The Role of Approximate Number System in Different Mathematics Skills Across Grades

Abstract

Although approximate number system (ANS) has been found to predict mathematics ability, it remains unclear if both aspects of ANS (symbolic and non-symbolic estimation) contribute equally well to mathematics performance and if their contribution varies as a function of the mathematics outcome and grade level. Thus, in this study, we examined the effects of both aspects of ANS on different mathematics skills across three grade levels. Three hundred eleven children (100 children from kindergarten, 107 children from Grade 2, and 104 children from Grade 4) from two kindergartens and three elementary schools in Shanghai, China, were assessed on measures of ANS (dot estimation and number line estimation), general cognitive ability (nonverbal intelligence, inhibition, and working memory), and mathematics abilities (numerical operations and mathematical problem solving in all grades, early mathematical skills in kindergarten, and calculation fluency in Grades 2 and 4). Results of hierarchical regression analyses showed that, in kindergarten, non-symbolic estimation predicted all mathematics skills even after controlling for age, gender, and general cognitive ability. In Grades 2 and 4, symbolic estimation accounted for unique variance in mathematical problem solving, but not in calculation fluency. Symbolic estimation also predicted numerical operations in Grade 4. Taken together, these findings suggest that in the early phases of mathematics development different aspects of ANS contribute to different mathematics skills.

Examining the relation between PASS cognitive processes and superior reading and mathematics performance

“…To date, the majority of studies on the relationship between PASS scores with reading and mathematics performance have been conducted either with typically developing children (e.g., Cai et al, 2018;Das et al, 2008;Georgiou et al, 2015;Kroesbergen et al, 2010;Papadopoulos, 2001;Wang et al, 2012) or with children experiencing reading or mathematics disabilities (e.g., Cai et al, 2013;Das et al, 2007;Iglesias-Sarmiento & Deaño, 2011;Joseph et al, 2003;Kroesbergen et al, 2003). For example, in a study with Grade 3 English-speaking children, Das et al (2007) reported that the probability of a child being a poor reader if his or her standard score in successive processing was below 80 was 0.76.…”

Mathematics Competence Level: The Contribution of Non-symbolic and Spatial Magnitude Comparison Skills

“… Bonny and Lourenco (2012) found that preschoolers (3–5 years of age) with more precise number representations were generally more mathematically competent, as assessed by a standardized test of early math achievement. However, results in this area vary ( Feigenson et al, 2013 ; Kroesbergen and Leseman, 2013 ) and not all studies have found significant links between non-symbolic number performance and mathematics achievement in children (e.g., Vanbinst et al, 2012 ; Kroesbergen and Leseman, 2013 ; Sasanguie et al, 2013 ). These differences in research findings could be related to the kind of tasks used to assess comparison skills.…”

“…The ANS is a pre-linguistic cognitive system for representing and processing quantity information and has received a great deal of attention in recent years ( Dehaene, 1997 ; Cantlon et al, 2009 ; Gallistel, 2011 ; Gilmore et al, 2014 ; Leibovich et al, 2017 ; Peng et al, 2017 ; Cai et al, 2018 ; Odic and Starr, 2018 ). The ANS supports the representation and processing of different magnitudes ( Cantlon et al, 2009 ) and according to Dehaene (1997) , it is a universal system present in animals, children, and adults.…”

“…From the first perspective, Cai et al (2018) examined the effects of symbolic (number line task) and non-symbolic estimation (point comparison task) on mathematics skills across three grade levels (kindergarten, children from grade 2, and children from grade 4). Their results showed that in kindergarten, non-symbolic estimation predicted all early mathematics skills while in grades 2 and 4, symbolic estimation accounted for unique variance in mathematical problem solving, but not in calculation fluency.…”

“…Given the interest in the results of previous research ( Agrillo et al, 2013 ; Cai et al, 2018 ; Kucian et al, 2018 ), and that Cai et al (2018) found different performance in kindergarten and primary school, it would be useful to analyze the task set in McCaskey et al (2017) in children younger than 6 years old and compare the results with those from Kucian et al (2018) in older students between 8.2 and 12.9 years of age.…”