“Kiss My Math”? What in the world does that mean? According to author Danica McKellar, it means this: “Um, excuse me, I’m going to do whatever I want with my life, and I’m sure as heck not going to let a little math get in my way.”
Danica McKellar, an actor who gained fame through her role as Winnie Cooper on “The Wonder Years” and who graduated summa cum laude with a degree in mathematics from UCLA, has done it again. Pursuing her goal of helping middle school girls survive — and ultimately master — middle school mathematics classes, she has written a follow-up to the equally impudently named Math Doesn’t Suck. MDS introduced her young readers to primes, multiples, factors, rates, percentages, fractions, decimals, ratios and proportions, and a first look at variables and solving for the ever-mysterious x. In KMM, she takes the next step into pre-algebra, leading her readers through arithmetic with signed numbers, absolute value, arithmetic with variables, associativity, commutativity, distributivity, word problems, order of operations, functions, slopes, graphs, algebraic expressions, mathematical statements, and solving and graphing equations and inequalities.
Two notes of caution: the author uses many metaphors that might be disconcerting to us professional mathematicians, and the book has the flavor of a teen magazine, full of sidebars, personal notes, and other “interruptions.” That’s just fine: she’s not talking to us, but to middle-school girls who are terrified of math. And when you need to communicate with a particular segment of the population, you had better speak their language — and she certainly does! Here are some examples.
Integers are “mint-egers.” Social cliques, those groupings that are only too familiar to middle-school girls, lead right into the associative property, and daily work and school commutes lead to the commutative property. (And by the way, she explains that those properties aren’t just boring rules but aids to help simplify expressions.) Mirrors and double mirrors help explain negations and working with negative numbers. Every middle-schooler knows about backpacks, bags full of unknown stuff — and bags are metaphors for unknowns. Variables show up again in a discussion about blind dates. Wrapping and unwrapping presents are her lead-in to inverse operations. Exponents are like high-powered executives.
More familiar are functions as sausage machines. Something written in parentheses reminds her of someone whispering, and that leads right into describing a function table in terms of ordered pairs. The origin is where everything originates. A chapter called “Can a Guy Be Too Cute?” introduces single-variable inequalities, how to solve them, and how to graph them. Ski slopes, quite naturally, introduce slopes of lines. She explains how to remember that the slope equals the rise over the run in terms of what she calls the Bubblegum Trick. (You have to read it to believe it, but it will certainly make an impression!)
The chapter introducing word problems entitled “Didn’t That Guy Say He Was Going to Call?” is particularly effective. In it, the author reminds her young readers — who know this all too well — that “guy-speak” and “girl-speak” are two different languages, and translations are very hard to come by. But translating between “math-speak” and English is not nearly that bad, and she has some very sound methods for showing this. She points out that a mathematical sentence is very much like an English sentence: they both have verbs, and they both express complete thoughts. A mathematical expression does not have a verb: it is “just one or more math terms and operations, sort of hanging out. An expression is just kinda … there.” She follows this with a list of the mathematical verbs =, ≈, ≠, <, >, ≤, and ≥, along with their English translations. This is good mathematical instruction at work.
The author works out many examples for her young audience, lead them through problems step-by-step, and includes helpful tips about studying and taking tests. There are numerous sidebars and digressions, including Quick Notes (“Always check your answers”), Watch Outs (“The mirror rule for reversing inequalities only works for multiplication and division, not for addition and subtraction”), and testimonials and e-mails from women who were once afraid of mathematics but are now professionals who use that same mathematics in their jobs.
There are takeaway tips (“When confronted with a word problem that you don’t know how to start, begin by labeling things. Then find relationships between the things you’ve labeled, and translate English into math”), troubleshooting guides, and short looks at Danica’s Diary — her own reflections about such subjects as popularity, why “dumbing yourself down” is dumb, worrying, almost getting ripped off at a store, relationships, and imagination versus reality.
Through all the glitz and frivolous tone and numerous reminders of our own painful middle school years, there is sound and basic teaching going on here. Finally, in the spirit of “know your audience,” teachers should read this book, too: it might be helpful.
Ezra Brown (firstname.lastname@example.org) is Alumni Distinguished Professor of Mathematics at Virginia Tech, with degrees from Rice and LSU. He is a number theorist by trade, but his first publication was about tournaments and Hadamard matrices. He is a fairly regular contributor to the MAA journals. He sings (everything from blues to opera), plays a tolerable jazz piano, and his wife Jo is teaching him to be a gardener. He occasionally bakes biscuits for his students.