Uncertain Principles

Kanem's piece sort of undercuts itself. Yes, it may not matter when one learns to walk, but it does help to learn how to walk before hiking the Appalachian Trail. He complains about the engineering curriculum at his school requiring calculus, but what if the four years of courses require calculus? I suppose they could redesign things so one could learn calculus as a freshman, but he seems to be arguing that it should be just as reasonable to learn calculus as a senior, and not have to deal with all those calculus dependent courses just because one wants to major in engineering. Yes, I agree prerequisites suck, but so does coming into a class clueless.

Posted by: Kaleberg | November 1, 2009 5:23 PM

No, the argument is that students are being asked to learn things that they don't have the background for, at the expense of things that could properly prepare them for calculus.

I recall learning matrix inversion in Algebra 2, a class that average students at my high school took in 11th grade and the many students who were advanced took in 10th or even 9th grade. That is, we were taught the mechanics of matrix inversion. I don't think there was any explanation of why (beyond gaining the ability to solve certain homework and exam problems) someone would want to go through the trouble. And this is a case where there is a straightforward application to solving systems of linear equations, something else that was taught in that class.

That was in the early 1980s. Now, apparently, they are teaching matrix inversion in the year my average peers would have taken pre-algebra. That implies that they don't even have the missed opportunity to tie matrix inversion to systems of linear equations. Also, the problems will necessarily be simplified, most likely to 2x2 matrices, with no easy way to generalize to larger matrices. (In my Algebra 2 class we were working with 3x3 matrices as well, but generalizing from N=3 to 4 is the hard step.) I don't see how the students can really learn it, except in the sense of rote memorization, which is of no help when you encounter it in a slightly different guise a few years later.

Posted by: Eric Lund | November 2, 2009 8:28 AM