Productive failure (PF) is a learning paradigm that reverses the standard order of instruction by asking students to solve problems prior to instruction. This paradigm has been shown to be effective for fostering student learning. To date, however, the role of student emotion in productive failure has not been investigated. In other paradigms, there is some evidence that failure elicits negative emotions and that these emotions can interfere with learning. This leads to a conundrum given productive failure’s positive effect on learning. To shed light on this, we report on results from a study (N = 48) in the productive failure paradigm. For the analysis, we used a mixed-methods approach to investigate the distribution of emotions in productive failure, how these changed across different instructional activities, and the relation between emotions and posttest performance.

We use the computational Bayesian learning model in Piantadosi, Tenenbaum, and Goodman (2012) to explore how different combinations of cognitive primitives and frequency distributions affect the learning of natural numbers. We find that the model converges on the natural numbers through attested developmental stages only under very restricted sets of primitives and frequency distributions. Assuming the size principle familiar from Bayesian approaches to inductive generalization, it would be natural to conclude that there are sharp constraints on the primitives out of which humans build natural numbers, some of which we hope to elucidate below.