The role of attentional networks in the access to the numerical magnitude of fractions in adults / El rol de las redes atencionales en el acceso a la magnitud numérica de fracciones en adultos

Abstract

This study explored the relationship between the efficiency of alerting, orienting and executive control networks (attentional executive function) and accessing numerical magnitudes in adults, during a fraction comparison task, presenting pairs of fractions either with (CC) or without (WCC) common components. The results indicate that CC fractions are processed in a componential style, are affected by a whole number bias (WNB) and that performance in this block does not depend on the efficiency of attentional networks. By contrast, pairs of WCC fractions are processed in a holistic way, the WNB interacts with the numerical distance between fractions and performance in this block correlates with the efficiency of attentional orienting and executive control systems. Taken together, our findings show that the efficient selection of information and inhibitory control of intervening variables play an important role in processing fractions, particularly when the task requires the use of more holistic strategies to access the numerical magnitude of the fraction.

Various ways to determine rational number size: an exploration across primary and secondary education

“…The students' profiles obtained in the present study extend previous research on natural number bias, since the existence of other incorrect ways of thinking, such as gap thinking and reverse bias, indicates that the phenomenon of natural number bias is not the sole explanation for primary and secondary school students' difficulties in determining rational number size. In that sense, our results could explain the controversial results obtained in previous research, where incongruent items obtained higher levels of accuracy than congruent ones (Barraza et al 2017;DeWolf and Vosniadou 2015;Gómez et al 2015;Obersteiner and Alibali 2018;Obersteiner et al 2013).…”

“…This kind of reasoning may also explain the results of some previous studies where a better performance was found regarding incongruent items than congruent items (DeWolf and Vosniadou 2011Vosniadou , 2015Obersteiner et al 2013). Current research has taken into account these alternative ways of thinking about the size of fractions, having been observed in primary and secondary school students (Gómez and Dartnell 2018;Rinne et al 2017), and in adults (Barraza et al 2017;Fazio et al 2016;Obersteiner and Alibali 2018).…”

“…However, research results have not always pointed in the same direction. Studies with high performing students (Gómez et al 2015) and with experts in mathematics (Barraza et al 2017;DeWolf and Vosniadou 2015;Obersteiner and Alibali 2018;Obersteiner et al 2013) have shown higher levels of accuracy in incongruent items than in congruent items, especially in the case of fraction comparison. This raises questions as to whether the natural number bias actually explains all errors and it highlights the need to consider further explanations involving, for instance, some of the commonly used strategies for comparing fractions (Gómez et al 2017).…”

“…In this sense, this study intended to extend the results obtained by Gómez and Dartnell (2018) in their cluster analysis by including the gap condition and decimal number comparisons. Furthermore, we included a wide age range (from 5 th to 10 th grade) since the majority of the previous studies had shown that older students obtained opposite results regarding congruency (Barraza et al 2017;DeWolf and Vosniadou 2015;Obersteiner and Alibali 2018).…”

Comparing fraction magnitudes: Adults’ verbal reports reveal strategy flexibility and adaptivity, but also bias

“…How do people decide which of two fractions is larger? Although younger children often fail to compare even simple fractions accurately (Rinne et al, 2017), educated adults are usually quick and accurate, even when given challenging, unfamiliar fraction pairs (e.g., 31/71 vs. 13/23; Barraza et al, 2017;DeWolf & Vosniadou, 2015;Morales et al, 2020). However, it is unclear what strategies adults use to achieve their high performance in mental fraction comparison.…”