The New York Times recently published a piece called “The Faulty Logic of the Math Wars” by W. Stephen Wilson (a math professor at Johns Hopkins University) and Alice Crary. It focuses on the beliefs and practices of those known as math reformers. For over twenty years, there has been a battle between two philosophies of how best to teach math in the K-12 arena. The differences of opinion have resulted in what has come to be known as the “math wars”.This is the part of what we're being force-fed at my school that drives me nuts:
While the article itself is worth reading, I found the reaction of the readers to be equally fascinating. They revealed the ideological divide that defines this “war”. I was reminded of Tom Wolfe’s famous description of the reaction of the New Yorker literati to his 1965 article in the New York Herald Tribune that criticized the culture of The New Yorker magazine: “They screamed like weenies over a wood fire.”
Many of those who commented on the Times article about math agreed with the premise of the article and expressed their appreciation for viewpoint that supported the teaching of standard algorithms such as adding and multiplying multi-digit numbers. Others accused the authors of casting the situation as one of either/or, and that their claims that the teaching of standard algorithms in the early grades is avoided is an exaggeration.
Which brings us to what is actually meant by “understanding”. What the reform camp means by understanding is different than from what many mathematicians and those in the more traditional camp mean. The reform approach to “understanding” is teaching small children never to trust the math, unless you can visualize why it works. If you can’t “visualize” it, you can’t explain it. And if you can’t explain it, then you don’t “understand” it. According to Robert Craigen, math professor at University of Manitoba, “Forcing students to use inefficient procedures that require ham-handed handling of place value so that they articulate “meaning” out loud in every stage is the arithmetic equivalent of forcing a reader to keep his finger on the page and to sound out every word, every time, with no progression of reading skill.”I like evidence. I definitely like this suggestion:
Why don’t those arguing for better math education look at what those students are doing who are succeeding in pursuing majors in science, engineering or math? It is likely that you will see students learning standard algorithms and practicing many drills and problems (deemed dull, tedious and “mind numbing”) and other techniques viewed by reformers as not resulting in true, deep understanding. But such an outcome based investigation is not occurring.The article closes thusly:
And in answer to the statement that we’re all saying the same thing: No. We’re not saying the same thing at all.No, we most assuredly are not.