I often wonder where I went wrong with my own math education. Often, I'll blame Charlie and The Chocolate Factory. I found that book in the hallway of my elementary school one day and read it during math class for the next two weeks. I have no memories of learning multiplication during that time, though I did develop a long love of all book by Roald Dahl amid glances at the chalkboard and the front-of-the-class multiplication chart.
After months of personal book reading during math class, I still recall in painful, cringe-inducing memories of sitting crouched beside my dad's Lazy Boy chair. I was in tears and utter frustration, realizing that I knew little multiplication beyond the "sevens," and even then my "threes" and "fours" were shaky. I had allowed myself to be left behind in my learning for at least six months, maybe longer. But it wasn't my math grade that had revealed my utter lack of learning — amazingly (or perhaps pathetically), I had received either an A or B in class. Rather, my father had asked me a simple problem inv
olving fractions, which revealed how little I had learned. I now realize that it revealed far more — I missed the chance to develop a genuine, natural instinct for math. Fractions, graphs, and equations would go on to become my personal Vietnam, complete with post-traumatic stress disorder with all things math.
Today, The New York Times explains that a lot of American kids have a few holes in their academic game. Graphs and equations are included in these so-called holes. As reporter Benedict Carey explains the US education system is awash with computerized learning tools and pilot programs of all kinds. And while scientists still don’t understand the best way to teach "perceptual intuition," researchers and some teachers are convinced that "if millions of children can develop a trained eye for video combat games and doctored Facebook photos, they can surely do the same for graphs and equations."
Thus, a move from school curriculums that emphasize top-down instruction, especially for topics like math and science, may be in order. Here's what typically happens (and, actually, the approach I took last night for a stats class that I am taking): "Learn the rules first — the theorems, the order of operations, Newton’s laws — then make a run at the problem list at the end of the chapter." But as Carey explains, recent research has found that true experts have something at least as valuable as a mastery of the rules: gut instinct, an instantaneous grasp of the type of problem they’re up against."
In response to this research, some cognitive scientists suggest that schools and students might do better with this "bottom-up ability," called perceptual learning. Carey writes that new studies suggest that "the brain is a pattern-recognition machine, after all, and when focused properly, it can quickly deepen a person’s grasp of a principle." In other words, the author writes, "there’s no reason someone with a good eye for fashion or wordplay cannot develop an intuition for classifying rocks or mammals or algebraic equations, given a little interest or motivation."
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