Our schools are using abacuses to teach math and fountain pens to teach writing. My opening sentence is a gross exaggeration but the fact is most schools are using the tools of yesterday in order to teach the workforce of tomorrow. Specifically the way we teach higher mathematics is poor because the most useful tool ever invented for doing math is being almost completely ignored, Programming.

When I was in elementary school our computer class consisted of playing Oregon Trail and typing. By the time I got to high school they did offer a computer programming class as an elective. We did the basics, printing things to the screen, using control logic and loops, a great way to introduce somebody to computer programming. I consider that class to be a success but the entire methodology used to teach me mathematics in high school a failure. An intro to computer programming class such as the one I had in high school should have really been given to elementary school students. In high school where students are learning mathematics like algebra, geometry and trigonometry there is no excuse not to have a computer as a major part of that study. Specifically by writing programs that use the skills students are learning.

When you program on any non trivial problem you exercise your abstract thinking ability, your problem solving skills and have the opportunity to put mathematics that may otherwise seem useless, to action. You learn to develop methodologies to come up to solutions to problems. Geometry and trigonometry, 2D and 3D graphics offer a play ground where abstract problems can be visualized and there can be direct interaction. Algebra and pre-calculus are used all the time in non trivial problems, the concept of functions, recursion, set theory, algorithm development, all used when programming. The most important single benefit of programming for the math student is the application of his work to a problem who’s solution can be a lot more exciting then a number on a piece of paper.

Many students are using programmable calculators in the high schools but I feel even that is insufficient. If students were writing programs on desktop computers with an actual programming language that is used for more then just molding math then they could get the sense that they are learning a skill that may have use in their every day lives. Even if they don’t intend to be programmers they may have a web site in which they can use their new found programming skills to enhance their content.

Computers answer the question that is heard throughout high school math classes, “When will we ever user this stuff in the real world?”. Students are all too often expected to take it on faith that they will need math for some magical purpose later on in life. Many of them will not, there are numerous jobs some of which pay quite well in which knowing anything but basic arithmetic is not required. Many doctors and lawyers can probably go their whole careers without using any kind of higher mathematics and we generally consider those two professions as among the more educated amongst the population. The problem is of course it is not knowable in high school what career a student may end up perusing. All too often students in higher education do not peruse a degree in the field they really desire because they are afraid of the mathematics involved. I was one of those students who asked “when will I ever use this math in real life”. I wish now that I had seen that in the future I would need mathematics to do what I love doing. I paid for that lack of fore site in college where I had to play catch-up on the math front. I am lucky that I had enough background to get me though, I wonder how many students never even tried to peruse their dreams because lack of confidence in mathematics.

* Abacuses or abaci, I choice the less used abacuses because the word is Arabic and abaci is a Latin pluralisation of an Arabic word, see here.