Wednesday, June 8, 2011

Math education and Ana Darcy's children

We have seen, in Distant Cousin: Repatriation and Distant Cousin: Reincarnation, how the extraterrestrial Ana Darcy and her New Mexican husband Matt have spared no expense in educating their children from an early age. They have always been careful to conduct it in a spirit of fun, following their children's interests--with only a little parental encouragement to practice their music, drawing, writing, and other homework. Both children grew up speaking several languages, because they had been exposed to those languages, and both were reading from an early age (see posts 1 2 3 4).

Their son Julio, in particular, turned out to be keenly interested in mathematics. Julio may have had some innate interest in math, but he also had help: from enlightened parents, from tutors, and from a small bit of otherwordly technology. Here's an excerpt from chapter 1 of Distant Cousin: Reincarnation, published in 2007:

"[Matt] believed [his wife, that] education was apparently crucial on Thomo, Darcy's home planet. Her ancestors had been moved there from Earth thousands of years ago and had had a difficult time surviving, but they had prevailed in style if Darcy was any example. As young as the twins were, they had already surpassed their father in mathematics. [Matt] was hardly gifted in math, but to be bested repeatedly by seven year olds took a little getting used to. Julio in particular loved the math cube that had been a present from Darcy's Uncle Rothan. This was a transparent cube, nearly four inches on a side, which amounted to three-dimensional graph paper. It was wireless—whatever powered it was a mystery to Matt. A small keyboard came with it, and entering coordinates and values in the base unit produced a glowing web of blue lines within the cube that showed the various resulting graphs in different colors. Change the values, and the graph would change. Julio was always bringing it to him asking him to guess what equation had produced it. He never could."

A recent article in The New York Times suggests that this unusual technique by which Julio learned mathematical concepts is now beginning to be realized as particularly effective by educators on Earth.

The article begins thusly:

Like any other high school junior, Wynn Haimer has a few holes in his academic game. Graphs and equations, for instance: He gets the idea, fine — one is a linear representation of the other — but making those conversions is often a headache.

Or at least it was. For about a month now, Wynn, 17, has been practicing at home using an unusual online program that prompts him to match graphs to equations, dozens upon dozens of them, and fast, often before he has time to work out the correct answer. An equation appears on the screen, and below it three graphs (or vice versa, a graph with three equations). He clicks on one and the screen flashes to tell him whether he’s right or wrong and jumps to the next problem.

“I’m much better at it,” he said…. “In the beginning it was difficult, having to work so quickly; but you sort of get used to it, and in the end it’s more intuitive. It becomes more effortless.”

The article goes on to point out:

For years school curriculums have emphasized top-down instruction, especially for topics like math and science. 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. Yet 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. Like the ballplayer who can “read” pitches early, or the chess master who “sees” the best move, they’ve developed a great eye.

Now, a small group of cognitive scientists is arguing that schools and students could take far more advantage of this same bottom-up ability, called perceptual learning. The brain is a pattern-recognition machine, after all, and when focused properly, it can quickly deepen a person’s grasp of a principle, new studies suggest. Better yet, perceptual knowledge builds automatically: 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.

That is precisely what Julio learned to do, years before the technique became understood well enough to publicize.

The people of Thomo, Ana's people, barely survived harsh conditions on their new planet, as we know from the Distant Cousin stories. Their eventual success was due in large part to their collective dedication to education, which they well knew was the ultimate key to survival.

It is no different for us on Earth. In difficult times, whether a result of weather, war, disease, or economic problems, we must not forget that education can be our salvation, whatever it costs. Indeed, it should be one of our top priorities.

Bilingual education and early bilingual literacy: 1  2  3  4
Meet Ana Darcy!

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