Street-fighting math from MIT
by rrusczyk, Feb 26, 2010, 6:50 PM
Among MIT's Open Courseware is some street-fighting mathematics, which consists of quick-and-dirty ways to avoid errors, make reasonable guesses, and find clever solutions. One excerpt I particularly like is this:
I think this is something a lot of people don't appreciate -- the top problem solvers are not necessarily the people who are best at finding the beautiful approaches quickly. They're often the people who can find any approach that works, which they may (or may not) then refine into the beautiful approach with more thinking. This is also one of the things I like about good math contest problems. The typical textbook problem is written with one solution method in mind. A good contest problem often has lots of successful approaches, and the interrelations between them can be illuminating, as well.
This is also a reason that our materials focus on the sausage getting made (the thought process we go through to find a solution) rather than the prepared meal (a polished solution) -- the latter is not nearly as illuminating, or as important, to the student who is trying to learn not the just the results, but how to produce results of their own.
Quote:
Here’s what friends who went to the US Math Olympiad training session told me they were taught: Find the answer by any cheap method that you can find; once you know, or are reasonably sure of the answer, you often can then find a more elegant method and never mention the original cheap methods.
I think this is something a lot of people don't appreciate -- the top problem solvers are not necessarily the people who are best at finding the beautiful approaches quickly. They're often the people who can find any approach that works, which they may (or may not) then refine into the beautiful approach with more thinking. This is also one of the things I like about good math contest problems. The typical textbook problem is written with one solution method in mind. A good contest problem often has lots of successful approaches, and the interrelations between them can be illuminating, as well.
This is also a reason that our materials focus on the sausage getting made (the thought process we go through to find a solution) rather than the prepared meal (a polished solution) -- the latter is not nearly as illuminating, or as important, to the student who is trying to learn not the just the results, but how to produce results of their own.
February 2012
January 2012