The effect of contrasting cases during problem solving prior to and after instruction

Abstract

Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep features of the target content, which prepares them to better process the subsequent instruction. Unclear is whether this effect results from merely changing the order of the learning phases (i.e., instruction or problem solving first) or from additional features, such as presenting problem-solving material in the form of cases that differ in one feature at a time. Contrasting such cases may highlight the deep features and provide grounded feedback to students’ problem-solving attempts. In addition, the effect of the order of instruction and problem solving on procedural fluency is still unclear. The present experiment (N = 181, mean age = 14.53) investigated in a 2 × 2 design the effects of order (instruction or problem solving first) and of contrasting cases in the problem-solving material (yes/no) on conceptual understanding and procedural fluency. Additionally, the quality and quantity of students’ solution attempts from the problem-solving phase were coded. Regarding the learning outcomes, the ANOVA results suggest that for procedural fluency instruction prior to problem solving was more beneficial than problem solving prior to instruction. Merely delaying instruction did not increase conceptual understanding. The contrasting cases did not affect the quality of solution attempts, nor the posttest results. As expected, students who received instruction first generated fewer, but higher-quality solution attempts.