Some comments on the comments

A continued conversation based on the New York Times article: How to Fix Our Math Education, By SOL GARFUNKEL and DAVID MUMFORD

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Sol Garfunkel
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Some comments on the comments

Postby Sol Garfunkel » Tue Sep 13, 2011 12:28 pm

We have received a number of comments here and on the NYTimes pages about our article. I will respond from time to time about those comments. But to begin, it is important to note that the Times piece was cut down from a much longer article in order to fit the Op-Ed constraints. As a consequence, some of the complaints reflect that compression. For example, several people have commented that we seem to have left out geometry from our straw man curriculum. The many geometric examples were a casualty of the editorial process. In the original,e.g. we explicitly looked at the reflective property of ellipses as used in breaking up kidney stones and several other practical uses of graph theory, Voronoi diagrams, etc. There were of course several comments to the effect that we had ignored the teaching of mathematics for its own sake, its beauty, etc. We are both mathematicians (David being infinitely more accomplished than I). We both appreciate the beauty and internal logic of our discipline. Our fear is that in the name of that beauty we have and continue to lose far too many students far too early. Certainly we hope that students will learn to appreciate mathematics for its own sake. But to base our teaching on this hope, rather on showing the usefulness of our subject is simply to court disaster.

With national standards and (soon) national tests, we have taken on a great responsibility. We are asking teachers to teach in a more uniform way. We are likely to stifle creativity and diversity in the name of a 'common' curriculum and psychometrically blessed assessments. If there is one way and that way is all about abstraction, then we argue we will discourage too many students. This was precisely what led to the 1989 NCTM Standards - a desire to widen the pipeline, to have mathematics be a pump not a filter. We believe that contextual learning gives us the best chance.

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