(no subject)

[noahgibbs]

When I was in junior high, first learning algebra, we learned the laborious rules where you add a three to both sides, or multiply the whole thing by seven, or distributed the "times four" to both sides of the sum in parentheses.

And we went through class exercises to remember them. One day we'd spend the whole time solving equations where you needed to subtract a number from each side to get the answer, the next day one where you had to multiply. Several weeks after that you had to put everything on one side of the equation and then use the quadratic formula.

And after learning enough of these things, I found them happening automatically. I'd copy the equation onto my paper and find that before I was even paying attention to it, I'd subtracted off the extra six, divided both sides by two and there was the answer. When it first happened, it was like magic -- I wasn't thinking about it, my pencil just kept moving until the answer popped out.

Did this happen to everybody, or just to me?

Comments

[queen-elvis.livejournal.com]

Happened to me. I don't have the math skillz like I have the verbal skillz, so I think being an automaton actually helped me in math classes.

[bellacrow.livejournal.com]

ugh, not I

I got put in Algebra before I was ready to handle abstract concepts and that soured the whole match experience for me, plus having a dad with a degree in math... *sigh*

[sui66iy.livejournal.com]

Yes, this is a normal part of the learning process. Cognitive psychologists who have spent time trying to understand the difference between experts and novices sometimes refer to this as developing a "schema". You also hear the phrases "compiling" and talk about a task become "automatic".

I suspect that one of the reasons that experts can be bad teachers is that so many aspects of a problem space have become automatic for them that they honestly can't remember/understand how a novice would see the problem. It's not just that solutions are obvious to the expert, it's that the obviousness comes from an unconscious deep understanding that really isn't articulable (to others or themselves).

One way to measure how automatic a process has become is to try to do multiple things at once. A good driver can easily hold a complex conversation while driving in difficult traffic; a new driver had better shut up and concentrate on the road.

I suspect one of the borders between being a "genius" and being a regular old expert is the ability to apply patterns compiled for one purpose to what appear to be completely different situations; this may be part of how great intuitive leaps are made. But at this point I'm just talking out of my ass.

[angelbob.livejournal.com]

Interesting. I need to find time to talk to you about this at some point. I'd noticed something similar, but since I was coming at it from a hypnotherapy background I was thinking of it quite differently.

"Schema" -- that works. It's good to have a word for that.

I've got some very different theories on genius that use the same ideas, but to some extent they're self-serving. I know, shocking. I'd want to actually talk to a genius before I came to any conclusions :-)

Anyway, yeah, the way I usually introduced this topic (for lack of the word "schema", really) was to start from the phrase "those who can, do, those who can't, teach" -- a related but different set of things. I'd argue that the best teachers effectively never develop a schema for an activity, or do so for their own use but also develop their non-schema abilities to uncommon levels. Anyway, that's a topic for another day.

Schema and Genius

[jd5p.livejournal.com]

I tend to think of a genius as a person for whom establishing abilities or schema comes fast. Like so fast it seems scary to others. My uncle grew up with a guy he described as a genius, every summer during school he would learn a new language, as in by the end of one summer he was fluent in Chinese. This could have come from having a fantastic memory, bordering on photographic.
I guess thinking about it a genius would also have to be adaptable to new situations where certain talents wouldn't seem to apply, yet they make them. So I guess I kinda agree with you.

Re: Schema and Genius

[angelbob.livejournal.com]

I suppose it would depend on the kind of genius. The ability to establish schema very fast would make for a very good language genius, tennis expert or marksman, as well as some kinds of mathematician. You would expect being able to break out of old schema (rather than form new ones) to be more useful to, say, a theoretical physicist, who will no doubt need to change them more often. Things don't usually stop being true in tennis as often as in quantum physics :-)

Though I suppose it depends on how you look at it. Maybe that would still be necessary in other disciplines, just to correct mistakes. Dunno.

Re: Schema and Genius

[sui66iy.livejournal.com]

Yeah, "genius" is such a fuzzy word that it seems almost meaningless. I would tend to reserve it for people who are highly innovative thinkers: it's not enough to think like everyone else, only faster. Geniuses in my mind redefine conceptual categories so that whole generations of super-smart-not-geniuses have work to do fleshing out all the ramifications.

But this is maybe Genius with a capital G. There's not much sense in sense in arguing over common usages. (Ob. Genius is like pornography: I know it when I see it.)

the power of the pencil

[shipofools999.livejournal.com]

Once I have learned it, I found I need the pencil to solve things. My math skills are much more powerful with a pencil and paper than by actually thinking.

~pirategrl