Disentangling the Mechanisms of Symbolic Number Processing in Adults’ Mathematics and Arithmetic Achievement

Abstract

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol‐magnitude associations), processing relative order of symbols (i.e., symbol‐symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots‐number word matching task—thought to be a measure of symbol‐magnitude associations (numerical magnitude processing)—a numeral‐ordering task that focuses on symbol‐symbol associations (numerical order processing), and a digit‐number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain‐general factors (intellectual ability, working memory, inhibitory control, and non‐numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults’ arithmetic skills build upon symbol‐magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.

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

“…In contrast to the canonical distance effect, inconsistent findings have been reported in the few studies that have investigated the correlative association between the reverse distance effect and arithmetic abilities. Some studies have found a negative (i.e., the smaller the reverse distance effect, the better arithmetic performance; Goffin and Ansari, 2016), while other studies have found a positive (i.e., the larger the reverse distance effect, the better arithmetic performance; Vogel et al, 2019) or no relationship at all (Orrantia et al, 2019;Vogel et al, 2015;Vogel et al, 2017;Vos et al, 2017). These findings are in contrast to the consistently positive correlations reported for the canonical distance effect.…”

“…Numerical order processing has been proposed as a significant predictor of arithmetic abilities (for a review see Lyons et al, 2016). However, research on the relationship between the reverse distance effect (i.e., as an index of numerical order processing) and arithmetic abilities has demonstrated mixed findings: some studies have found negative (Goffin and Ansari, 2016), positive (Vogel et al, 2019) or no relationship (Vogel et al, 2015;Vogel et al, 2017;Vos et al, 2017;Orrantia et al, 2019). In the present work, we provided evidence that the estimates of the reverse distance effect are subject to qualitative individual differences (i.e., not all participants show a reverse distance effect) and that these individual differences can obscure the relationship with arithmetic abilities.…”

Ordinality: The importance of its trial list composition and examining its relation with adults’ arithmetic and mathematical reasoning

“…In the second order task (balanced order task), regular, irregular, and non-ordered sequences were included. This task is similar to the task that was presented in Experiment 1 and resembles the tasks in some previous studies (Lyons & Beilock, 2009;Orrantia et al, 2019). We will refer to this order task as the balanced order task because regular and irregular trials were represented equally among the ordered trials.…”

“…In the order task, participants have to decide if a sequence is presented in an order or not. Results from previous studies have indicated that there is a strong relation between performance on the order task and arithmetic performance in both children (Attout & Majerus, 2017;Lyons & Ansari, 2015;Lyons et al, 2014;O'Connor et al, 2018O'Connor et al, , 2019Sasanguie & Vos, 2018;Sommerauer et al, 2020;Vogel et al, 2015) and adults (Goffin & Ansari, 2016;Lyons & Beilock, 2009;Morsanyi et al, 2017;Orrantia et al, 2019;Sasanguie et al, 2017;Sella et al, 2020;Vogel et al, 2017Vogel et al, , 2019Vos et al, 2017). However, the mechanisms underlying this relationship remain relatively underspecified.…”

Intellectual Contribution of Specialized Thesauruses to Cognitive Technologies

“…The role of cognitive graphics and its interpretation increases in various spheres of human activity. For example, in work [1] the option of identification of some mathematical abilities on the basis of the mechanism of the analysis of symbolical information is offered.…”