Mathematics for Human Survival is a text with a mission, and the agenda is not hidden, but right up front. On page i, we are presented with the "Warning to Humanity," a document written in 1992 and signed by 1700 scientists, which sounds the alarm that human beings are on a "collision course" with the natural world. "If not checked, many of our current practices put at serious risk the future that we wish for human society and the plant and animal kingdoms, and may so alter the living world that it will be unable to sustain life in the manner that we know."
What has this got to do with the learning of mathematics? The book is written for young people who want to grow up in "a world of peace, where all types of people live together in harmony, or at least in tolerance" (p. v). Claiming that "we all need to be able to read mathematics in context, sort out what the numbers mean, and draw conclusions," (p. vi) the goal of the author is to help prepare students to do just this, read and become comfortable applying mathematics in their professions and in their decision-making processes as citizens of the world. Professor Kenschaft, who knows "that joyful survival is possible despite dismal prospects," also hopes that the exercises and mathematical concepts learned in the book will prod readers to "reconsider financial and lifestyle choices" (p. vi) and ultimately help us to heed the warning and survive and live sustainably on this lovely planet we call home.
Before I comment on the soul of the book, a few words on the body. It consists of nine chapters, beginning with a section on understanding big numbers and moving on to cover basic descriptive statistics; exponential, linear and logistic growth patterns; and voting procedures. There is an appendix containing a "World Population Data Sheet" for the year 2000, used liberally in many of the exercises and examples. In my review copy, there was no index and no bibliography (the latter I assume will be included in the final edition, as there are abbreviated references throughout, which are incomplete without such a list of readings). The text would be appropriate for an introductory level college math course for students with minimal or weak high school skills (rounding, order of magnitude arguments, percentages, ratios and proportion are treated extensively). It might also work well for a general education quantitative literacy course or even, perhaps, an adult education refresher math course.
But the book is bound to be controversial. I can hear many of my colleagues protesting that "pure" mathematics should be (and indeed is) value-free, and that it is completely inappropriate to use a math text as a soapbox to advance a particular political agenda. I must admit that I personally found page one's "Warning to Humanity" a refreshing contrast to the first page of the numerical analysis text I chose for this semester, which begins: "For a simple example of a nonlinear equation, consider the problem of aiming a cannon to hit a target at distance d. The cannon is assumed to have muzzle velocity V0 and elevation θ. (G. W. Stewart, Afternotes on Numerical Analysis, SIAM, 1996, p. 3.) Dont get me wrong, I think Stewart is a terrific text, thats why I chose it, but I also think that our standard mainstream texts, purportedly value-free, are in fact "shot through" with implicit values and unexamined assumptions (about race, class, gender, economics, and politics, to name a few!) embedded in the word problems and examples. At least Pat Kenschaft makes her values and assumptions explicit.
However, what about students (and/or professors) who don't share the author's assumptions? Will they be alienated? Possibly. Is this reminiscent of texts that relied on exclusive use of the male pronoun and examples geared to boys' experiences, which discriminated against generations of girls and made them feel excluded from "relevant" mathematics? Somewhat, but there are a host of other texts available for those who don't like the examples in this one, whereas it is only recently that there are alternative texts with gender neutral and female-friendly examples included.
More important, does the book really succeed in promoting the critical thinking it sets out to stimulate? I am not sure it does. I would like to see the author apply the caveats from Chapter 8 (Collecting Data), where the reader is told that "the search for truth is essential, but slippery," (p. 291) to her own examples. For instance, in a typical exercise, a report is cited that claims that 25-year olds who smoke 1-9 cigarettes a day can be expected to live 4.6 years less than those who never smoked regularly, and then we are asked questions like "how many seconds of lifetime does each cigarette cost?" (p. 10) Call me picky, but I would prefer to see the question phrased: If the results of this study are accurate, how many seconds of lifetime would each cigarette cost? The message of Chapter 8 would be much stronger if it were integrated throughout the book, and a healthy critical attitude was encouraged from the beginning, rather than waiting until the penultimate chapter.
To be fair, in her note "Details of Using the Book," the author says she "believes strongly that Chapter 8 is the most important chapter in the book" (p. viii), and gives her reasons for putting it toward the end. However I'd guess almost no students (and perhaps not even many of their teachers) will read that paragraph, and the text itself does not reinforce the importance of comparing and deciding between conflicting claims. Just one more example. In the section on means, medians and modes, we are asked to compute the median and the mean of the amounts of money paid out from insurance companies for weather-related natural disasters worldwide in the five years 1995-1999. The solution claims: "This time the mean is significantly larger than the median because the insurance pay-outs due to weather-related natural disasters increased radically during the last two years of the time period. (This is generally regarded as a major symptom of worldwide climate change.)" [emphasis added] (p. 57) A critical reader should ask: Generally regarded by whom? and On what basis? The two years that raise the mean could be anomalous and by themselves are not grounds enough to claim a global trend. Gratuitous statements can do one's cause more harm than good. I happen to agree with the author in this case, and so merely smiled, but I could imagine my outrage at an analogous parenthetical remark in a review that claimed the publication of this textbook (and others like it) is "generally regarded as a major symptom of the liberal bias in academia."
Let me reiterate that I share the author's concerns about human survival wholeheartedly and concur that mathematics has an important role to play. That is why I am so adamant in insisting that students who wish to become advocates for the environment (who are all too readily labeled as "soft" and scientifically illiterate) develop critical habits of thought. They must be able to recognize and compose sound arguments that cannot be discredited for making alarmist, wild and unsubstantiated claims, extrapolating from insufficient data. Although I applaud the intent behind this text, and found the context provided by the examples and exercises a welcome change from maximizing profits and projectile motion, I found it too heavy-handed in leaning towards telling students what to think, rather than how to think about issues critical for human survival.
Bonnie Shulman (firstname.lastname@example.org) is Associate Professor of Mathematics at Bates College in Lewiston, ME. Her special interests include history and philosophy of mathematics, and she is working on a book on Mathematics and the Moral Sciences.