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Vito Prosciutto: Teaching community college math on the road to a PhD.

Sunday, June 05, 2005

19:35
Myth 2: Inventing your own algorithms versus learning the standards 

Children develop a deeper understanding of mathematics and a greater sense of ownership when they are expected to invent and use their own methods for performing the basic arithmetical operations, rather than study, understand and practice the standard algorithms.

Here's another one that I seem to have missed in the ed program. From my own personal experience, this can be closely linked with the discovery learning approach. Consider, for example the Lizzie Method for factoring a trinomial in the form ax2+bx+c. If Lizzie hadn't experimented with her own algorithms, she wouldn't have (re)discovered this approach to factoring.

As for standard algorithms, the Mathematically Correct people bring up long division and I agree (to an extent) that this is really important thing for students to learn, not just because it leads into polynomial long division but because it provides good practice in addition/subtraction/multiplication. But there's more to this than they seem to realize. When I do divisibility testing by hand, for example, I often work right to left in long division instead of left to right because it allows me to more quickly rule out possible factors.

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