David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Teaching Philosophy 23 (2):169-187 (2000)
Newell and Simon’s seminal Human Problem Solving (1972) characterized a problem in terms of a goal state, a starting state, and a set of transition rules which define legitimate transitions from one state to another.1 Problem solving thus becomes a process of searching through a set of alternative states (the "problem space") in an effort to find a path leading from starting state to the goal state. The search process can be guided by heuristic principles which function to reduce the problem space by judging some alternatives to be more worthy of exploration than others. This characterization of a problem and the problem solving process fits well the nature of deductive proof construction. Premise(s) and conclusion play the role of starting state and goal state, and valid rules of transformation serve as rules of legitimate transition among states. In fact, Human Problem Solving empirically investigated three particular problem solving tasks, and one of these is proof construction.... in sentential logic using an inferencereplacement rule set. This empirical research identifies several strategies which facilitate problem solving, such as means-ends reasoning, difference reduction, and working backwards from goal toward starting state. As detailed below, these methods have obvious applications to proof construction as taught in logic textbooks. Newell and Simon’s aim was to explain and predict the actual behavior of problem solvers. Beyond this, however, their empirical findings have normative consequences for how problem solvers should behave if they want to be successful. Moreover, these findings can have normative pedagogical consequences for the teaching of proof construction.
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