The semantic control network mediates the relationship between symbolic numerical order processing and arithmetic performance in children

Sommerauer, Gerrit; Graß, Karl-Heinz; Grabner, Roland H.; Vogel, Stephan

doi:10.1016/j.neuropsychologia.2020.107405

Cited by 24 publications

(30 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…been interpreted as evidence for the involvement of different cognitive processing mechanisms (Turconi et al, 2006;Vogel et al, 2015;Lyons et al, 2016). While the reverse distance effect has been related to multiple strategies such as long-term memory retrieval and sequential-procedural comparisons (Lyons et al, 2016;Sasanguie and Vos, 2018;Vogel et al, 2019;Sella et al, 2020;Sommerauer et al, 2020), the canonical distance effect has been associated to the mental representation of numerical quantities (Moyer and Landauer, 1967). Independent of the cognitive mechanisms that generate the reverse and the canonical distance effects, the present data support the view that both distance effects are unrelated with one another as we only found a small positive effect size correlation (see full correlation table in Supplementary Material) between the two indices (r positive-effect sample 0.11).…”

Section: Discussionmentioning

confidence: 99%

“…Several studies have confirmed the existence of a reverse distance effect in children (Lyons and Ansari, 2015;Vogel et al, 2015) as well as in adults (Franklin et al, 2009;Lyons and Beilock, 2011;Lyons and Beilock, 2013;Vogel et al, 2017;Vogel et al, 2019;Vos et al, 2017;Sella et al, 2020). And although the nature of the reverse distance effect is not well understood, some research indicates that it is associated with an effective retrieval mechanism of learned ordinal sequences from longterm memory (Lyons et al, 2016;Sasanguie and Vos, 2018;Vogel et al, 2019;Sella et al, 2020;Sommerauer et al, 2020). While items with larger distances might be solved via a sequential and procedural comparison process (e.g., 2 4 6 2 > 4 and 4 > 6), small distances (especially consecutive items) might be retrieved as sequence-lists (e.g., chunks, Dehaene et al, 2015) from long-term memory.…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

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

2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Retrieval from long-term memory and comparison play an important role in arithmetic performance (Campbell & Xue, 2001). As mentioned above and as indicated by several reviews and experimental studies, associative (or retrieval-based) strategies and comparison also play a role in ordinality (LeFevre & Bisanz, 1986;Lyons et al, 2016;Marshuetz & Smith, 2006;Rubinsten & Sury, 2011;Sasanguie et al, 2017;Sella et al, 2020;Sommerauer et al, 2020;Sury & Rubinsten, 2012;Vos et al, 2017). These strategies could potentially be driving the relation between ordinality and arithmetic performance.…”

Section: Introductionmentioning

confidence: 93%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Vos

Gevers

Reynvoet

et al. 2021

Quarterly Journal of Experimental Psychology

View full text Add to dashboard Cite

Understanding whether a sequence is presented in an order or not (i.e., ordinality) is a robust predictor of adults’ arithmetic performance, but the mechanisms underlying this skill and its relationship with mathematics remain unclear. In this study, we examined (a) the cognitive strategies involved in ordinality inferred from behavioural effects observed in different types of sequences and (b) whether ordinality is also related to mathematical reasoning besides arithmetic. In Experiment 1, participants performed an arithmetic, a mathematical reasoning test, and an order task, which had balanced trials on the basis of order, direction, regularity, and distance. We observed standard distance effects (DEs) for ordered and non-ordered sequences, which suggest reliance on magnitude comparison strategies. This contradicts past studies that reported reversed distance effects (RDEs) for some types of sequences, which suggest reliance on retrieval strategies. Also, we found that ordinality predicted arithmetic but not mathematical reasoning when controlling for fluid intelligence. In Experiment 2, we investigated whether the aforementioned absence of RDEs was because of our trial list composition. Participants performed two order tasks: in both tasks, no RDE was found demonstrating the fragility of the RDE. In addition, results showed that the strategies used when processing ordinality were modulated by the trial list composition and presentation order of the tasks. Altogether, these findings reveal that ordinality is strongly related to arithmetic and that the strategies used when processing ordinality are highly dependent on the context in which the task is presented.

show abstract

“…These different behavioural signatures indicate that possibly different strategies are used for different types of trial in the symbolic number ordering task. Accordingly, it has been suggested that "magnitude-based" processes are used with not-ordered triplets, whereas "memorybased" mechanisms used with ordered triplets (Lyons et al, 2016;Sommerauer et al, 2020;Vos et al, 2017;Vogel et al, 2019). When presented with a not-ordered triplet, participants can only compare the magnitude of the individual digits?…”

Section: Introductionmentioning

confidence: 99%

Symbolic Number Ordering and its Underlying Strategies Examined Through Self-Reports

Dubinkina

Sella

Reynvoet

2021

Journal of Cognition

View full text Add to dashboard Cite

Symbolic number ordering has been related to arithmetic fluency; however, the nature of this relation remains unclear. Here we investigate whether the implementation of strategies can explain the relation between number ordering and arithmetic fluency. In the first study, participants (N = 16) performed a symbolic number ordering task (i.e., "is a triplet of digits presented in order or not?") and verbally reported the strategy they used after each trial. The analysis of the verbal responses led to the identification of three main strategies: memory retrieval, triplet decomposition, and arithmetic operation. All the remaining strategies were grouped in the fourth category "other". In the second study, participants were presented with a description of the four strategies. Afterwards, they (N = 61) judged the order of triplets of digits as fast and as accurately as possible and, after each trial, they indicated the implemented strategy by selecting one of the four pre-determined strategies. Participants also completed a standardized test to assess their arithmetic fluency. Memory retrieval strategy was used more often for ordered trials than for non-ordered trials and more for consecutive than non-consecutive triplets. Reaction times on trials solved by memory retrieval were related to the participants' arithmetic fluency score. For the first time, we provide evidence that the relation between symbolic number ordering and arithmetic fluency is related to faster execution of memory retrieval strategies.

show abstract

The semantic control network mediates the relationship between symbolic numerical order processing and arithmetic performance in children

Cited by 24 publications

References 49 publications

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

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

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

Symbolic Number Ordering and its Underlying Strategies Examined Through Self-Reports

Contact Info

Product

Resources

About