from The Textbook Letter, September-October 2000

Reviewing a mathematics textbook

Glencoe Pre-Algebra
An Integrated Transition to Algebra & Geometry
2001. 843 pages. ISBN of the student's edition: 0-07-8228873-5.
Glencoe/McGraw-Hill, 8787 Orion Place, Columbus, Ohio 43240.
(Glencoe/McGraw-Hill is a unit of The McGraw-Hill Companies.)

Less Is Better -- but It Still Isn't Good

Tom VanCourt

Fuzzy math (which is known by several other names as well, including "new new math," "maybe math," "rain-forest math" and "math appreciation") is the replacement for the disastrous "new math" fad of the 1960s and 1970s. New math was a collection of corrupted factoids drawn from real mathematical disciplines, such as set theory and number theory. Fuzzy math is a corruption of notions drawn from pop culture and especially from pop psychology. . . To the extent that [devotees of fuzzy math] concern themselves with math lessons, they emphasize such things as "interactive learning" and making students work on "open-ended" problems. . . . .
It is easy to recognize fuzzy-math textbooks. They fairly glow with racial awareness and political correctness, as manifested in frequent, self-conscious, irrelevant references to blacks, women and other members of Victim groups. The books also display a vivid, though sometimes confused, awareness of health issues and environmental issues, and they have swarms of bright-colored pictures that bear little relation, or no relation at all, to the text.

           from my review of the 1997 version of Glencoe Pre-Algebra

Glencoe Pre-Algebra, 2001, is the most recent incarnation of a book that I have reviewed twice before, in its 1997 and 1999 versions.

The 1997 was a confused and confusing tribute to fuzzy math. It had 843 pages, and it had an abundance of pointless pictures and inane anecdotes and politically correct sidebars, but it didn't have much to do with mathematics [see note 1, below]. The 1999 version was an 843-page mimic of the 1997, though Glencoe had attempted to make the 1999 look different and trendy by embellishing it with some "interNET CONNECTION" activities. These activities were poorly conceived and unworkable, and they merely functioned as a new class of distractions to ensnare and befuddle students [note 2].

As I plowed through the 1999 version, I reckoned that simply having less of it would be an improvement. The 2001 version suggests that the same thought occurred to someone at Glencoe. Glencoe Pre-Algebra still has 843 pages, but some of the meaningless decorations and gimmicks that were in the 1999 book have been removed, and certain items of false "information" that appeared in the 1999 have been excised. These alterations are worth noting, even though they have not sufficed to turn Glencoe Pre-Algebra into an acceptable text.

Constructive Omission

The 1999 version's most visible failing was the frenetic design of its pages. Nearly every page had at least one illustration or boxed article to divert students from the subject at hand, and many of the pages had more than one. Now Glencoe has removed at least 175 pictures (most of which have simply been replaced by whitespace) without causing any loss of anything that might have had any instructional value.

The chapter-opening spreads have been improved too. In the 1999 book, there was a splashy, pointless spread at the start of every chapter, offering (for example) a history of junk food, an array of factoids about fitness, or a burst of advertising for jeans manufactured by Levi Strauss & Co. [note 3]  In the 2001, the opening spreads have been overhauled and the entertainments for adolescents have been discarded. Now a typical spread has a description of some problem that students will learn to handle as they study the chapter, along with a list of "Prerequisite Skills" that the students need to have acquired from earlier chapters.

In the 1999 version, the chapters ended with "Alternative Assessment" sections that typically combined dumbed-down make-work with cheerful motivational messages -- messages like "Use the talents that you possess, for the trees would be silent if no birds sang but the best." The 2001 version has "Alternative Assessment" sections too, but without the fatuous sermonettes.

Glencoe also has thrown out some (but not all) of the irrelevant sidebars that I saw in the 1999 book -- and by removing those sidebars, Glencoe also has removed some of the most egregious factual misconceptions that disgraced the 1999. The 2001 version doesn't lead students to imagine that whales are fishes, or that cyanide isn't an important pollutant, or that ethanol won't mix with water, or that chemical reactions between dissimilar metals occur only in living systems.

Most of the other differences between the two versions are small but welcome. For example: The 1999 version wrongly stated that the tennis-player Venus Williams was 15 years old, but the 2001 book says only that she is a superstar in the world of tennis [note 4]. And a problem involving a bicycle racer has been rewritten to feature Lance Armstrong instead of Miguel Indurain (who enjoyed his heyday in the early 1990s). More significantly, Glencoe has excised many of the proprietary names of products or organizations that appeared in the 1999 version. The advertising for Levi Strauss & Co. is gone, and such product-names as Scrabble and Reebok have been deleted from problems. Glencoe clearly has changed its policy regarding the use of commercial names, and I think this change is important. A textbook shouldn't promote products as if it were a magazine for teens.

Much More to Do

The changes that I've cited have made Glencoe Pre-Algebra better, but making it better hasn't made it good. Glencoe Pre-Algebra still presents a mad whirl of poorly connected topics, still flaunts distracting pictures and activities by the score, still suffers from severe defects in its organization and its attempts to deal with mathematical ideas, and still makes us wonder how anyone might learn any math from its pages. Moreover, it still challenges us to identify its intended audience. Using infantile toys to "model" the addition of integers isn't just ponderous -- in a pre-algebra context, it seems ridiculous. If students don't yet know how to add integers, why are those students trying to take a pre-algebra course?

Glencoe Pre-Algebra is still sloppy, too. It still contains, in its narrative text and in its sets of problems, too many items that are incomprehensible or simply wrong. I am glad to know that Glencoe's editors have rectified the matter of Venus Williams's age, but I am distressed to see the many things that they have not rectified. For example, the Chinese-calendar problem on page 173 still cannot be solved with the facts given. The name of the Rivest-Shamir-Adleman algorithm still is misspelled (page 186). The ex-senator Carol Moseley-Braun (with her name misspelled) still is depicted as a member of the Senate, intent on seeking re-election (page 204). Glencoe's writers still are claiming that memorizing the value of pi is an example of deductive reasoning (page 255), and they still are teaching the false concept that a woman's weight should be a linear function of her height (page 429). Their misleading account of the history of metric measurement is still is in place (page 358), as is their defective material about fractals (page 618).

The 1999 version explicitly required students to use the Texas Instruments TI-82 graphing calculator, which was obsolete and hard to find. The 2001 version doesn't prescribe any particular model of calculator -- but (like the 1999 version) it dictates specific sequences of keystrokes which, if executed by rote, will supposedly enable students to use their calculators to get specific results. Glencoe evidently assumes that all graphing calculators have identical keyboards and function identically. In any case, students who merely follow unexplained instructions for pressing keys will not learn anything about math or even about how calculators work. Worse, Glencoe still portrays automated calculation as an infallible font of truth. Glencoe still fails to explain that calculator-users may make mistakes during the keying of data, and that the result of every calculation must therefore be checked.

Glencoe Pre-Algebra is still a manual of fuzz, even if the fuzz has been thinned in some places. Glencoe's writers and editors have much more work to do before Glencoe Pre-Algebra can become a respectable textbook of mathematics.


  1. See "Glencoe's Manual of Fuzz" in TTL, May-June 1999. [return to text]

  2. See "This Schoolbook Is Stuck in Time" in TTL, September-October 1999. [return to text]

  3. See "Keeping an Eye on the Scams, Shams and Swindles" in TTL, July-August 1999. [return to text]

  4. The claim that Venus Williams was 15 years old had appeared in the 1997 version too! (Venus Williams was born on 17 June 1980. In June 1997 her age was 17, and in June 1999 her age was 19.) [return to text]

Tom VanCourt teaches software engineering and design at Boston University's Metropolitan College. His interest in precollege mathematics textbooks originated from his work with a charitable organization that creates audiotapes of schoolbooks, for use by blind or dyslexic students. He lives in Charlestown, Massachusetts.


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