Requiring Proofs in Geometry Class

Re “A Plea in Defense of Euclidean Geometry,” by Barry Simon, Commentary, Feb. 6: My Algebra II students at Manual Arts High School, most of whom were in my geometry class last year, were very interested to hear that less than half of the freshmen in a calculus/probability class at Caltech were given two-column proofs as an integral part of their high school geometry curriculum.

About half of the students in my three geometry classes failed because they could not be bothered to learn the vocabulary required to write proofs, or to remember to bring their notebooks and pencils every day, for that matter. The other half of the students moaned and groaned about having to write proofs, but they wrote them and they wrote them well. The top-scoring student among all three classes could not have earned her A had she not written proofs as well as she solved algebra-based problems. Another student transferred into my class mid-semester, never having seen proofs at his old school. This was not an excuse for him to fail, but a challenge to work harder. Several more students than there is room for wanted me to include their achievements; they are now, a year later, still that proud of their work.

While we must work to reach students who, for many reasons, are not finding academic success, lowering expectations presents both a lie to these students and robs motivated students of the academic and analytic skills they will need.

CAROL MAY

Los Angeles

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Simon is right on in decrying the decline of Euclidean geometry in our high schools. Geometry is one of the few courses in high school that require you to think rather than just memorize facts. I’m sure this is why some high school students don’t like it, because thinking is hard--particularly if you’re not used to it. In my opinion, geometry should be required rather than phased out.

WARREN B. DACE

Los Angeles