Down With Geometry

One of my favorite bloggers, Kevin Drum, decided to relieve the tedium of our current political anarchy by whacking the hornets’ nest of the high school mathematics curriculum, in particular the subject of plane geometry.  You can tell from the tag list on my blog that I hold plane geometry in high regard and can’t let this gibe pass without some rebuttal, futile as it may be.  Actually, I am not going to weigh in on the general issue of the current math curriculum that much, but rather make a few observations from my own experience over the years as it relates to Kevin’s post

See Down With Geometry

(Update 2/9/2021)   Vindication! 

The comments to an interesting article on “Girls and Math” warmed my heart.  But first, a word about the article:

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Girls and Math

Raji Jayaraman and Peter N Burns, 8 February 2021

We both have daughters who are good at math, but opted out of advanced math. In so doing, they effectively closed off entry into math-intensive fields of study at university such as physics, engineering, economics, and computer science. They used to be enthusiastic about math, but as early as grade three this enthusiasm waned, and they weren’t alone. It was a pattern we observed repeatedly in their female friends during those early school years, as boys slowly inched ahead.

This turns out to be something of a statistical regularity. Girls don’t start school hating math or doing worse at it than boys. Then, somewhere in elementary school, this changes for many girls and in some (though not all) countries, a gender gap in math performance appears. …

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Basically the answer to the problem is still a mystery.  There are the usual suggestions given, such as competitive exams and girls’ supposed preference for language and reading.  But there are too many counter-examples both in the US and other countries for these reasons to be the last word.

The two comments to the article from females were particularly interesting (my emphasis):

Brooks Riley •  February 8, 2021 1:42 PM

Although I’m sure that some of the theories have merit, I can’t help but wonder if there isn’t an emotional component other than ‘competitive stress’. I was good at math but had no interest in it, so it rather galled me that my math SATs were so high. Geometry was the only math course I loved—because it was spatial, less abstract, productive. Could there be something in the emotional development of girls that tends to turn them off math at a certain age?

Felila •  February 8, 2021 6:30 PM

I was good at math in high school. I loved geometry; I would sit in the back of the class and work ahead in the book. Just like doing puzzles. I went on to algebra. I was the only girl in the class, which was taught by the football coach. Who clearly had no interest at all in math. If that’s math, no more math for me. Until much later, when I discovered that it could be fun. Yay calculus, statistics, and discrete math.

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So here is a thought.  The comparison of music to mathematics is probably worn out, but there is one further comment that might be helpful.  No one thinks music consists of scales, but most people think mathematics is arithmetic and memorizing addition and multiplication tables.  Scales and other things are what we have to practice (ad nauseum and boringly) in order to be able to perform real music adequately.  Similarly, a basic facility with addition and multiplication (and their inverses) is necessary to do real math, hand calculators notwithstanding (mental estimations require memorizing basic arithmetic).  Now what motivates the young music student (if anything can) is the early ability to play a song, like Twinkle, Twinkle, Little Star.  At each stage of increasing proficiency a student gets to perform real music at some level and begins to experience the exhilaration that comes from doing it.  Where is the Twinkle, Twinkle, Little Star’s counterpart in math?  For me it didn’t come until algebra and especially plane geometry.  But in my day that was some 9 or 10 years into my education.  I think that is the problem, and not just for girls.

It is possible that modern math activities in grade school do provide some Twinkle, Twinkle, Little Star moments.  What I have seen online is certainly a lot more interesting than the dry math “scales” I had to endure for years.  But for me, calculation has always been a bit of a burden and only necessary to support some “big idea” I was trying to establish.  Plane geometry (in contrast to analytic geometry) involves little or no calculation, only reasoning with some basic, non-numerical objects and relationships.  Has anyone experimented with introducing plane geometry at an earlier stage in a child’s math education?  Felilia’s comment above that plane geometry was like doing puzzles was a tip-off to me that the subject might benefit from an earlier introduction in the curriculum. 

Anyway, my heart is warmed by the additional accolades for plane geometry that these women have provided.  May it survive another 2000 years.

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