The Central Executive Mediates the Relationship Between Children’s Approximate Number System Acuity and Arithmetic Strategy Utilization in Computational Estimation

Abstract

Studies investigating the relationship between working memory (WM) and approximate number system (ANS) acuity in the area of arithmetic strategy utilization are scarce. The choice/no choice method paradigm was used in the present study to determine whether and how ANS acuity and WM components affected strategy utilization. The results showed that the central executive (CE) mediated the relationship between ANS acuity and strategy utilization. Furthermore, quantile regression analyses revealed that the association between CE and strategy choice was robust from the first to highest quantile. Notably, the relationship between ANS acuity and strategy choice was significant at the median and higher quantiles (i.e., 0.5, 0.75, and 0.85 quantiles), but not significant at lower quantiles (i.e., 0.15 and 0.25 quantiles). These results suggest that domain-general skills play a crucial role in the relationship between children’s ANS acuity and mathematical ability. The impact of ANS acuity and CE on strategy choice was dependent on the distribution of the strategy utilization level. These results provide a further understanding of the utilization of cognitive strategies.

The relationship between number line estimation and mathematical reasoning: a quantile regression approach

“…On the one hand, they suggest that children who exhibited weaker mathematical reasoning also probably have limited calculation skills, which could explain a weaker relationship between both skills for the lower and intermediate quantiles as compared to the higher quantile. This explanation resembles the one proposed by Li et al, (2018) in reference to the approximate number system performance not being predictive of strategy choice in multiplication for the lower quantiles. Alternatively, Fuchs et al, (2020) propose that children who showed low and intermediate mathematical reasoning performance tend to approach word problems by adding the numbers presented on the problems, without engaging with mathematical reasoning.…”

“…However, statistical comparisons across quantiles are not reported. Furthermore, Li et al, (2018) found that approximate number system performance in fourth grade significantly predicted concurrent strategy choice on a double-digit multiplication task for median and high quantiles (50 th , 75 th and 85 th ), but not for lower performance (15 th and 25 th ), though statistical comparison between quantiles were not reported. Li et al, (2018) offer several possible interpretations for their findings.…”

“…Furthermore, Li et al, (2018) found that approximate number system performance in fourth grade significantly predicted concurrent strategy choice on a double-digit multiplication task for median and high quantiles (50 th , 75 th and 85 th ), but not for lower performance (15 th and 25 th ), though statistical comparison between quantiles were not reported. Li et al, (2018) offer several possible interpretations for their findings. They initially suggest that children with poorer strategy choice also show poorer approximate number system performance; this would mean that they have to rely on more general cognitive skills such as executive functions as a compensatory mechanism.…”

Approximate number system discrimination training for 7-8 year olds improves approximate, but not exact, arithmetics, and only in children with low pre-training arithmetic scores

“…Children chose the numerically greater collection well above chance; this suggests that while they may sometimes have been led astray by the numerically smaller collection having a larger total surface area, they could still succeed on a majority of trials. Some portion of the difference in performance across the stimulus sets could be due to the differing EF demands of the stimuli (Gilmore et al, 2013;Li et al, 2018 He, Zhou, Zhou, He, & Chen, 2015;Hollingsworth, Simmons, Coates, & Cross, 1991;Izard & Dehaene, 2008;Leibovich & Henik, 2013;Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004).…”

“…While some studies suggest that executive functions (EF) might serve as the underlying link between better ANS performance and better school mathematics performance (Gilmore et al, 2013;Li et al, 2018), some recent work has found the opposite to be true (i.e., that ANS precision and number language or number knowledge survive as the only unique predictors of school math ability while EF are not unique (Malone et al, 2020(Malone et al, , 2019Purpura & Logan, 2015). This is an area that will benefit from additional exploration.…”