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

Mateusz Hohol,Hans-Christoph Nuerk,Bartosz Brożek,Klaus Willmes,Krzysztof Cipora,Edward Nęcka

doi:10.1038/s41598-020-68202-z

Abstract

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.

Highlights

Analogue magnitude is one of multiple mental representations of symbolic numbers, and the numerical distance effect (NDE) and the numerical size effect (NSE) constitute its primary instances. Even though these phenomena were previously revealed in various human cultures and age groups, as well as in non-human animals, there is no consensus about their relationship to mathematical skills
Engineers, social scientists, and the reference group, we found no between group differences in the NSE and the NDE
This observation allows us to infer that the professional training and practice of mathematicians does not change their analogue magnitude representation of numbers or alternatively, that possessing a specific type of magnitude representation does not foster mastering professional mathematical skills

Summary

Objectives

In the present study, we aim to investigate the relationship between two phenomena characterizing the analogue representation of number magnitude—namely, the NDE and the NSE—and the mathematical skills level operationalized in terms of formal education. To this end, we tested four groups of participants: professional mathematicians, engineers, social scientists, all at the level of advanced doctoral studies in their respective domain, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. Taking into account that previous studies provided a somewhat inconsistent picture of relationships between the analogue numerical magnitude representations and mathematical skills, as discussed earlier, it is hard to state directional hypotheses regarding the NDE and the NSE of professional mathematicians.

Methods

Discussion

Conclusion