Prior math achievement and inventive production predict learning from productive failure

A frequent concern about constructivist instruction is that it works well, mainly for students with higher domain knowledge. We present findings from a set of two quasi-experimental pretest-intervention-posttest studies investigating the relationship between prior math achievement and learning in the context of a specific type of constructivist instruction, Productive Failure. Students from two Singapore public schools with significantly different prior math achievement profiles were asked to design solutions to complex problems prior to receiving instruction on the targeted concepts. Process results revealed that students who were significantly dissimilar in prior math achievement seemed to be strikingly similar in terms of their inventive production, that is, the variety of solutions they were able to design. Interestingly, it was inventive production that had a stronger association with learning from PF than pre-existing differences in math achievement. These findings, consistent across both topics, demonstrate the value of engaging students in opportunities for inventive production while learning math, regardless of prior math achievement.