Visual perception can account for the close relation between numerosity processing and computational fluency.

Wei Wei,Xinlin Zhou,Chuansheng Chen,Jiaxin Cui,Yiyun Zhang

doi:10.3389/fpsyg.2015.01364

Abstract

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0–11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.

Highlights

The current study aimed to investigate the cognitive mechanism underlying the close relation between numerosity processing and arithmetic performance reported in previous studies
We first replicated the previous finding of a strong relation between numerosity processing and arithmetic performance
We further found that figure matching was more closely associated with numerosity comparison than were other types of cognitive processing

Summary

Introduction

Many previous studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance (e.g., Halberda et al, 2008; Libertus et al, 2011; Lyons and Beilock, 2011).Researchers have attributed this association to the fact that both tasks share approximate number or magnitude processing (e.g., Halberda et al, 2008).Cognitive correlates of computational fluencySome recent studies, have questioned the magnitude hypothesis (e.g., Inglis et al, 2011; Sasanguie et al, 2012, 2013; Vanbinst et al, 2012; Gilmore et al, 2013). Using a non-symbolic quantity processing task (i.e., spatially intermixed blue and yellow dots were presented on a computer screen for 200 ms, and subjects had to judge which color of dots was more numerous), Halberda et al (2008) found that 14year-old children’s performance on this task was correlated with scores on standardized mathematical achievement tests (Woodcock–Johnson revised calculation subtest and Test of Early Mathematics Ability) It should be noted, several studies have failed to find a significant association between numerosity processing and arithmetic performance (Rousselle and Noël, 2007; Holloway and Ansari, 2009; Price et al, 2012; Sasanguie et al, 2014). As Gilmore and colleagues (Gilmore et al, 2007) argued, that young children rely on their numerosity ability to learn symbolic mathematics

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