What’s It Mean to “Get” Math?
With my children not yet to the age at which I might have to consider battles with their teachers for their young mathematical souls, my opinion of the “new math” isn’t sufficiently strong to inspire rants. Still, such statements as the following raise fundamental questions:
One problem, [Pat Cooney, math coordinator for six public schools in Ridgefield, CT,] says, is that parents remember math as offering only one way to solve a problem. “We’re saying that there’s more than one way,” Cooney says. “The outcome will be the same, but how we get there will be different.” Thus, when a parent is asked to multiply 88 by 5, we’ll do it with pen and paper, multiplying 8 by 5 and carrying over the 4, etc. But a child today might reason that 5 is half of 10, and 88 times 10 is 880, so 88 times 5 is half of that, 440 — poof, no pen, no paper.
“The traditional way is really a shortcut,” Cooney says. “We want kids to be so confident with numbers that it becomes intuitive.”
Or, the parent might understand that numbers can be broken into their components, with the functions performed on each and then added together at the end. In that case, they would break 88 into 80 and 8, multiply each by five — referencing a chart that they memorized decades ago and never forgot — and then add the results together: 400 plus 40 is 440. That’s ultimately what the traditional method teaches. Poof. No pen, no paper, and yet a fundamental understanding of what each digit represents and its relationship to the others.
Although, as I said, I don’t have thorough experience with it, the New Math appears to treat numbers as whole things that may be broken up and combined. The traditional approach is to treat numbers as representative symbols of multiple things that can join together or break apart. In the former case, everything is ultimately a fraction of a greater whole; in the latter, everything greater than one is a collection of independent items that have relationships. (Even fractions, in that view, are smaller individuals that make up the larger grouping, sort of like discussing atoms in molecules.)
Would it be too much to inject a quip about the fundamental difference between the liberal and the conservative mind, here?