If my seatmate on an airplane asks me what I do for a living, I tell the truth: I’m a mathematician. This generally triggers one of two responses. Either I’m told that I must be brilliant. . . or I hear about the person’s inability to balance a checkbook. The truth is, I’m not brilliant, just persistent, and I hate balancing my checkbook. Both responses, however, point to a fundamental misunderstanding about what mathematics is supposed to do and its current — and unfortunate — trajectory in American education.
Calculators have long since overthrown the need to perform addition, subtraction, multiplication, or division by hand. We still teach this basic arithmetic, though, because we want students to grasp the contours of numbers and look for patterns, to have a sense of what the right answer might be. But what happens next in most schools is the road-to-math-Hades: the single-file death march that leads towards calculus.
We are pretty much the only country on the planet that teaches math this way, where students are forced to memorize formulas and procedures. And so kids miss the more organic experience of playing with mathematical puzzles, experimenting and searching for patterns, finding delight in their own discoveries. Most students learn to detest — or at best, endure — math, and this is why our students are falling behind their international peers.
When students memorize the Pythagorean theorem or the quadratic formula and apply it with slightly different numbers, they actually get worse at the bigger picture. Our brains are slow to recognize information when it is out of context. This is why real-world math problems are so much harder — and more fascinating — than the contrived textbook exercises.
What I’ve found instead is that a student who has developed the ability to turn a real-world scenario into a mathematical problem, who is alert to false reasoning, and who can manipulate numbers and equations is likely far better prepared for college math than a student who has experienced a year of rote calculus.
What can we do as parents? At my house, we sometimes talk through simple logic puzzles over dinner. There are lots of good examples on the Internet, even pirate puzzles to please my son. Sudoku, despite claims to the contrary, is all about logical problem solving.
Or how about family board games night once a week? I’m not talking Candyland-style games, all luck and no skill. Some favorites in my household include logic puzzles like Rush Hour and board games like TransAmerica, Clue, and Carcassonne. Of course, there’s also always checkers and chess. These games teach kids to think logically several steps ahead, all while having fun. And they are far more effective than the SAT prep booklets which litter the homes of high school juniors each year.
I’m not down on mathematical training. I’m just down on the persistent memorization approach, which works your intellectual muscles about as effectively as lifting loaves of Wonder Bread helps build your biceps. We are failing our children if all we teach them are dry formulas. The benefits just don’t add up.