# Recent & Upcoming Talks

### Individual differences and contextual influences on children’s attention to numerosity

We replicated our previous findings with the Attention to Number (AtN) task (Chan & Mazzocco, 2017; Mazzocco et al., 2020) findings with a more ethnically- and socioeconomically-diverse sample of children than reported previously, with a main effect of the Salience of competing features on the frequency of numerosity-based matches. We examined if developmental differences begin to emerge in primary school, by testing for effects of Age and Salience on frequency of numerosity-based matches among 5- to 8-year-olds, among whom main effects of Salience emerged without a main effect or interactions with Age. Finally, we modified the AtN task to maximize children’s opportunity to nominate numerosity-based matches, and found that prior results continue to replicate.

### The company a number keeps: Multiplicative processing of largely composite numbers

We examined whether there is increased inhibition for retrieving a factor for a specific number as its compositeness (how many unique factors it has) increases. We found this pattern in two factoring tasks for ‘table facts’ from the well-practiced 12x12 multiplication fact table, but not for other facts. This supports that factors may be represented as a ‘factor neighborhood’, but that these effects are complex.

### Erroneous estimation of the factorial function and improvement through calibration experiences

We attempted a first-ever replication (N = 140) of Tversky and Kahneman’s (1973) finding that people massively underestimate $8!$ under time pressure, and that this is moderated by presentation in descending order ($8\times7\times6\times5\times4\times3\times2\times1$; Median = $2,250$) vs. ascending order ($1\times2\times3\times4\times5\times6\times7\times8$; Median = $512$). We successfully replicated the massive underestimation but not a significant between-participants effect. However, we uniquely found a within-participants effect when participants answered both orders. After being shown calibration information (the correct value of either $6!$ or $10!$), participants’ subsequent estimates for $8!$ drastically improved, especially for $10!$. Our findings suggest that people’s underestimation may be (1) lessened by repeated estimates, and (2) greatly reduced by providing an upper-bound reference ($10!$). This may have implications for mathematics and computer science instruction.

### (In)flexibility in strategy choice when solving missing-operand algebra problems

We measured undergraduates’ time to solve missing-operand algebra problems (e.g., $x + 3 = 5$) and ‘decoded’ individual strategy choice by regressing on their time to verify arithmetic facts related to the direct, arithmetic pattern-matching strategy (e.g., $2 + 3 = 5$) and to the inverse algebraic transformation strategy (e.g., $5 – 3 = 2$). As validated by participant self-reports, we found individual differences in strategy preference (direct vs. inverse).