ISSN 1671-3710
CN 11-4766/R

Advances in Psychological Science ›› 2021, Vol. 29 ›› Issue (12): 2161-2171.

• Regular Articles •

### The relation between non-symbolic magnitude representation and symbolic fraction representation

MAO Huomin1, LIU Qin2, LV Jianxiang2, MOU Yi2

1. 1Zhu Hai Sun Yat-sen University Primary School, Zhuhai 519031, China;
2Department of Psychology, Sun Yat-sen University, Guangzhou 51006, China
• Received:2021-02-08 Online:2021-12-15 Published:2021-10-26

Abstract: A fundamental research question in numerical development concerns the relation between early emerging non-symbolic magnitude representation and symbolic numbers and mathematics learning. Especially, whether non-symbolic magnitude representation is a cognitive foundation for symbolic numbers and mathematic learning. Since early infants, one can represent the magnitude of a set of items (single magnitude) and the proportion between two magnitudes non-verbally (i.e., non-symbolic magnitude representation). Many of existing studies have examined the relation between non-symbolic representations for single magnitudes and symbolic number or mathematics learning. In contrast, few studies have investigated whether and how non-symbolic representations for the proportion between magnitudes relate with symbolic numbers or mathematics. Given that fraction is a critical concept of symbolic proportion, and it is an important concept taught in elementary mathematics, the present article reviewed and summarized studies on the relations between the representations for non-symbolic proportions and symbolic fractions. Previous studies showed that the precision of individuals’ non-symbolic magnitude representations for proportions were correlated with the precision of representations for symbolic fractions. In addition, both non-symbolic proportions and symbolic fractions activate some common brain regions, suggesting their common neural foundations. However, these correlational findings may not necessarily mean that non-symbolic magnitude representations for proportions provide a cognitive foundation for learning of symbolic fractions. First, when examining the relation between representations for non-symbolic proportions and symbolic fractions, most of existing studies did not rigorously control for general cognitive abilities. Therefore, it is not clear if non-symbolic proportion representations are uniquely correlated with symbolic fraction representations. Second, while most studies found the concurrent correlations between non-symbolic proportion and symbolic fraction representations, little has been done to examine if the two are related longitudinally. Third, besides demonstrating the correlations, more studies are needed to reveal how symbolic fraction representations are built on non-symbolic proportion representations. These discussions are also informative for mathematics education.

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