The Reification of Goal Structures in a Calculus Tutor: Effects on Problem‐Solving Performance

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Abstract
In an initial experiment with a minimal version of a calculus tutor, it was determined through analyses of verbal protocol data that students were attempting to execute a fairly standard working‐backwards, means‐ends strategy to solve systems of equations, but were having difficulty maintaining the requisite goal stack. To remedy this problem, an enhancement to the interface of the tutor was designed which allowed students to post and display the subgoals required by the means‐ends strategy. As students progressed through problems, individual subgoals were boxed and shaded to indicate which subgoals were active and which had been satisfied, respectively. An experiment testing the effects of this type of goal posting showed that student problem‐solving performance improved in terms of both speed and accuracy while the goal blackboard was present. Furthermore, many of the positive effects persisted after the goal blackboard was taken away. Two explanations for the beneficial effects of goal posting are offered. The first is that the display served as external memory which maintained goal structures that would have otherwise been lost in the shuffle of problem solving. The second, perhaps more compelling explanation is that, in the process of posting goals, subjects learned something about the underlying structure of problems.

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