a defense of boring math

There’s something wrong with the way we teach mathematics today.

So you will quickly hear if you talk to quite a few graduate students, professors, instructors, students, random people on the street… I do agree. There is something wrong with mathematical education (in the US, along with plenty of other places I would guess).

What exactly the problem is somewhat harder to say, but something that you will hear from graduate students and professors, people who have had exposure to “higher” mathematics, will often include the complaint what we teach is tedious, mundane, useless computations and manipulations. Questions have cookie-cutter forms that one presents multiple times throughout, demanding exacting details. Questions of any interest or requiring any independent though are not allowed in fear that students will complain or ignore them.

There is certainly truth to this. And I cannot say that I have anything resembling a solution to this problem or that I’m even a decent math instructor to have authority or experience to talk about what one should do. But despite this, I think that the demonizing of this mechanical understanding can be detrimental to the ultimate goal.

It’s been my understanding that mechanical understanding precedes deeper conceptual understanding. As far as I recall I memorized a list of numbers before I learned how to count things. When I first learned addition, I admit I sometimes leaped-frogged the number line, but with enough practice I just memorized what two arbitrary one-digit numbers added up to and then carried out an algorithm. Similarly I memorized the multiplication table without really caring about any deeper implication.

I think that in order to get a real grasp of calculus-track mathematics, one has to feel comfortable with numbers. And that one gets comfortable with numbers by familiarity with them, even in mundane and routine ways.