Danica McKellar achieved early fame playing opposite Fred Savage in The Wonder Years. She graduated from UCLA summa cum laude with a major in mathematics. Her work there as well as her first book received high praise from none other than Terence Tao. She has parlayed her fame as an actor into a successful series of books aimed at middle school girls: Math Doesn’t Suck, Kiss My Math, and most recently Hot X.
As with the previous two volumes, Hot X is both a mathematics book and a self-help manual for tween girls. Interspersed with the mathematics (Algebra I in this case) are numerous short quotes from students along with several longer testimonials from adult women who described how they overcame their fear (or dislike) of mathematics and forged successful careers in part because of their mathematics ability. Here’s an example from page 35: “Before I took algebra, I saw it as some sort of punishment! Now that I’ve gotten the hang of it, I never thought I would ever say this, but it can actually be really fun.” (Dominique, 16) The author uses a casual “us versus them” approach in which the “them” role is played by mathematics, middle school boys and math teachers. As a result, it is definitely not an appropriate book for boys and may offend some teachers.
The mathematics is for the most part very well done. McKellar provides lots of good examples and seems to have a knack for simplifying things without oversimplifying. Her treatment of the standard word problems in elementary algebra is first rate although the chapter titles and non-mathematical banter are a bit off-putting for someone well past his tween years. Here are three examples.
The Guy of Your Dreams - Motion Problems using d = rt
Savvy Business Chick — Word Problems: Percents and Simple Interest
Ms. Exponent Gets Her Whip — The Product, Power, and Quotient Rules for Exponents.
Ms. Exponent is quite the woman: “She’s the high-powered executive who runs her business from up high in her corner office and orders mergers and martinis with a quick call to her cute assistant named Brett.” (Page 239)
The mathematical explanations usually hit their mark in terms of the level of understanding we can expect from middle school children. Here are two examples.
Negative Exponents: Ms. Exponent explains why 20 = 1, 2–1 = 1/2, 2–2 = 1/4 by constructing a chart listing positive powers of two: 23 = 8, 22 = 4, 21 = 2 and pointing out that the values are cut in half each time. She then says “…should the values continue getting cut in half? They’d go from 1 to 1/2 to 1/4 to 1/8. And yep, the pattern continues, and there is justice in the world.” (page 259)
Reducing or Simplifying Fractions: The author refers to fractions such as 2/2 or a/a as copycat fractions since they all equal 1. Such fractions, she informs us, can always be eliminated from a product since multiplying by 1 has no affect. To simplify a fraction such as (3ab+5a)/(4a–ac) we need to find the “hidden copycat” a/a. To do that we factor the top and bottom according to rules discussed earlier. McKellar has a very clever method for finding common factors she calls the birthday cake method. The idea is to factor out the first common term you see and then try again. She uses notion similar to that for long division. See page 23 for details.
There are a few mathematical errors — most of them involve assuming that the mathematics we deal with in middle school generalizes to all of mathematics. Here are a few examples:
The final sentence in a discussion of solving equations like 3x + 2y =7 for either x or y: “Turns out, we can solve for anything in terms of … anything.” (Page 79)
The definition of a linear equation in standard form: “Here’s a linear equation in standard form: Ax +By = C … where A, B, and C are integers with no factors in common, A > 0…” (page 133) She then explicitly prohibits any non-integer coefficients.
“Squaring a number is like saying ‘What’s the area of a square whose sides are this length’.” (page 274). Unlike several other places, this is not accompanied with the caveat that the number must be positive.
While the math is mostly right and the informal tone is likely to help some girls the overall tone of the book bothered me a bit. While it is more than appropriate to empower young girls, the smirky “let’s get the boys” undertone seems inappropriate. Replacing a social structure in which women are marginalized with one in which men become so doesn’t represent progress to me. That being said, I think this book might possibly be very helpful for some middle school girls. I will leave it to you, dear reader, to decide if you know any such girls.
Richard Wilders is Marie and Bernice Gantzert Professor in the Liberal Arts and Sciences and Professor of Mathematics at North Central College. His primary areas of interest are the history and philosophy of mathematics and of science. He has been a member of the Illinois Section of the Mathematical Association of America for 30 years and is a recipient of its Distinguished Service Award. His email address is email@example.com.