If you’ve ever come up against a “maths wall”, you’ll know what I mean when I say you can spend hours, or even days, trying to get from one line in a proof to the next.
When you do eventually get there, and the proof makes sense, you pop the theorem or result into your pocket.
Then, you repeat.
After a while, the stuff you did earlier on gets a little hazy, so you go back to it when you have time and re-read the course notes, as well as your own (usually littered with exclamation marks, asterisks, smileys, and “this came from there”s).
I’m now finding, at “level three” with the OU (read “final year” undergrad) that stuff is coming in so thick and fast that my brain is simply being overwhelmed.
As mentioned in my previous post, I find myself relying on the results of a proof and, as a result, I’m clearly missing some “big picture”.
I’m impressed by people who follow a whole course and can piece bits together with some sort of invisible thread – theorem a leads to theorem b which, in this context, allows…. blah blah.
Meanwhile, I seem to be at the “isolated results” stage.
A maths teacher I know asked me how I’d solve a problem the other day. It was a case of glancing at it and going through a mechanical process to obtain the result.
Great, he said, but how did you know to do that?
Well, since blah is blah, then blah leads to blah…. I explained.
Of course, he said, with a puzzled look.
Somewhere along the line, he’d developed a knowledge gap – or rather, failed to address the gap.
I’m feeling the same at the moment.
Page by page, it all makes sense.
Bigger picture – not yet.
Certainly not yet, though I’m working on it.
And that’s the painful, frustrating bit, which leads to insecurity (on my part at least).
I’m not worried if a bigger picture connection will come up in the exam – I’m actually worried that I’ll look at the course notes (or even need them for work) in a few years time, and it will all be a mystery.