Prior research has yielded mixed findings on whether learners’ certainty reflects veridical probabilities from observed evidence. We compared predictions from an idealized model of learning to humans’ subjective reports of certainty during a Boolean concept-learning task in order to examine subjective certainty over the course of abstract, logical concept learning. Our analysis evaluated theoretically motivated potential predictors of certainty to determine how well each predicted participants’ subjective reports of certainty. Regression analyses that controlled for individual differences demonstrated that despite learning curves tracking the ideal learning models, reported certainty was best explained by performance rather than measures derived from a learning model. In particular, participants’ confidence was driven primarily by how well they observed themselves doing, not by idealized statistical inferences made from the data they observed.

Piazza et al. reported a strong correlation between education and approximate number sense (ANS) acuity in a remote Amazonian population, suggesting that symbolic and nonsymbolic numerical thinking mutually enhance one another over in mathematics instruction. But Piazza et al. ran their task using a computer display, which may have exaggerated the connection between the two tasks, because participants with greater education (and hence better exact numerical abilities) may have been more comfortable with the task. To explore this possibility, we ran an ANS task in a remote population using two presentation methods: (a) a computer interface and (b) physical cards, within participants. If we only analyze the effect of education on ANS as measured by the computer version of the task, we replicate Piazza et al.’s finding. But importantly, the effect of education on the card version of the task is not significant, suggesting that the use of a computer display exaggerates effects. These results highlight the importance of task considerations when working with nonindustrialized cultures, especially those with low education. Furthermore, these results raise doubts about the proposal advanced by Piazza et al. that education enhances the acuity of the approximate number sense.