When a student comes to me and says she can’t concentrate on her projects because of how she’s doing in another one of her classes, I tend to feel a violent ambivalence.
When someone is asked to prove that two trigonometric expressions are equal by using arcane identities, especially when this someone is a barely abstract-thinking 16 year old, I can’t help but wonder at the logic of it all. Is this practice–for surely a problem this steeped in meaninglessness must only be seen as some level of abstract proving-gound-ness–really worth the life-long aversion to analytical methods that it’s creating?
That gets me really thinking! Is the goal of all this math to create analytical thinkers? Is it? Really?! If you believe all of the saccharine posters hanging on lowest-bidder brick walls in schools everywhere, math is, in some ineffable way, “learning how to think.”
Or, is that the goal of making math a part of school?
As a mathematician, I find it beautiful when two unknown things connect. I find it exhilarating, the connection between pattern, numbers, and the world. This is much the same feeling as when I turn out a good pair of shoes or a fine piece of furniture.
But, school? Math is for learning to think and quantify. To reason and objectify. To abstract and re-abstract.
If those are the mental capabilities we expect in our students, then how do you grade what our math curriculum does for students, and why is doing a trig identity the only way to prove a student has gotten there?