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Understanding the relationship between symbolic numerical abilities and individual differences in mathematical competencies has become a central research endeavor in the last years. Evidence on this foundational relationship is often based on two behavioral signatures of numerical magnitude and numerical order processing: the  canonical  and the  reverse distance effect.  The  former  indicates faster reaction times for the comparison of numerals that are far in distance (e.g., 2 8) compared to numerals that are close in distance (e.g., 2 3). The latter indicates faster reaction times for the ordinal judgment of numerals (i.e., are numerals in ascending/descending order) that are close in distance (e.g., 2 3 4) compared to numerals that are far in distance (e.g., 2 4 6). While a substantial body of literature has reported consistent associations between the  canonical distance effect  and arithmetic abilities, rather inconsistent findings have been found for the  reverse distance effect . Here, we tested the hypothesis that estimates of the  reverse distance effect  show qualitative differences (i.e., not all participants show a  reverse distance effect  in the expected direction) rather than quantitative differences (i.e., all individuals show a  reverse distance effect , but to a different degree), and that inconsistent findings might be a consequence of this variation. We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.e., are three numerals presented in order or not), a paper pencil test of arithmetic fluency, as well as a standardized test to assess more complex forms of mathematical competencies. We found discriminatory evidence for the two distance effects. While estimates of the  canonical distance effect  showed quantitative differences, estimates of the  reverse distance effect  showed qualitative differences .  Comparisons between individuals who demonstrated an effect and individuals who demonstrated no  reverse distance effect  confirmed a significant moderation on the correlation with mathematical abilities. Significantly larger effects were found in the group who showed an effect. These findings confirm that estimates of the  reverse distance effect  are subject to qualitative differences and that we need to better characterize the underlying mechanisms/strategies that might lead to these qualitative differences.

frontiers in education

Quantitative and Qualitative Differences in the Canonical and the Reverse Distance Effect and Their Selective Association With Arithmetic and Mathematical Competencies