About why there is a shift from cardinal to ordinal processing in the association with arithmetic between first and second grade

Abstract

Digit comparison is strongly related to individual differences in children's arithmetic ability. Why this is the case, however, remains unclear to date. Therefore, we investigated the relative contribution of three possible cognitive mechanisms in first and second graders' digit comparison performance: digit identification, digit-number word matching and digit ordering ability. Furthermore, we examined whether these components could account for the well-established relation between digit comparison performance and arithmetic. As expected, all candidate predictors were related to digit comparison in both age groups. Moreover, in first graders, digit ordering and in second graders both digit identification and digit ordering explained unique variance in digit comparison performance. However, when entering these unique predictors of digit comparison into a mediation model with digit comparison as predictor and arithmetic as outcome, we observed that whereas in second graders digit ordering was a full mediator, in first graders this was not the case. For them, the reverse was true and digit comparison fully mediated the relation between digit ordering and arithmetic. These results suggest that between first and second grade, there is a shift in the predictive value for arithmetic from cardinal processing and procedural knowledge to ordinal processing and retrieving declarative knowledge from memory; a process which is possibly due to a change in arithmetic strategies at that age. A video abstract of this article can be viewed at: https://youtu.be/dDB0IGi2Hf8.

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

“…Interestingly, the effect of numeral ordering on arithmetic is “less contaminated” than the effect of magnitude processing (more than 38% of the total effect of magnitude processing on arithmetic was indirectly accounted by numeral ordering), which suggests that numeral ordering may be a more “unique” predictor in adults’ arithmetic. This supports Sasanguie and Vos () finding that a developmental shift from cardinality to ordinality may occur. That said, our findings also suggest that such shift should be interpreted with caution as both measures of cardinal representations and ordinal abilities might draw on a common magnitude‐based mechanism.…”

“…Such uniqueness should be further investigated. Finally, our findings add to recent research that fails to observe a significant relationship between the reverse distance effect and arithmetic (Sasanguie & Vos, ), which calls for further research on how numeral ordinality is measured.…”

“…Notably, the analysis does not reveal any indirect effect when the reverse effect is tested (i.e., performance on numeral ordering as predictor of mathematics achievement), which prompts the authors to claim that numeral ordering is at the core of the relationship between symbol number processing and arithmetic achievement. Sasanguie and Vos () have reported similar results with second‐grade children (numeral order was a full intermediator of the relation between numerical magnitude processing and arithmetic), and they argue that a developmental shift from symbol‐magnitude associations to symbol‐symbol associations may exist to explain differences in arithmetic achievement (numeral magnitude was a full intermediator of the relation between numerical order and arithmetic in first‐grade children).…”

“…In this vein, recent studies (see Lyons, Vogel, & Ansari, 2016, for a review) have demonstrated that ordering abilities relate to arithmetic skills in both children (Lyons & Ansari, 2015b;Lyons et al, 2014;Sasanguie & Vos, 2018) and adults (Goffin & Ansari, 2016;Lyons & Beilock, 2011;Sasanguie, Lyons, De Smedt, & Reynvoet, 2017;Vos, Sasanguie, Gevers, & Reynvoet, 2017). For instance, Goffin and Ansari (2016) have found that a reverse distance effect (along with task-related performance measures) in a numeral-ordering task is a robust predictor of math achievement (measured as a composite of two different math domains: calculation and arithmetic).…”

The Stability of Individual Differences in Basic Mathematics‐Related Skills in Young Children at the Start of Formal Education

“…There is now considerable evidence in support of a link between order‐processing skills and mathematical abilities. Although it appears that numerical ordering skills become particularly important from around the age of 6 or 7 (Attout & Majerus, ; Lyons, Price, Vaessen, Blomert, & Ansari, ; Sasanguie & Vos, ), there is also now emerging evidence in support of a role of nonnumerical ordering in mathematical development in the case of younger children (Attout, Noël, & Majerus, ; Morsanyi, van Bers, O'Connor, & McCormack, ; O'Connor, Morsanyi, & McCormack, ). Nonnumerical order processing measures can be broadly divided into two categories: those involving the retrieval of a familiar sequence from long‐term memory, such as the order of familiar daily events, familiar everyday sequences, the months of the year, or letters (Morsanyi, O'Mahony, & McCormack, ; O'Connor et al, ; Sasanguie, De Smedt, & Reynvoet, ; Vos, Sasanguie, Gevers, & Reynvoet, ), and those involving the retrieval of a novel, arbitrary sequence from short‐term memory (order working memory [WM] task; Attout & Majerus, , ; Attout et al, ).…”