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I haven't had much time to write about problem solving, etc. lately, but something over at MyBiasedCoin caught my eye. The author asks whether it's a good idea to have a problem archive containing exam questions and solutions. (The exams would actually be drawn from the archive.) Several people, myself included, replied that it would be a good idea to have both problems and solutions. However, the author doesn't think including solutions is a good idea, because he feels that it's more important for students to think about CS theory problems the right way. If you've been following me over the past few years, you can imagine what my reaction to this was. (I don't disagree, but I still think making solutions available is helpful for students so they don't get stuck.) He hasn't replied yet, and perhaps he won't, but I hope some others respond. I'm particularly interested in hearing from people who can describe their "acquisition process" of CS theory – if they encountered any difficulties, how they worked through them, etc. Were they ever tested before working through their difficulties, and did they get lower grades than they'd hoped?

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( 1 comment — Leave a comment )
(Anonymous)
Jul. 28th, 2009 05:42 pm (UTC)
Against closed databases of problems
In order to advance the mathematical art, problems and their should be made available. If a student memorizes the solution to 500 problems, does he then gain an unfair advantage over his peers in solution of the Riemann hypothesis or in understanding the values of the zeta function at odd arguments or in settling P=NP?

The advice to students never to look at solutions before attempt to solve a problem is exactly reversed for researchers: always look at the solutions before attempting to solve a research problem.

Educators have to manage three kinds of cognitive load: intrinsic, which measures the degree of interrelatedness between items; extraneous, which interferes with learning by cluttering short-term memory (think of that biography of Riemann in the sidebar of any calculus text); and germane load, which leads to the formation of schemas (long term memories which aid in perception, thinking and problem solving).

Having a library of solved problems available would help to reduce the cognitive load of students and researchers. Instructors keep problem solutions secret because they do not want to have to change their comfortable routines.
( 1 comment — Leave a comment )

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