula you need for it, now do two just like it” approach is one example, but it’s in the third chapter that the authors’ contempt for mathematical justification really comes through. That section (on polynomials) is awash with a dozen methods of estimating bounds of zeroes of function by using synthetic division. Synthetic division itself is presented without proof, and the applications are all given as formulas without any justification. Later, in chapter 4, we get eight rules of logarithms without a lick of explanation. Contrary to its goal of emphasizing problem solving by opting not to muddy the waters with theory, this approach leaves students with so little grasp of the underlying content that they can’t solve any problems beyond the exact ones presented in the text.

These are just some of the problems with Chapters 1-4; I haven’t taught the second-semester course, which uses Chapters 5-8. The book fails by all standards: it falls far short of its own goals of creating a usable text, it fails by the standards of every instructor I know who has used it, and it fails the students who use it. I have taught a variety of first-year college math classes, and never have I found a textbook so difficult to work from. Every attempt to instill some theoretical comprehension is undermined by the scattered, calculator-dependent approach of the text. My students agree: I’ve had several tell me that they have never had such an unreadable text. I’d advise math departments to search around for a twenty-year-old college algebra text that’s still in print, and use it. (If they can’t, they should write to the publisher of such a text for permission to copy it.) Older texts omit the calculator mumbo-jumbo and insist are designed to instill mastery of a rudimentary set of skills, rather than memorization of a handful of formulas - and that’s the best way to prepare future calculus students.