Saturday, August 7, 2010

Limits to Cognative Ability

In my experience in tutoring math and physics, and in my own experience in learning these subjects, there is something to be said for a disbelief in one's own ability as a prominent limiting factor in performance.

My high school math teacher once commented that "girls only think they are stupid at math because we spent two decades telling them them were stupid in it." And on some level I think he's right, of both girls and boys.
Think about the angst associated, among the general population, with the word "calculus." Yet I've watched people take the class and learn things and realized after all that it's not so bad.

About half the time, I would estimate, that I've tutored anyone who was decently intelligent and even people who were less so, it wasn't so much an innate inability to do a problem or grasp a concept that got in the way. It was more a thought, possessed by said person, that he or she just could not do the problem. If someone perceives that the problem is not doable, or that the work required to do the problem is too overwhelming, he or she won't do it. We're lazy, a bit. There is a requirement for some cognitive ability, but I think what counts even more is mental fortitude. That is the ability to push past the barriers of "wow this will be hard", or "I don't know where to start", and just starting, just trying something, just summing up what you do know and taking it a step at a time.

You've got to ignore the forest and look at the trees.

So of course, if you're told by your parents or your educators or society at large, that math is too hard for you and that you don't need it, you're going to get overwhelmed when you look at something and don't know where to start, and just assume it's you. If you don't see the importance of math, it's easy to stay stuck that way.

I wasn't a math person. And maybe I'm still not. There was a point in time after I graduated where I kept taking and re-taking the math section of the GRE, hoping to score high enough to score (pardon the pun) a part time teaching/tutoring job with Kaplan learning.  And even though I'm a math minor, I kept failing to get what I needed, because of the combination of not remembering a few math concepts adequately, making arithmetic mistakes because I hate it and can't focus on it, mis-reading a few problems here and there, and not finishing on time.  Over and over, my score improved but was still held back from the required 90% by one or two of each thing every time.  Those are limitations, perhaps on cognitive speed if not ability, of human error I can't seem to overcome, and of not having learned all the math concepts or to not remembering them well enough. Only two of those, lack of speed and propensity to human error, may be intrinsic to me, but can still to some degree be overcome with practice.
I am up 300 points from what I scored on the high school SAT in math.  I came to college seeing math as a subject I wasn't good at and didn't need, and I emerged a physics major.  Because of the physics major, I don't get overwhelmed by the forest anymore. It taught me to ignore that inner voice that worries about ability, (at least when it comes to academics) to ignore the arduous nature of the work, to pick out the things I do know and just start. I've tried to teach my tutees that process, and always the thing that sets the light bulb off is the observation that you know, there's a logic to it, a pattern, it's not really so bad if you just do it.

Organize, prioritize, and start.  That's what you have to do to "get" math and physics, at least enough to wade into it and determine if you really have what it takes. I am convinced that as many as half of college-material people who think they aren't good at math are limiting their full potential just because they think they can't do it.  Math angst denies math performance.  Another third of math trouble comes from being out of practice or never having gotten into the practice of thinking mathematically in the first place.   Plenty of people have trouble with calculus because they took pre-calculus multiple years ago.  So only one sixth of it is sheer talent, sheer cognitive ability. Of course, the ability to ignore the forest and look at the trees may be be a personality thing, associated with inherent ability. But the brain is very, very plastic, able to get good at difficult things through practice. Confidence in mathematics is a freeing process, that needs to take place for more individuals. The widest gulf separating people who are good at, and consequently, like math, from people who don't, is confidence.

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