Should there be an AP Linear Alegbra Course?

Mariomaruf
Fri, 23 Dec 2011 23:27:35 +0000

Most universities put theoretical emphasis on the study of linear algebra which is usually overwhelming for even a college sophomore because the art of writing proofs is a difficult skill to master. The AP Program is designed to give students experience in introductory college-level material in a wide variety of disciplines so that they can get a taste for things that interest them, and proof-writing is a skill developed only by dedicated mathematicians who would have that as their major. The Khan Academy video lectures for linear algebra are best used as supplements to clarify ideas a student taking linear algebra might find difficult or confusing; they do not teach the course in its entirety.

Proof-less linear algebra is comparable in difficulty to developing calculus after pre-calc where you learn methods for recognizing and solving a limited range of problems, and it would be viable to teach to high-schoolers, but colleges wouldn’t accept it as a replacement for their own course. Few professors are dedicated to the teaching of linear algebra and even fewer high school teachers remember the material well after dealing with lesser math for a while, leaving a small pool of people to develop the course.

The AP Program is fine with the amount of math it has and the overachievers who finish calculus in their junior year of high school are encouraged to get a taste for college while simultaneously pursuing their interests by taking courses at a local community college. I know kids who had up to 3 slots free in their senior year which they could have used to attend something like linear algebra and earn credits.

Using Khan Academy will usually just end up making linear algebra easy when you take it in a year or two, but don’t let that free time stop you from pursuing a passion for math. Check out MIT’s video lectures for linear algebra which are similarly proof-less but more in-depth. You’ll probably need a book for the proof part of the package though.