During lunch at work and when I don't have other stuff to do, I'm going through math on Khan Academy. I'm still brushing up on algebra before I get to the new stuff and I'm being constantly amazed at how much easier it is and how much more sense it makes than my memories of high school math.
I think math is taught, or at least was taught to me, as a process of rote memorization. I was taught the mechanical motions to go through to flip an equation around, then had to do 30 repetitions as homework to ensure it was memorized. I don't feel like I got a handle on theory.
That may be unfair; I don't know what mathematical instruction is really like in primary and secondary school, and maybe I just wasn't getting it. But as I've gone through the units on different forms of linear equations, for example, it feels like a completely different experience.
I can intuitively understand why one form is better than another for different purposes when expressing a two variable linear equation. I can flip them around with only a little mental arithmetic because I can picture the line they are describing as I think about moving numbers around. I can do four or five problems and, if I decide I understand it well enough, can move on to the next thing at my own pace.
I wish all students could be taught by tutors and have this kind of learning experience with someone who could move them ahead much faster than a generic process could.
On a side note, as I sit practicing with a pen and steno pad, I have a slide rule next to me for arithmetic and I'm becoming pretty confident with multiplication and division on it too! (In fact, the slide rule is the one in my user icon for this post. My simplest one, it's a Pickett Microline 120 in eye-saver yellow.)
I told a coworker what I was doing and he said it sounded like torture to him. Which is funny, but makes me a little sad about public perception of the nature and difficulty of these skills too.
