Tricks for dividing and why they work.
Free online math courses from MIT, Harvard, etc. Great idea. So then why would anybody want to pay?
Currently, I’m a graduate teaching assistant, teaching a precalc class. We are using Sheldon Axler’s book A Prelude to Calculus. Besides the somewhat lame title, it’s actually a pretty good book. There are lots of great problems as well as some really great conceptual problems, which are, most unfortunately, many students’ first experience dealing with proof.
The first assignment I gave them which had just a few proofs went quite poorly for them (and depressed me). However, what’s really interesting, and something I think is just going to become more and more common in the future, is homework online. This is the first time that I’ve had students complete their assignments online, and I really like it. The ability to fix errors “Just in Time”, in general, helps them immensely. I’ve graded too many homeworks where students make the same conceptual mistake over and over again. And when I correct their errors, most don’t bother to look to see what they did wrong. The other nice feature is that I get a really pretty graph that shows how the class on the whole did on each question.
Of course, it’s not a perfect system. It can’t tell the difference between lower case and upper case nor does is see a difference between an essentially correct, but unsimplified solutions and correct solutions. I also can’t see how they arrived at a solution, so it’s possible they are just guessing at a solution, or worse, making conceptual errors that will still have them arrive at the correct answer.
What’s really interesting is the students’ reaction to the system. In general they HATE it. With a passion. It’s surprising to say the least. Most are used to computers, and have had them in the classroom for some time, yet they actually prefer the old way. That’s surprising to me.
Here’s a 4d Rubik’s Cube to solve, if the 3d just isn’t enough. The easiest way to solve it is to just imagine 5 dimensions, and then subtract 1.
I’ve seen this before, but it’s still worth a laugh.
Gotta love that British Humor
