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Working in the domain of intelligent tutoring systems, I have to prove (or disprove) that explicit teaching of high-level strategies will allow students to use learned strategies across different domains.

I implemented a tutorial system teaching the best way to add a sequence of natural numbers. The procedural knowledge here is being the addition process, and the higher level strategy is choosing the order of the numbers to add. Another tutorial system implemented is a system teaching the reduction of boolean expressions. The procedural knowledge here is the application of the different boolean reduction rules, and the higher level is the wise choice of the rules to apply to obtain an effective reduction with minimum steps.

Yet these two domains are too different to have the same strategies, unless we use very abstract terms (e.g. "start with the easy parts"). What I desperately seek is two rather simple teachable domains which would be different enough to have different procedural knowledge, yet similar enough to have a set of common explicit strategies. I guess the answer would be in the domain of physics and/or math. I could also examine "fake" domains, i.e., domains that exists solely to prove my point mentioned earlier.

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Nothing wrong with it at all. Welcome to the site! It would be nice, though, if you had some idea from which a respondent could start formulating an answer (like your physics and math, but more specific). Or if "fake"domains are okay, some parameters of those would be helpful as well. –  Chuck Sherrington Jul 23 '12 at 1:49
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What is wrong with the following 2 or 3 domains: addition, multiplication, and (maybe) matrix multiplication? For the first two you can exploit both associative and commutative laws, for the second you only have the associative law to help you. For all 3 domains you have a heuristic notion of size you can use to guide which terms to combine first, etc. Further, picking the optimal order in which to multiple matrices (of varying but compatible dimensions) is a well studied problem in computer science, with known hardness results. –  Artem Kaznatcheev Jul 23 '12 at 1:54
    
Did you include the Gauss anecdote when teaching the best way to add a sequence of natural numbers? –  bfrs Jul 23 '12 at 7:12
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I think "teaching of high-level strategies will allow students to use learned strategies across different domains" is the very rationale of mathematics. Math gives very good examples of both abstract strategies for solving problems across different domains and also specific, explicit strategies. You don't seem to want the abstract strategies, but if you change your mind on that, George Polya's How to Solve It is one of the best books on this topic.

Your other constraint is that the domains should be simple, otherwise differential equations or graph theory would be great examples of explicit solution strategies having applications across multiple domains.

I guess something that will meet your needs well is linear algebra and, in particular, solution strategies for systems of linear equations.

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