Effects of instructions and representation on mathematical problem-solving

We investigated whether specific instructions have different representations for target problems, and hence whether task representations mostly affect the direction of typical errors in permutation problem-solving. We hypothesized that different instructions produce specific representations of a permutation problem in an identical description. The 39 participants were randomly assigned to the three groups: the equation instruction group, the subgoal instruction group, and the control group. Results confirmed our prediction that the treatment groups solved the problem more correctly than the control group. More importantly, a subgoal instruction (a set of steps in a meaningful task) decreased the typical mistakes. Educational implications are discussed.