Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.

Verbal working memory load dissociates common indices of the numerical distance effect: Implications for the study of numerical cognition

In four experiments, we explore the role that verbal WM plays in numerical comparison. Experiment 1 demonstrates that verbal WM load differentially impacts the two most common variants of numerical comparison tasks, evidenced by distinct modulation of the size of the numerical distance effect (NDE). Specifically, when comparing one Arabic digit to a standard, the size of the NDE increases as a function of increased verbal WM load; however, when comparing two simultaneously presented Arabic digits, the size of the NDE decreases (and here is eliminated) as a function of an increased verbal WM load. Experiment 2, using the same task structure but different stimuli (physical size judgments), provides support for the notion that this pattern of results is unique to tasks employing numerical stimuli. Experiment 3 demonstrates that the patterns observed in Experiment 1 are not an artifact of the stimulus pairs used. Experiment 4 provides evidence that the differing pattern of results observed between Experiment 1 and Experiment 2 are due to differences in stimuli (numerical vs. non-numerical) rather than to other differences between tasks. These results are discussed in terms of current theories of numerical comparison.

Symbolic numerical distance effect does not follow the values of the numbers

In a comparison task, the larger the distance between the two numbers to be compared, the better the performance, a phenomenon termed the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In everyday number use the value of the numbers and the association between the numbers and the small-large categories strongly correlate, thus, the two explanations have the same predictions for the distance effect. To dissociate the two potential sources of the distance effect, in the present study participants learned new artificial number digits between 1 and 3, and between 7 and 9, thus, leaving out the numbers between 4 and 6. It was found that the omitted number range (the distance between 3 and 7) was considered in the distance effect as 1, and not as 4, suggesting that the distance effect does not follow the values of the numbers predicted by the dominant explanation, but it follows the small-large property association predicted by the alternative explanations.