Abstract
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: thecanonicaland thereverse distance effect.Theformerindicates 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 thecanonical distance effectand arithmetic abilities, rather inconsistent findings have been found for thereverse distance effect. Here, we tested the hypothesis that estimates of thereverse distance effectshow qualitative differences (i.e., not all participants show areverse distance effectin the expected direction) rather than quantitative differences (i.e., all individuals show areverse 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 thecanonical distance effectshowed quantitative differences, estimates of thereverse distance effectshowed qualitative differences.Comparisons between individuals who demonstrated an effect and individuals who demonstrated noreverse distance effectconfirmed 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 thereverse distance effectare subject to qualitative differences and that we need to better characterize the underlying mechanisms/strategies that might lead to these qualitative differences.
Highlights
In the past years, there has been an increase in interest to better understand the cognitive foundation of symbolic numerical abilities and its relationship to arithmetic and mathematical competencies
Using data from a group of adults who performed a computerized numerical comparison task, a numerical order verification task, a paper-pencil test of arithmetic fluency, as well as a standardized measure assessing mathematical abilities, we tested the following hypotheses: 1) Is there a canonical and a reverse distance effect on the group level? Based on a large body of evidence we expected to replicate a) significant faster reaction times for large distances compared to small distances in the numerical comparison task, and b) significant faster reaction times for small distances compared to large distances in the correct order condition of the numerical order verification task
We provided evidence that the estimates of the reverse distance effect are subject to qualitative individual differences and that these individual differences can obscure the relationship with arithmetic abilities
Summary
There has been an increase in interest to better understand the cognitive foundation of symbolic numerical abilities and its relationship to arithmetic and mathematical competencies. Individual variations of these strategies could result in qualitative differences (e.g., some might use magnitude comparison mechanisms more often than others) that might have obscured the correlation of the reverse distance effect with arithmetic and mathematical abilities in previous studies Evidence to answer this question is extremely sparse, since existing studies have assumed a quantitative structure for the reverse distance effect (e.g., Goffin and Ansari, 2016; Vogel et al, 2017; Vogel et al, 2019). Using data from a group of adults who performed a computerized numerical comparison task, a numerical order verification task, a paper-pencil test of arithmetic fluency, as well as a standardized measure assessing mathematical abilities, we tested the following hypotheses: 1) Is there a canonical and a reverse distance effect on the group level? Based on a large body of evidence we expected to replicate a) significant faster reaction times for large distances compared to small distances in the numerical comparison task, and b) significant faster reaction times for small distances compared to large distances in the correct order condition of the numerical order verification task. 2) Are individual differences in the distance effects quantitative or qualitative? Based on our hypothesis described above, we expected that the best Bayesian model fit for the estimates of the reversed distance effect would be an unconstrained model (i.e., not all participants show a distance effect in the expected direction), while the best fit for the estimates of the canonical distance effect would be a positive-effect model (i.e., all individuals show a canonical distance effect, but to a different degree). 3) Do the model estimates of the reverse distance effect moderate the association with arithmetic and mathematical abilities? Based on our hypothesis, we expected that if the estimates of the reverse distance effect are subject to qualitative differences, the correlative association with arithmetic and mathematical abilities should be significantly larger in a selected group of individuals who truly show a reverse distance effect, in comparison to a group of individuals who show no evidence for a reverse distance effect
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