November 27, 2010

Happy Birthday, New-Math Guy
(Edward Begle)

Edward Begle, who was born on this day in 1914 in Michigan, became a mathematician—a topologist, to be exact. (Topology is the study of shapes and spatial properties of things, even when those things are deformed—say, bent or curved around or stretched.) 

When the Soviet Union surprised the world by successfully launching a man into outer space (the 1957 Sputnik 1 launch), many people in the U.S. became upset. Americans had thought of themselves as leaders in space technology. Some people called for better education, especially in math and science. Because of these calls for newer, better math instruction, a group called the School Mathematics Study Group was launched, and Begle was chosen to be the director.

In the 1960s the group released educational materials for all levels of school (K-12), and the these materials and the philosophy behind them were dubbed “The New Math.”

Begle thought that traditional math relied too heavily on memorization and drill of algorithmic processes. (An algorithm is a set of steps designed to solve a problem. For example, when doing long division--425 divided by 25--you might say to yourself, “25 goes into 42 one time, 1 times 25 is 25; 42 take away 25 is 17; bring down the 5; 25 goes into 175 seven times, 7 times 25 is 175; 175 take away 175 is zero. So 425 divided by 25 is 17.” These repeated steps of dividing, multiplying, subtracting, and “bringing down” make up the algorithm of long division.) Many kids successfully memorized “math facts” but then later forgot them, and many kids didn't know which algorithm to use to solve particular math problems.

Begle thought it was more important that kids develop understanding of the fundamentals of mathematics.

Begle was right about all of that, and yet “New Math” has been considered a giant flop. By and large, students, parents, and even teachers didn't like it, and it was abandoned rather quickly. It is still sometimes referred to, even today—but almost always with scorn.

New Math and Me

I went to school while the New Math was being taught, and I actually liked it! We learned lots of stuff about sets, Venn diagrams, and number bases. I understood it, and I still remember it pretty well—although how much I've actually USED it is another thing altogether.

I was also taught traditional math algorithms with traditional drills and timed tests—and I hated that stuff! I obediently memorized algorithms but didn't understand most of it, and eventually things I supposedly knew how to do mushed into one big glom of half-remembered muck. I would get the steps to adding fractions mixed up with the steps to reducing fractions, say, or forget when and how to cross multiply. I became more and more sure that I was terrible at math.

Years later, I learned the “why” of all those steps and all those processes—and I got a lot better at math. If I can 't remember an algorithm, my understanding of what I'm actually doing helps to me re-invent it. My own experience, plus tons of research findings, show that Begle was correct when he said that understanding is more important than memorization.

If he was right, what went wrong with New Math?

Some of the topics introduced with the New Math materials were far outside of kids' experiences, and when stuff is completely irrelevant, it's usually hard to learn. Also, some of the abstract concepts were taught too early, when kids should be using real things that they can count and sort and measure. Finally, most teachers and parents felt uncomfortable with the new-ish concepts and wondered why on earth anyone needed to know that stuff, so the lessons were undercut by their attitudes.

If you've never learned about Number Bases...

...give the topic a whirl with Cut the Knot lessons.

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