Dimensions of Heuristic Use in Mathematical Problem Solving: Evidence from Early Secondary School Students

Mathematical problem solving is a highly complex competence that needs to be supported throughout the learning process. This study examines the role of problem-solving heuristics among 73 sixth-grade students in a German secondary school (Gesamtschule). Specifically, we focus on the empirical relationship between the occurrence of heuristics, their suitability, and application, as well as their contribution to problem-solving success. To this end, we developed a heuristic training that introduced strategy keys (heuristic aid cards) accompanied by explanatory videos. By leveraging variations in the successful application of the heuristics between students and across multiple sessions (73 students in 4 training situations and 3 problems in a final test), we discover from regression models with student and task-fixed effects that a successful use of heuristics (i.e., an heuristic occurred, that heuristic had a high suitability regarding the problem, and it was applied correctly) leads to more successful mathematical problem solving. Regarding the underlying mechanism, we find that all dimensions of heuristic use (occurrence, suitability, and application of heuristics) are positively related to problem-solving success. When comparing the predictive capacity of all three aspects, we identified the correct application of heuristics as particularly conducive for better problem-solving success. In comparing the group of students with high to those with low initial math competence, we find no significant differences in the relationship between heuristic use and problemsolving success across achievement groups. Our results emphasize the crucial role of heuristic application in mathematical problem solving, which generally benefits students regardless of their overall math competence.