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

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...

[1]  John R. Anderson,et al.  Novice LISP Errors: Undetected Losses of Information from Working Memory , 1985, Hum. Comput. Interact..

[2]  John Sweller,et al.  Cognitive Load During Problem Solving: Effects on Learning , 1988, Cogn. Sci..

[3]  James G. Greeno,et al.  Theory of rule induction: Knowledge acquired in concept learning, serial pattern learning, and problem solving. , 1974 .

[4]  Kate Ehrlich,et al.  Cognitive strategies and looping constructs: an empirical study , 1983, CACM.

[5]  Stephen K. Reed,et al.  Modeling strategy shifts in a problem-solving task , 1976, Cognitive Psychology.

[6]  D. Klahr,et al.  Formal assessment of problem-solving and planning processes in preschool children , 1981, Cognitive Psychology.

[7]  John R. Anderson,et al.  Dynamic Student Modelling in an Intelligent Tutor for LISP Programming , 1985, IJCAI.

[8]  Kurt VanLehn,et al.  Felicity conditions for human skill acquisition: validating an ai-based theory , 1983 .

[9]  John R. Anderson,et al.  Cognitive principles in the design of computer tutors , 1984 .

[10]  G. Thomas.  Calculus and Analytic Geometry , 1953 .

[11]  George W. Ernst,et al.  GPS : a case study in generality and problem solving , 1971 .

[12]  Dorothea P. Simon,et al.  Expert and Novice Performance in Solving Physics Problems , 1980, Science.

[13]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[14]  J. Sweller,et al.  Effects of Subgoal Density and Location on Learning during Problem Solving. , 1982 .

[15]  Stephen K. Reed,et al.  Effect of the Problem Space on Subgoal Facilitation. , 1976 .

[16]  H. Simon,et al.  The functional equivalence of problem solving skills , 1975, Cognitive Psychology.

[17]  Stellan Ohlsson,et al.  Psychological evaluation of path hypotheses in cognitive diagnosis , 1988 .

[18]  John R. Anderson,et al.  The Geometry Tutor , 1985, IJCAI.

[19]  E. Hille,et al.  Calculus: One and Several Variables , 1971 .

[20]  William J. Clancey.  Methodology for building an intelligent tutoring system , 1987 .

[21]  P. Pirolli,et al.  The role of learning from examples in the acquisition of recursive programming skills. , 1985 .

[22]  H. Simon,et al.  Why are some problems hard? Evidence from Tower of Hanoi , 1985, Cognitive Psychology.

[23]  John R. Anderson.  The Architecture of Cognition , 1983 .

[24]  Allen Newell,et al.  The Prospects for Psychological Science in Human-Computer Interaction , 1985, Hum. Comput. Interact..