Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement

Xenidou-Dervou, Iro; Molenaar, Dylan; Ansari, Daniel; Schoot, M. van der; Lieshout, E.C.D.M. van

doi:10.1016/j.learninstruc.2016.11.001

Cited by 47 publications

(39 citation statements)

References 68 publications

(140 reference statements)

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“…If that were the case, then similar developmental growth rates should be expected between symbolic and non-symbolic magnitude processing. Contrary to this assumption, a longitudinal study from kindergarten to second grade found that the two processes had different developmental trajectories; with symbolic processing showing greater developmental growth across the three grades as compared to non-symbolic processing (Xenidou-Dervou, Molenaar, Ansari, van der Schoot, & van Lieshout, 2017). In the same line, Matejko & Ansari (2016) found that the ANS acuity and symbolic task performance were significantly different at the first time point in kindergarten but those differences disappeared by the end of that year (i.e.…”

Section: Discussionmentioning

confidence: 93%

“…Other studies have found evidence for the scaffolding hypothesis, but only for certain ages and domains. A recent behavioral study showed that kindergarteners' ANS acuity predicted math achievement at the end of second grade (above and beyond IQ and WM abilities), but no longer for first or second graders (Xenidou-Dervou et al, 2017), suggesting that the ANS might have a time-specific role in building later math skills. Purpura and Logan (2015) reported that the ANS may scaffold math abilities only for lower skill children.…”

Section: Discussionmentioning

confidence: 99%

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Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

Suárez‐Pellicioni

Booth

2018

Human Brain Mapping

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The objective of this study was to investigate, using a brain measure of approximate number system (ANS) acuity, whether the precision of the ANS is crucial for the development of symbolic numerical abilities (i.e., scaffolding hypothesis) and/or whether the experience with symbolic number processing refines the ANS (i.e., refinement hypothesis). To this aim, 38 children solved a dot comparison task inside the scanner when they were approximately 10-years old (Time 1) and once again approximately 2 years later (Time 2). To study the scaffolding hypothesis, a regression analysis was carried out by entering ANS acuity at T1 as the predictor and symbolic math performance at T2 as the dependent measure. Symbolic math performance, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. In order to study the refinement hypothesis, the regression analysis included symbolic math performance at T1 as the predictor and ANS acuity at T2 as the dependent measure, while ANS acuity, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. Our results supported the refinement hypothesis, by finding that the higher the initial level of symbolic math performance, the greater the intraparietal sulcus activation was at T2 (i.e., more precise representation of quantity). To the best of our knowledge, our finding constitutes the first evidence showing that expertise in the manipulation of symbols, which is a cultural invention, has the power to refine the neural representation of quantity in the evolutionarily ancient, approximate system of quantity representation.

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Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

Suárez‐Pellicioni

Booth

2018

Human Brain Mapping

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“…In particular, the performance on this task has been supposed to index knowledge about the cardinality of the number symbol (i.e., the fact that the Arabic symbol “5″ refers to five items; Goffin & Ansari, ; Lyons & Beilock, ). In addition, numerous studies have consistently shown that individual differences in the performance on this digit comparison task are a robust predictor of individual differences in arithmetic ability (e.g., Budgen & Ansari, ; Castronovo & Göbel, ; De Smedt, Verschaffel, & Ghesquière, ; Göbel, Watson, Lervåg, & Hulme, ; Holloway & Ansari, ; Kolkman, Kroesbergen, & Leseman, ; Landerl & Kölle, ; Lyons, Price, Vaessen, Blomert, & Ansari, ; Moyer & Landauer, ; Mussolin, Meijas, & Noël, ; Sasanguie, De Smedt, Defever, & Reynvoet, ; Sasanguie, Göbel, Moll, Smets, & Reynvoet, ; Vanbinst, Ghesquière, & De Smedt, ; Vogel, Remark, & Ansari, ; Xenidou‐Dervou, Molenaar, Ansari, van der Schoot, & van Lieshout, ; for a review, see De Smedt, Noël, Gilmore, & Ansari, ; for a meta‐analysis, see Schneider et al., ). Moreover, studies investigating participants with mathematical learning difficulties have observed that they perform worse on a digit comparison task compared to control participants (Ashkenazi, Mark‐Zigdon, & Henik, ; Brankaer, Ghesquière, & De Smedt, ; De Smedt & Gilmore, ; Landerl, Bevan, & Butterworth, ; Landerl, Fussenegger, Moll, & Willburger, ; Rousselle & Noël, ; Vanbinst, Ghesquière, & De Smedt, ; for a meta‐analysis, see Schwenk et al., ).…”

Section: Introductionmentioning

confidence: 99%

“…Xenidou-Dervou, Molenaar, Ansari, van der Schoot, & van Lieshout, 2016; for a review, see De Smedt, Noël, Gilmore, & Ansari, 2013; for a meta-analysis, see Schneider et al, 2017). Moreover, studies investigating participants with mathematical learning difficulties have observed that they perform worse on a digit comparison task compared to control participants (Ashkenazi, Mark-Zigdon, & Henik, 2009;Brankaer, Ghesquière, & De Smedt, 2014;De Smedt & Gilmore, 2011;Landerl, Bevan, & Butterworth, 2004;Landerl, Fussenegger, Moll, & Willburger, 2009;Rousselle & Noël, 2007;Vanbinst, Ghesquière, & De Smedt, 2014; for a meta-analysis, see Schwenk et al, 2017).…”

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confidence: 99%

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

Sasanguie

Vos

2018

Developmental Science

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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.

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“…As mentioned above, while many studies have tried to identify which early predictors are important to numerical development, there is a relative lack of understanding as to the stability of these skills over time. Nevertheless, there are a few longitudinal studies that reported data regarding the stability of performance on some basic numerical tasks (e.g., Attout et al, ; Reeve, Reynolds, Humberstone, & Butterworth, ; Xenidou‐Dervou, Molenaar, Ansari, van der Schoot, & van Lieshout, ), the findings of which are summarized in Table . These results suggest that although performance on these tasks shows some consistency over time during the first school years, the strength of the correlations is generally weak to moderate, and sometimes even nonsignificant.…”

Section: Table Showing the Results Of Three Longitudinal Studies Regamentioning

confidence: 99%

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

O’Connor

Morsanyi

McCormack

2019

Mind Brain and Education

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The current study investigated the development of children's performance on tasks that have been suggested to underlie early mathematics skills, including measures of cardinality, ordinality, and intelligence. Eighty‐seven children were tested in their first (T1) and second (T2) school year (at ages 5 and 6). Children's performance on all tasks demonstrated good reliability and significantly improved with age. Correlational analyses revealed that performance on some mathematics‐related tasks were nonsignificantly correlated between T1 and T2 (number line and number comparison), showing that these skills are relatively unstable. Detailed analyses also indicated that the way children solve these tasks show qualitative changes over time. By contrast, children's performance on measures of intelligence and nonnumerical ordering abilities were strongly correlated between T1 and T2. Additionally, ordering skills also showed moderate to strong correlations with counting procedures both cross‐sectionally and longitudinally. These results suggest that, initially, mathematics skills strongly rely on nonmathematical abilities.

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Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement

Cited by 47 publications

References 68 publications

Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

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

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

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