In Mindstorms (the groundbreaking book, not the Lego set) Seymour Papert writes that part of what drives the mathematical curriculum is the technology available to students.
As I see it, a major factor that determined what mathematics went into school math was what could be done in the setting of school classrooms with the primitive technology of pencil and paper. For example, children can draw graphs with pencil and paper. So it was decidet to let children draw many graphs. The same considerations influenced the emphasis on certain kinds of geometry. For example, in school math “analytic geometry” has become synonymous with the representation of curves by equations. As a result every educated person vaguely remembers that
is the equation for a parabola. And although most parents have very little idea why anyone should know this, they become indignant when their children do not. They assume that there must be a profound and objective reason known to those who better understand these things. [...] Very few people ever suspect that the reason for what is included and what is not included in school math might be as crudely technological as the ease of production of parabolas with pencils!
Somewhat dangerously, I disagree with Seymour Papert just a little bit. Or maybe I am a generation younger and the school system changed in the meantime. Either way, I think that the biases of our current educational system are less due to available technology, and more towards that which can be quantitatively tested. That which we can test, we now test extensively, and that which cannot be tested in a standardized way, we pass over. Unfortunately, this is exactly wrong if we want to help mold students which are better able to function in the future.
That which can be quantitatively tested is usually better done by a computer! They add faster and more accurately, they factor polynomials more quickly, draw functions more quickly, etc , etc, etc. It is only those things which we cannot test quantitatively where humans have any advantage over machines. Computers are pretty bad at coming up with useful models of a real-world situation, and they really suck at being creative (all by themselves, that is — human/computer teams can be fantastically creative and productive and superb modelers). The biases of our educational system are forcing students to become more computer-like, but these are actually the least-relevant skills for the future! Students, responding to this obvious disconnect between the skills and knowledge they need and the skills and knowledge they are taught then have a few paths: they can drop out; they can cynically treat school as a game; they can ignore school and teach themselves on the weekends; or they can cling to the belief that somehow this will all pay off in the end because it would just be insane if the goals of school and the needs of adult life were actually as divergent as it seems.
I did the last. But as near as I can tell, our current focus on quantitative testing all but ensures that the next generation of students will be worse-prepared to face the world than the current generation. By only teaching that which we can test, we optimize our educational system to teach the skills most likely to quickly become obsolete!
