Reviewing a mathematics textbook

Glencoe Pre-Algebra
An Integrated Transition to Algebra & Geometry
1999. 843 pages. ISBN of the student's edition: 0-02-833240-7.
Glencoe/McGraw-Hill, 936 Eastwind Drive, Westerville, Ohio 43081.
(Glencoe/McGraw-Hill is a division of the McGraw-Hill Companies.)

This Schoolbook Is Stuck in Time

Tom VanCourt

In fuzzy-math courses, students learn little about the established principles of mathematics, or about rigorous mathematical reasoning, or about the classic theorems and proofs that, over the centuries, have made mathematics what it is today. Indeed, the promoters of fuzzy math discount the mathematical knowledge that humanity has accumulated over the centuries, and they insist that students must reinvent what we already know. The students are supposed to do this by engaging in quasimathematical pastimes, by performing mindless drills with calculators, and by reading irrelevant material that promotes a sociopolitical ideology derived from multi-culti, environmentalism and radical feminism.

All those follies of fuzzy math were conspicuous in the 1997 Glencoe Pre-Algebra -- a confused, confusing book that swarmed with irrelevant pictures, pointless anecdotes, politically correct sidebars, and ideological inanities. After reading that 1997 book, I was left wondering how anyone could learn any math from it [see note 1, below].

The 1999 version of Glencoe Pre-Algebra is no better. I have compared the two versions side-by-side, and I have found very few differences between them. Glencoe has reprinted all the old errors and contradictions that I described in my review of the 1997 book, as well as the irrelevant stories, the racial fancies, and the other inanities. Indeed, Glencoe Pre-Algebra is stuck in time:

• On page 6 of the 1999 book, we find Glencoe's claim that the athlete Venus Williams is 15 years old -- the same claim that appeared two years ago in the 1997 version! Glencoe's wizards of fuzzy math seem not to understand that a person's age increases continually, at the rate of 1 year per year [note 2].

• On page 173 of the 1999 book, Glencoe repeats a problem that ostensibly deals with the Chinese lunar calendar, complete with the statement that "1998 is the Year of the Tiger." In 1997 that statement was wrong because 1998 hadn't arrived yet -- and now the statement is wrong because 1998 has slipped into the past. (This isn't all that's wrong: The Chinese-calendar problem still can't be solved, because Glencoe's writers have failed to provide the information that is needed for solving it.)

• On page 204 of the 1999 version, Glencoe has reprinted a racial-awareness item, slightly disguised as an arithmetic problem: "In the United States, presidents are elected every four years. Senators are elected every six years. In 1992, a presidential election year, Carol Moseley Braun of Illinois became the first African-American woman elected to the U.S. Senate. If she continues to run and win each time her term expires, when is [sic] the next presidential election year in which Senator Braun will run?" Carol Moseley-Braun (please note the correct spelling of her name) is no longer a United States senator. When she ran for re-election in 1998, she was defeated by Peter G. Fitzgerald.

• On page 273 Glencoe has reprinted a gaudy graph titled "Total Number of Computer Viruses," which shows some numbers for the years 1986 through 1994. The graph was obsolete when it appeared in the 1997 Glencoe Pre-Algebra, and now it is even more so.

• Pages 4 and 5: Glencoe's advertising for Levi's jeans is still in place and still begins with a fake "news" report, and Glencoe is still misrepresenting the fake report as an article from The Columbus Dispatch, a real newspaper that is published in Columbus, Ohio [note 3].

• Page 16 still carries a "Real-World Application" article which allegedly deals with the physiology of the human heart, and the article still is illustrated with a silly cartoon of a valentine heart, not with a picture of a real-world heart.

• Page 186 still has a worthless gee-whiz item about the cracking of the RSA 129 encryption key in 1994: The item still fails to explain RSA 129's historical importance and still fails to disclose that keys larger than 129 digits have been cracked since 1994, and Glencoe continues to misspell the name of the mathematician Adi Shamir. (The S in RSA stands for Shamir.)

• Page 255: Glencoe continues to claim that recalling the value of pi is "an example of deductive reasoning." The rote memorization of a number has nothing to do with reasoning.

• Page 376 still has an "Earth Watch" environmental sidebar that bears the trendy headline "Saving the Whales" -- and the sidebar still deals with fishes instead of whales.

• Page 429 still presents an exercise which teaches the erroneous notion that a woman's weight is directly proportional to her height.

• Page 518 still has an "Earth Watch" environmental sidebar that ignores reality. Glencoe's writers still are moaning about the use of cyanide in gold mining, and they still are guessing that the principal environmental hazard associated with the cyanide process is the liberation of "poisonous heavy metals such as lead, mercury, and arsenic." In fact, the principal hazard is the direct poisoning of water courses by the cyanide itself, which is fiercely toxic to plants, animals and all other aerobic organisms -- far more toxic than any metal is. Mines that employ the cyanide process generate cyanide-laden wastewater, and the wastewater typically is stored in man-made ponds behind low earthen dams. If one of these dams leaks or collapses and the escaping wastewater flows into nearby streams, the cyanide can annihilate entire populations of aquatic organisms and can kill any humans or livestock that drink from the poisoned streams. This is what happened in Guyana in August 1995, on a spectacular scale, when thousands of tons of wastewater from South America's largest gold mine leaked into the Essiquibo River. Apparently, Glencoe's writers still haven't heard about the Essiquibo disaster.

• The color scheme on the front cover has been revised, and the back cover is now green rather than red.

• The back cover now shows McGraw-Hill's logo and a note that identifies Glencoe as "A Division of The McGraw-Hill Companies."

• Page 436: In the 1997 book, page 436 had an "Earth Watch" environmental sidebar labeled "Tropical Rain Forests." That sidebar has now been replaced by one called "Keeping Watch Over the Oceans," in which Glencoe's writers babble about "substances that can threaten our oceans." They use ethyl alcohol as an example, and they pose this problem to the student: "A material that has a lower density will float on one that has a higher density. A 250-milliliter sample of seawater has a mass of 260 grams. Would a spill of ethyl alcohol float on seawater? Justify your answer." My own answer, which I can justify with a visit to any bar, is that the alcohol would dissolve: Ethyl alcohol is readily soluble in water.

• Page 446: In a sample problem that deals with proportions, an irrelevant picture has been replaced by a helpful note about estimating the correct answer to the problem. This is an improvement!

• Page 578: Another improvement is evident in a passage about "Similar Triangles and Indirect Measurement." When it appeared in the 1997 book, the passage included a section, headlined "Modeling with Manipulatives," which gave instructions for some puerile groping that involved toys ("manipulatives") called "geobands" and a "geoboard." Now that section has been eliminated, though the Glencoe writers haven't bothered to change the headline: It still says "Modeling with Manipulatives."

This may sound familiar. The "interNET CONNECTION" notes in the 1999 Glencoe Pre-Algebra are much like the ones that Max G. Rodel recently found in Glencoe's Chemistry: Concepts and Applications [note 4] and much like the ones that frustrated William J. Bennetta when he reviewed Glencoe's Biology: An Everyday Experience [note 5].

Every "interNET CONNECTION" note in Glencoe Pre-Algebra provides a new way for the reader to wander away from the topic at hand and to become lost among irrelevancies, as I learned during my own examination of Glencoe's Web offerings. For example:

On page 132 of the book, in the chapter "Solving One-Step Equations and Inequalities," an arithmetic problem involves the exchanging of currency: "Paloma's social studies class was planning an imaginary trip to Kenya. Paloma had to find out about the rate of exchange for money in Kenya. She learned that money in Kenya is based on shillings and that the current exchange rate was one U.S. dollar for 40 shillings. If one night at a hotel cost 960 shillings, how much would that be in U.S. dollars?" Adjacent to that problem is an "interNET CONNECTION" note: "For the latest exchange rates, visit: www.glencoe.com/sec/math/prealg/mathnet". I couldn't perceive that this would be of any use to a student, since the only exchange rate that the student needed to know was the rate stated in the problem (40:1), and there was no other exchange-rate problem in the rest of the chapter. But I followed Glencoe's directions anyway, and I inspected the prealg/mathnet page to see what a student would find there.

The prealg/mathnet page said nothing at all about exchange rates. The prealg/mathnet page was a menu that gave me a choice between items pertaining to Glencoe Pre-Algebra and items related to another book, Mathematics Connections: Integrated and Applied. I clicked to select the 1999 Glencoe Pre-Algebra, and I got another menu. This one was obviously intended for use by teachers, not students, and it offered links to six bins of material: "Online Study Tools," "Chapter Introductions," "Investigations," "Data Updates," "Group Activities," "Classroom Vignettes." Because none of those six bins had been mentioned in the "interNET CONNECTION" note on page 132 of the textbook, I had to use trial-and-error to discover which bin might contain information about "the latest exchange rates."

It turned out to be the "Data Updates" bin. When I clicked on "Data Updates," I got a new menu that offered one link for each chapter in the book. The link for chapter 3 said: "Chapter 3 (page 132) Current exchange rates." I clicked on it, and I was transported to a commercial Web page titled "The Universal Currency Converter" -- but the converter wasn't universal enough to include the Kenyan shilling. To find a conversion rate for the Kenyan shilling, I had to follow a link from "The Universal Currency Converter" to another Web page.

If there was any relation between those Web maneuvers and "Solving One-Step Equations and Inequalities" -- the subject of chapter 3 in Glencoe Pre-Algebra -- it was too subtle for me to grasp.

Here are some other observations that I made as I followed Glencoe's "interNET CONNECTION" notes:

• The note on page 270 of Glencoe Pre-Algebra told me to go to the prealg/mathnet page for "current information on roller coasters." The prealg/mathnet page had no such information, but I eventually discovered that the "Investigations" bin contained an item called "Roller Coaster Math," which comprised links to three Web pages. The first link took me to a commercial page sponsored by E.I. du Pont de Nemours and Company, the corporation commonly known as DuPont. DuPont's page offered a sketch of the early history of roller coasters, apparently because DuPont markets an isocyanate compound that is used in making an intermediate product that is used in making a polyurethane resin that is used in making roller-coaster wheels. The page had no mathematical content at all. The second link took me to a page of commercial advertising for the Cedar Point amusement park in Ohio. This page had no mathematical content beyond the mentioning of the numbers 14, 24 and 240: I learned that roller coasters are called "scream machines," that Cedar Park offered "14 scream machines -- more than any other place on the planet," and that Cedar Point's Power Tower "blasts you 24 stories into the sky or rockets you toward Earth from 240 feet up!" And that was the end of the math. Glencoe's third link was "Amusement park physics." I had high hopes for that one -- but when I clicked, I got a page of fluffy "physics appreciation" stuff that didn't teach any real physics and didn't use any math. There wasn't an equation in sight. I clicked on a subsidiary link called "Roller Coaster," which took me to a page where there was no math and where the only hint of physics was the statement that "The conversion of potential energy to kinetic energy is what drives the roller coaster." Would readers of Glencoe Pre-Algebra know enough physics to understand that statement?

• On page 431 of Glencoe Pre-Algebra -- in the chapter "Ratio, Proportion, and Percent" -- an "interNET CONNECTION" note said that Glencoe's prealg/mathnet Web page would show "up-to-date information on dinosaurs." This wasn't true -- but in Glencoe's "Chapter Introductions" bin I saw a link titled "Chapter 9 (page 431) Dinosaur Research." When I clicked on that link, I got the home page of the Field Museum of Natural History (in Chicago), and I saw a brief item about Sue, a Tyrannosaurus rex fossil that has been embroiled in commercial and legal controversies. Nothing on the Field Museum's page had anything to do with "Ratio, Proportion, and Percent" or any other aspect of math. I guess dinosaurs are just so cool that Glencoe had to stick them into Glencoe Pre-Algebra somewhere, no matter how irrelevant they were.

• In the same chapter of Glencoe's book, on page 455, a note said that Glencoe's prealg/mathnet Web page had "the latest Nielsen ratings." These were obviously offered as mere entertainment, since nothing in the chapter required a student to use "the latest Nielsen ratings" in any way. There was nothing about any Nielsen ratings on the prealg/mathnet Web page, but I persevered, clicked my way through Glencoe's various bins, and found that the "Data Updates" bin had a link labeled "Chapter 9 (page 455) Nielsen Ratings." This link took me to a Web page that had subordinate links to pages dealing with the popularity of television shows. On the day when I tried to use them, some of the links were broken.

• In On page 483 of Glencoe Pre-Algebra, an "interNET CONNECTION" note alleged that Glencoe's prealg/mathnet page would deliver "current information on game design." It didn't, but I eventually found, in the "Investigations" bin, a list of three links under the heading "It's Only A Game." I was pleasantly surprised to find that the links took me to Web pages that really had something to do with the theory of games. Unfortunately, none of that theory applied to the witless games described in Glencoe Pre-Algebra, and one of the linked pages was so far beyond the grasp of teenagers in a pre-algebra course that it looked absurd: It was an academic article titled "An Outline of the History of Game Theory," written for scholars who could digest such phrases as "minimax mixed strategy equilibrium," "payoff vector," "Nash's bargaining solution" and Zur Theorie der Gesellschaftsspiele (the title of a paper published in 1928 by the mathematician John von Neumann).

Glencoe has done little for students by appending "interNET CONNECTION" notes and Web pages to an obsolete book that is stuck in time. These add-ons typically are irrelevant distractions -- and when I remember that access to the Internet is a limited resource in many schools, I find that the add-ons have inflicted a net loss on the book's value [note 6].

When I wrote about the 1997 version of Glencoe Pre-Algebra, I said that I disliked the book's exclusive reliance on the Texas Instruments model TI-82 calculator. Now I dislike it even more. The TI-82 is now quite obsolete -- but because Glencoe Pre-Algebra is stuck in time, the calculator exercises in the 1999 version of this book are the same TI-82 exercises that were in the 1997 version. In the real world, the TI-82 has been supplanted by the TI-83, which Texas Instruments introduced in 1996, and I no longer can find a TI-82 in any store. Store clerks have told me that the TI-83 works in much the same way as the TI-82, but I would rather have learned about this from Glencoe. Though Glencoe's writers and editors have had plenty of time to incorporate the TI-83 into Glencoe Pre-Algebra, they haven't done so.

I saw little reason to recommend the 1997 version of Glencoe Pre-Algebra, and I see no reason at all to recommend the 1999.

Notes

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

2. Even in 1997 Glencoe's statement about Williams's age was erroneous. See "Time Warp" in TTL, July-August 1999, page 11. [return to text]

3. See "Keeping an Eye on the Scams, Shams and Swindles" in TTL, July-August 1999, page 13. [return to text]

4. See the review " 'interNET' Gimcracks in an Old, Dumb Book" in TTL, July-August 1999, page 1. [return to text]

5. See the review "Thirteen Dumbbells and an 'interNET' Too!" in TTL, July-August 1999, page 9. [return to text]

6. I can't say, of course, whether Glencoe has changed any of its Web pages since the day when I looked at them. [return to text]

Tom VanCourt is a software engineer. His review in this issue originated from his work with a charitable organization that makes audiotapes of textbooks, for use by blind or dyslexic students. He lives in Charlestown, Massachusetts.

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