The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence

Abstract

This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing nonsymbolic 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, nonsymbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of nonsymbolic 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 nonsymbolic 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 nonsymbolic representation was explained by fluid intelligence, whereas at the end of elementary school, nonsymbolic representation predicted subsequent symbolic representation independently of fluid intelligence.