Number line compression and the illusory perception of random numbers

Influence of surprise on reinforcement learning in younger and older adults

Surprise is a key component of many learning experiences, and yet its precise computational role, and how it changes with age, remain debated. One major challenge is that surprise often occurs jointly with other variables, such as uncertainty and outcome probability. To assess how humans learn from surprising events, and whether aging affects this process, we studied choices while participants learned from bandits with either Gaussian or bi-modal outcome distributions, which decoupled outcome probability, uncertainty, and surprise. A total of 102 participants (51 older, aged 50-73; 51 younger, 19-30 years) chose between three bandits, one of which had a bimodal outcome distribution. Behavioral analyses showed that both age-groups learned the average of the bimodal bandit less well. A trial-by-trial analysis indicated that participants performed choice reversals immediately following large absolute prediction errors, consistent with heightened sensitivity to surprise. This effect was stronger in older adults. Computational models indicated that learning rates in younger as well as older adults were influenced by surprise, rather than uncertainty, but also suggested large interindividual variability in the process underlying learning in our task. Our work bridges between behavioral economics research that has focused on how outcomes with low probability affect choice in older adults, and reinforcement learning work that has investigated age differences in the effects of uncertainty and suggests that older adults overly adapt to surprising events, even when accounting for probability and uncertainty effects.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Examining the presence and determinants of operational momentum in childhood

The operational momentum (OM) effect describes a systematic bias in estimating the outcomes of simple addition and subtraction problems. Outcomes of addition problems are overestimated while outcomes of subtraction problems are underestimated. The origin of OM remains debated. First, a flawed uncompression of numerical information during the course of mental arithmetic is supposed to cause OM due to linear arithmetic operations on a compressed magnitude code. Second, attentional shifts along the mental number line are thought to cause OM. A third hypothesis explains OM in 9-month olds by a cognitive heuristic of accepting more (less) than the original operand in addition (subtraction) problems. The current study attempts to disentangle these alternatives and systematically examines potential determinants of OM, such as reading fluency which has been found to modulate numerical-spatial associations. A group of 32 6- and 7-year-old children was tested in non-symbolic addition and subtraction problems, in which they had to choose the correct outcome from an array of several possible outcomes. Reading capacity was assessed for half of the children while attentional measures were assessed in the other half. Thirty-two adults were tested with the identical paradigm to validate its potential of revealing OM. Children (and adults) were readily able to solve the problems. We replicated previous findings of OM in the adults group. Using a Bayesian framework we observed an inverse OM effect in children, i.e., larger overestimations for subtraction compared to addition. A significant correlation between children's level of attentional control and their propensity to exhibit OM was observed. The observed pattern of results, in particular the inverse OM in children is hard to reconcile with the previously proposed theoretical frameworks. The observed link between OM and the attentional system might be interpreted as evidence partially supporting the attentional shift hypothesis.

Spatial intuition in elementary arithmetic: a neurocomputational account

Elementary arithmetic (e.g., addition, subtraction) in humans has been shown to exhibit spatial properties. Its exact nature has remained elusive, however. To address this issue, we combine two earlier models for parietal cortex: A model we recently proposed on number-space interactions and a modeling framework of parietal cortex that implements radial basis functions for performing spatial transformations. Together, they provide us with a framework in which elementary arithmetic is based on evolutionarily more basic spatial transformations, thus providing the first implemented instance of Dehaene and Cohen's recycling hypothesis.