Talking to my friend Jack yesterday and he told me something about his experience with the Differential Equations class he took in college: it was all rote memorization. There are dozens of equations that apply to dozens of situations, and the class involved learning to identify the situation and picking the equation that best applies to it. For both of us that was a complete break from the way we had learned math up to that point, and for both of us, it was repellant.
A couple of months ago I was looking for a new card game and I thought of bridge, so I started looking into it. It seems to suffer from the same problem. The game has been analyzed down to the molecular level and everything there is to know has been discovered, so there is a rule for every situation. "Correct" play is similar to differential equations in that involves recognizing the situation and then picking out correct rule to follow. No real critical thinking involved.
It strikes me that there is large fraction of the population that thrives on this kind of thing, shoot, our civilization and the rule-of-law are based on this kind of thinking. Like everything else, people vary in how well they adapt to this. There are some people who have trouble with following rules of any kind, and then there are people who want a rule for everything and want everyone to follow all of the rules. Where the arguments come from is when people disagree on just how many rules we need.
Silicon Forest
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In fact the whole of maths is like a carpentry toolkit. The expert just chooses the correct tool for that (part of the) job. It's know what tools to use when, and in which order, that make you the expert ;-) See
http://home.egge.net/~savory//stus_blog_pix/stumble%20upon%20once%20a%20carpenter%20always%20a%20carpenter.jpg
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