Cognitive Processes in Preparation for Problem Solving

The aim of this study was to examine the role of a software tool in diagnosing student's thinking during problem solving in mathematics with 41 college students. Students were asked to select relevant steps, facts and strategies represented on the screen and connect them by arrows, indicating their plan of solution. Only after the diagram was completed, students were allowed to solve the problem. The findings are: (i) forward chaining is significantly more predominant, and backward chaining is significantly less frequent, compared to other possibilities or arrow entering. This result is unexpected, because classical planning methods produce backward chaining in this task. (ii) Students scoring in the middle are more likely to enter convergent pairs of arrows compared to students who scored low or high. This finding enables diagnosing student problem solving. Both findings imply constraints on selection of cognitive architectures used for modeling student problem solving.