Messing up math

This op-ed from the Baltimore Sun elegantly describes my thoughts about how math education has gone awry. It is almost like math is a subject we don't understand, so we teach it in the most oddly incorrect ways.

We teach math, like algebra and trigonometry, which the vast majority of us never use afterward. There's a fine line between having a basic knowledge of a subject and slogging through college level detail on a subject. English, social studies, even the health curriculum seems to hit the right balance.

Conversely, we don't teach students math they could use in their daily life, and which could be mastered at a developmentally-appropriate age. Statistics and money management should replace trig and calculus before college. Mortgages and interest rates instead of sine and cosine.

The way we teach math also drives students away from the subject by making them memorize meaningless rules of advanced techniques. Without understanding the math they learn in middle and high school because it is not developmentally appropriate, students give up on the subject.


Autumn said...

It was a good article, but I am not in complete agreement with your interpretation. I think that elementary school math is what has gotten out of wack. They have simply messed with the order of topics so that they look 'advanced' and they don't master the basics sufficiently. I do think that trig and calculus are developmentally appropriate for high school, however, and if the elementary/middle school math program was better then these topics would not be so hard in high school.

Trackball of Truth said...

Autumn: thanks for commenting! I think we are more in agreement than not. But you may have missed the main point I probably didn't make very clearly. I think there ought to be 3 rules for teaching any material K-12:

1. It should be material that is used by the population. It should not be material that is never used by most people. Because otherwise the education system will write the subject off, as it has with math and science. Trig and calc are specialized math, meant for math-related college majors and should not be part of a general purpose high school education.

2. It should be developmentally appropriate so that it is truly understood, and not propped up by mindless memorization because it makes the kids look smart. Because people give up on a subject where they don't have true understanding.

A student should be capable of doing more than stepping through a cookie cutter formula of mechanics and truly understand the concept. For trig and calculus, that means doing proofs and so on. Even my physicist PhD wife scored a D on her first go around with calculus in high school.

This is similar to the difference between truly understanding a vocabulary words versus just memorizing a definition, but not able to use the antonyms or synonyms fluidly for a given word.

3. It should not drive people away from the subject, so as not to preclude their pursuit of it in college. Math and science education seem to be custom built to drive away as many people as possible.

I agree that the basics are not given their due in the earlier grades and this is part of the problem. Learning exponents in 5th grade takes time away from fractions, decimals and percentages. And I have spent too much time in my professional life explaining basic rules about proportions and averaging to MIT-level econometricians - and still not have them understand it.