The investigation of mathematical and related cognitive skills among adults

Abstract

Numbers can be seen everywhere. We perform symbolic operations (e.g. addition, subtraction, multiplication, and division) using exact numbers. One the other hand, we detect non-symbolic representations (e.g. comparing two arrays of dots) using approximate numbers with intuitive estimation. This cognitive system involved is often referred to as the approximate number system (ANS). ANS gives us an intuitive sense of numbers and the relations between numerical quantities. While some studies have shown significant relation between arithmetic performance and ANS performance in children, adolescents, and adults (Elliott et al., 2018; Libertus et al., 2011; Odic et al., 2016; Wang et al., 2017), others have shown a negligibly small or absent linkage (Guillaume et al., 2013; Inglis et al., 2011; Price et al., 2012). In a typical ANS comparison task, two arrays of dots are presented briefly to participants for judging which array contains a higher numerosity. Different task trial types (e.g. higher numerosity with larger accumulated dot area vs. lower numerosity with larger accumulated dot area) are used to prevent participants from relying on one visual cue. However, there is still a possibility of participants’ ANS performance being influenced by a competition between numerical and nonnumerical cues. To gain a better understanding on the relation between precise and approximate numerical abilities, studies have started a deeper investigation by separating the trial types used in the ANS task. Since mathematical learning has been suggested to involve patterns, this study took the first step in the literature to empirically examine whether there was a relation between mathematical skills and statistical learning (SL). Such learning allows us to unconsciously extract and represent regularities or patterns upon repeated exposures. A comprehensive analysis was conducted on participants' precise numerical performance and their ANS performance across different trial types and lengths in the ANS task. In this study, thirty-two adults (16 males and 16 females) participated. The average age of the participants was 23.5 years (SD = 3.86). Participants were tasked to complete a standardized nonsymbolic numerosity comparison task, a standardized math fluency test, and a regularity discrimination task. Results showed a nonsignificant correlation between participants’ arithmetic performance and ANS performance. However, by analyzing participants’ performance in different trial types, a significant correlation was found between participants’ SL ability and ANS performance in the Unequal Average Dot Size trials. By further analyzing participants’ performance in the first half and second half of the trial types, significant correlations between SL ability and ANS performance were found in the second half of the Equal Average Dot Size trials, and in the second half of the Unequal Average Dot Size trials. Meanwhile, participants’ performance in the first half of the Unequal Average Dot Size trials was found to be significantly correlated with their arithmetic performance. This study provided a comprehensive analysis on participants' precise numerical performance and their ANS performance across different trial types and lengths in the ANS task. The relation between participants’ ANS performance and their regularity discrimination ability was also explored.