Sunday, December 26, 2010

Not about computation

Dr. Robert H. Lewis, Professor of Mathematics at Fordham University wrote this brilliant essay on “Mathematics: The Most Misunderstood Subject

There’s so much good content in this essay that I’m going to take bits of it and discuss it over time.

Today, I’m going to talk about Mathematics as a liberal art, and part of a well-rounded education.

Dr. Lewis says:

Sadly, many people in America, indeed, I would have to say very many people in America, would find that a difficult and puzzling concept. The majority of educated Americans do not think of Mathematics when they think of a liberal education. Mathematics as essential for science, yes, for business and accounting, sure, but for a liberal education?

Mathematics is actually TWO of the classical 7 liberal arts. The classical liberal arts, from Roman times through early modern times were: Grammar, Rhetoric, Logic, Arithmetic, Astronomy, Music, and Geometry. Logic is both philosophy and mathematics, so depending on your point of view, math could be 3 of the 7 classical liberal arts.

Even today, Mathematics is usually in the Arts & Sciences departments of universities. And today, the term Liberal Arts is defined as “curriculum aimed at imparting general knowledge and developing general intellectual capacities.” That includes reading, writing, philosophy, history, culture, and mathematics, as well as introductory sciences.

At one job where I worked, my boss would continually think that being a math major meant that I was some kind of Rain Man (or savant) with calculations. I’m not. Oh, I can usually arrive at the right answer, but I’d rather use Excel or a calculator than churn out the calculations by hand. I’m kind of slow at calculations, and even use chisanbop to do some. Dr. Lewis says,

The great misconception about mathematics -- and it stifles and thwarts more students than any other single thing -- is the notion that mathematics is about formulas and cranking out computations.

When we do math in elementary school, it seems as though that is true. We do computation after computation. We do speed drills. We practice multiplication problems until they are second nature. We churn out number after number.

Then we get into Pre-Algebra and Algebra. Students think that the purpose of these courses is again to churn out a correct answer. Since they know how to find answers the long way, they don’t see the purpose in learning a new way to solve a problem.

Students are often reluctant to learn a more formulaic way of thinking. They resist writing down the steps that they use to solve equations, because the answer seems obvious.

But all that calculation work is prep work. All that calculation practice is to get the calculations out of the way, so that you can learn to think more abstractly without being distracted with the calculations. The calculating becomes second nature to you through practice and drilling.

As you become more sophisticated mathematically, it becomes less about calculating and more about learning new processes. From Dr. Lewis again, all the stuff you learn in elementary, middle, and even high school is “scaffolding”. It’s learning to use tools. By themselves, the tools don’t mean anything. Dr. Lewis says, “The real "building" in the mathematics sense is the true mathematical understanding, the true ability to think, perceive, and analyze mathematically.”

Very few people are getting this kind of mathematical education.

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