Empirical study The relation between ANS and symbolic arithmetic skills: The mediating role of number-numerosity mappings Terry Tin-Yau Wong a, *, Connie Suk-Han Ho b , Joey Tang c a Department of Psychological Studies, The Education University of Hong Kong, Hong Kong b Department of Psychology, The University of Hong Kong, Hong Kong c Society for the Promotion of Hospice Care, Hong Kong ARTICLE INFO Article history: Available online 10 June 2016 Keywords: Mathematical cognition Approximate Number System Number-numerosity mapping A B ST R AC T While recent meta-analyses have supported a positive relation between the Approximate Number System and math achievement (e.g., Chen & Li, 2014), the mechanism of this relation remains unclear. In this study, we examined whether the precision of mapping between number symbols and our representa- tion of numerosity accounts for the relation between the Approximate Number System and symbolic arithmetic skills. This precision of mapping was measured using numerical estimation tasks. A sample of 210 kindergarteners was tested on their Approximate Number System acuity. The subjects were tested two more times on their estimation skills and symbolic arithmetic skills when they were in Grade 1. Using the structural equation modelling, it was found that the number-numerosity mapping skills fully me- diated the relation between the Approximate Number System and symbolic arithmetic skills in a longitudinal model. It is suggested that higher acuity of the Approximate Number System facilitates the number- numerosity mapping process, which, in turn, brings about better symbolic arithmetic skills. The present findings suggest that the Approximate Number System and number-numerosity mapping may be some of the key domain-specific skills in mathematics learning. © 2016 Elsevier Inc. All rights reserved. 1. Introduction Humans are born with an ability to represent numerosity in a nonsymbolic manner (Feigenson, 2012; Izard, Sann, Spelke, & Streri, 2009; Xu & Spelke, 2000). This nonsymbolic numerosity represen- tation system, known as the Approximate Number System (ANS; Feigenson, Dehaene, & Spelke, 2004), has been proposed to be related to mathematics skills (e.g., Gilmore, McCarthy, & Spelke, 2010; Halberda, Mazzocco, & Feigenson, 2008), and recent meta-analyses confirmed the relation between the two (Chen & Li, 2014; Fazio, Bailey, Thompson, & Siegler, 2014; Schneider et al., 2016). However, what remains unclear is how this nonsymbolic ANS contributes to our mathematics skills, which are in exact symbolic form. While it has been suggested that the ANS provides the foundations for the association between number symbols and the quantities they rep- resent, which further allows the development of symbolic number knowledge (Geary, 2013), such possibility has not be explicitly tested. The current study was conducted to address this issue. Clarifying the mechanism behind this ANS-math relation would inform edu- cators about the effective strategies in teaching mathematics as well as the important skills that should be included in our mathemat- ics curriculum. 1.1. The Approximate Number System (ANS) In the précis of The Number Sense, Dehaene (2001) proposed that our ANS is biologically determined. It has a long evolutionary history, and certain parts of the brain are prewired for this ability. This is why infants and people from indigene cultures are able to process numerosity. It is suggested that numerosity is repre- sented in the brain in the form of a mental number line, and the representation is approximate (Feigenson et al., 2004). Some neu- rological findings further suggest that the ANS could be modelled as overlapping Gaussian distributions of activations on a logarith- mic scale (Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004). The logarithmic compression results in a greater degree of overlap- ping among activations of large numerosities and makes it more difficult for us to discriminate between large numerosities that differ by the same numerical distance. This compression also suggests that to discriminate two numerosities, it is the ratio of the two numerosities instead of the actual magnitudes that matters (i.e., numerosities cannot be reliably discriminated unless the ratio between them is large enough). These characteristics are the hall- mark of Weber’s Law. The width of these Gaussian distributions of activations, which determines the degree of overlap of different * Corresponding author at: Rm 24, 2/F, D1, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong. E-mail address: terrytywong@gmail.com (T.T.-Y. Wong). http://dx.doi.org/10.1016/j.cedpsych.2016.06.003 0361-476X/© 2016 Elsevier Inc. All rights reserved. Contemporary Educational Psychology 46 (2016) 208–217 Contents lists available at ScienceDirect Contemporary Educational Psychology journal homepage: www.elsevier.com/locate/cedpsych