A proof that math opens doors
(Page 2 of 2)
"In the '50s, we were in competition with the Russians to develop these space probes, so it was exciting," she says. "Today we hardly pay any attention when the shuttle goes up. It's kind of ho hum."Skip to next paragraph
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Finally, she returned to her first goal: teaching. In 1967, she accepted a professorship at California State University in Los Angeles, where she taught math to teachers.
Today, with "math wars" in full swing, her philosophy doesn't fit neatly with professional mathematicians - or math educators' constructivist, or discovery-oriented, approach. Instead, she blends tradition and progress in a way not easily categorized. Granville, for instance, is a product of rigorous, traditional math training. Yet she taught and wrote a book on "new math" - part of a short-lived 1960s movement to diverge from rote learning and teach deeper concepts.
She advocates letting students explore multiple ways of problem solving - emphasizing clever techniques not in the books. She is similarly adamant that math must not be taught as a "series of disconnected, meaningless technical procedures from dull and empty textbooks." Both are reassuring to the math reformers who are pushing to adopt programs that deal with concepts more, use calculators more, and memorize less.
Granville isn't ready to let current reform off the hook. Calculators in elementary classes should be rare, she says. Even in high school, their regular use can "cripple" the ability to manipulate equations and understand deep interrelationships in math, she says. If that's not enough to set a math-reformer's teeth on edge, she adds that basic addition and multiplication tables must be memorized early. Inability to automatically do "basic algorithms," make algebra and higher math exceedingly difficult for students, she says.
But perhaps the biggest problem, she says, is math teachers who don't really understand their trade because they've been allowed to skip math during training. "We teach that there is only one way to solve a problem, and we should let children explore various techniques," she says. "But we're not training teachers to provide this new approach."
When teachers allow calculators too much, don't have broad training in math, and do not know how to cover deeper concepts, the result is frustration, she says: "The children end up crippled in mathematics at an early age. Then, when they get to the college level, they are unable to handle college classes. It's tragic because almost every academic area requires some exposure to mathematics."
Granville offers no-nonsense advice: Don't give up. Even with her high-powered background, she was first rejected when she applied to teach at several white colleges. She didn't let that - or her gender - stand in her way.
"There's lot of talk about women and minorities in math, why they aren't there in great numbers," she says. "When I was young, nobody told me women couldn't do mathematics. Sometimes, I'm glad I wasn't born in the enlightened '90s."
During her recent Yale address, she implored professors: "Make children learn how to add, subtract, multiply, and divide, and they won't need calculators. How do you teach the beauty of mathematics, how do teach them to ... solve problems, to acquaint them with various strategies of problem solving so they can take these skills into any level of mathematics? That's the dilemma we face."
(c) Copyright 2000. The Christian Science Publishing Society