Abstract
This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing non-symbolic numerosity representations that refer to the Approximate Number System. To achieve this aim, we estimated the longitudinal relationships between accuracy in the Number Line (NL) test and “blue–yellow dots” test across elementary school children. Data from a four-wave longitudinal study involving schoolchildren in grades 1–4 in Russia and Kyrgyzstan (N = 490, mean age 7.65 years in grade 1) were analyzed. We applied structural equation modeling and tested several competing models. The results revealed that at the start of schooling, the accuracy in the NL test predicted subsequent accuracy in the “blue–yellow dots” test, whereas subsequently, non-symbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of non-symbolic representation on symbolic representation emerges after a child masters the basics of symbolic number knowledge, such as counting in the range of twenty and simple arithmetic. We also examined the extent to which the relationships between non-symbolic and symbolic representations might be explained by fluid intelligence, which was measured by Raven’s Standard Progressive Matrices test. The results revealed that the effect of symbolic representation on non-symbolic representation was explained by fluid intelligence, whereas at the end of elementary school, non-symbolic representation predicted subsequent symbolic representation independently of fluid intelligence.
Highlights
Considerable evidence suggests that the development of math competence is based on the ability to efficiently represent numerical magnitude information in symbolic formats and the acquisition of a symbolic number system (e.g., De Smedt et al, 2013; Schneider et al, 2017)
The “symbolic grounded problem,” which can be defined as the question of how symbolic number systems develop and how symbols acquire their meanings, has been extensively discussed
Some studies have found no close relationship between symbolic numerosity representations and Approximate Number System (ANS) at least at a young age (Matejko and Ansari, 2016), while other studies have demonstrated that in contrast to the “ANS hypothesis,” the acquisition of symbolic math skills may improve accuracy in non-symbolic representation, while the opposite links were non-significant (Mussolin et al, 2014)
Summary
Considerable evidence suggests that the development of math competence is based on the ability to efficiently represent numerical magnitude information in symbolic formats and the acquisition of a symbolic number system (e.g., De Smedt et al, 2013; Schneider et al, 2017). It is important to understand how the symbolic representation of numerosity develops and how symbols acquire their numerical meanings. This question is usually referred to as “the symbolic grounding problem” (e.g., Leibovich and Ansari, 2016). A widespread hypothesis posits that symbols acquire their meanings by being mapped onto pre-existed non-symbolic numerosity representations or an Approximate Number System (ANS). The ANS is usually defined as a system that allows individuals to perceive and approximately estimate numerosity without counting and using symbols (e.g., Feigenson et al, 2004; Dehaene, 2011). It has been postulated that the ability to represent and estimate numerosity in a symbolic format exists only in humans, whereas the ANS is evolutionarily ancient and innate. Cantlon and Brannon (2007) investigated non-symbolic arithmetic performance in monkeys and college students and found that the monkeys’ approximate mental arithmetic performance follows the same pattern as the students, who were tested using the same nonverbal addition task
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