Children’s Discrete Proportional Reasoning Is Related to Inhibitory Control and Enhanced by Priming Continuous Representations

Abstract

Children can successfully compare continuous proportions as early as age 4, yet struggle to compare discrete proportions least to age 10, especially when the discrete information is misleading. This study examined whether inhibitory control contributes to individual differences in discrete proportional reasoning and whether reasoning could be enhanced by priming continuous information. Forty-nine second-graders completed two tasks. In the Hearts and Flowers (H&F) task, a measure of inhibition, children pressed either on the corresponding or opposite side depending on the identity of the displayed figure. In the Spinners task, a measure of proportional reasoning, children chose the spinner with the proportionally larger red area, across continuous and two discrete formats. In the discrete adjacent format, the continuous stimuli were segmented into sections, which could be compatible with the proportional information or misleading; the discrete mixed format interspersed the colored sections from the discrete adjacent conditions. Finally, two priming groups were formed. Children who saw the continuous immediately before the discrete adjacent format formed the Continuous-priming group (n =26). Children who saw discrete mixed immediately before the discrete adjacent format formed the Discrete-priming group (n =23). Our results showed that children who performed better in the H&F task also had better performance on the discrete counting misleading trials. Furthermore, children in the Continuous-priming group outperformed children in the Discrete-priming group, specifically in contexts where discrete information was misleading. These results suggest that children’s proportional reasoning may be improved by fostering continuous representations of discrete stimuli and by enhancing inhibitory control skills.

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

“…While these results pointed towards the importance of semantic inhibition for rational number understanding, two recent studies have found that the Hearts and Flowers task, a developmentally appropriate measure of response inhibition (Wright & Diamond, 2014), also relates to rational number outcomes in children. Abreu-Mendoza, Coulanges, Ali, Powell, and Rosenberg-Lee (2020) found that better inhibitory control was related to better performance on a discrete proportional reasoning task, specifically when the number of segments conflicted with the correct response. Ren and Gunderson (2021) report that children with better inhibitory control displayed less use of an incorrect whole number strategy during a decimal comparison, training task, and also at post-test.…”

Testing the whole number interference hypothesis: contributions of inhibitory control and whole number knowledge to fraction understanding

“…A final question afforded by this data set was assessing the contribution of different measures of inhibitory control. Prior work has found associations between various Stroop tasks and rational number outcomes (Avgerinou & Tolmie, 2019;Coulanges et al, 2021;Gómez et al, 2015), and also the Hearts and Flowers task (Abreu-Mendoza et al, 2020;Ren & Gunderson, 2021). In fact, the Flanker task is the only measure of inhibitory control studied so far that has not been found to be associated with rational number performance (Matthews et al, 2016;Park & Matthews, 2021).…”

“…The majority of studies examining inhibitory control have found positive associations with rational number outcomes (Abreu-Mendoza et al, 2020;Avgerinou & Tolmie, 2019;Coulanges et al, 2021;Gómez et al, 2015;Ren & Gunderson, 2021), but not all (Matthews, Lewis, & Hubbard, 2016;Park & Matthews, 2021). Notably, Matthews et al (2016) found that inhibitory control was not related to performance on a non-symbolic fraction comparison task or to conceptual understanding of rational numbers, nor was it related to symbolic fraction comparison (Park & Matthews, 2021).…”

“…Although a handful of studies have looked at the role of working memory in fraction learning (Jordan et al, 2013), it is more frequently considered a control variable rather than a variable of interest (Bailey, Siegler, & Geary, 2014;Siegler et al, 2012). By contrast, a growing list of studies have examined correlations between inhibitory control and rational number comparison (Abreu-Mendoza, Coulanges, Ali, Powell, & Rosenberg-Lee, 2020;Avgerinou & Tolmie, 2019;Gómez, Jiménez, Bobadilla, Reyes, & Dartnell, 2015;Ren & Gunderson, 2021). Yet, these studies did not explicitly measure working memory.…”

“…Flanker task, studies that demonstrated relations with rational outcomes used variations of the Stroop task (Avgerinou & Tolmie, 2019;Coulanges et al, 2021;Gómez et al, 2015) or the Hearts and Flowers task (Abreu-Mendoza et al, 2020;Ren & Gunderson, 2021).…”