How do contrasting cases and self-explanation promote learning? Evidence from fraction division

Past research has shown that both contrasting cases instruction and prompts to self-explain promote students' learning in mathematics. However, it is not clear whether these instructional approaches enhance learning through similar mechanisms or whether each supports learning in distinct ways. The purpose of this study was to investigate the unique and combined effects of comparison, defined as noticing similarities and differences, and explanation, defined as making sense of problems, on student learning, and to assess whether these processes are more effective when combined than when implemented separately. We also investigated potential mechanisms involved in comparison and explanation. We addressed these issues in the domain of fraction division. Prompts to self-explain promoted conceptual learning, but inviting comparison, without prompts to self-explain, did not. The quality of students' self-explanations was affected by both prompts to self-explain and encouragement to compare. The findings suggest that contrasting cases instruction is effective, at least in part, because it typically involves self-explanation.