Abstract
Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in China (n = 71) and had substantially higher levels of mathematical skill compared to the other group who was educated in Canada (n = 68). Both groups completed a variety of symbolic number tasks, including measures of cardinal number knowledge (number comparisons), ordinal number knowledge (ordinal judgments) and arithmetic fluency, as well as other mathematical measures, including number line estimation, fraction/algebra arithmetic and word problem solving. We hypothesized that Chinese-educated individuals, whose mathematical experiences include a strong emphasis on acquiring fluent access to symbolic associations among numbers, would show more integrated number symbol knowledge compared to Canadian-educated individuals. Multi-group path analysis supported the hierarchical symbol integration hypothesis. We discuss the implications of these results for understanding why performance on simple number processing tasks is persistently related to measures of mathematical performance that also involve more complex and varied numerical skills.
Highlights
Symbolic number knowledge is strongly related to mathematical performance for both children and adults
Lyons, Price, Vaessen, Blomert, and Ansari (2014) found that symbolic ordinal judgments were the best predictor of arithmetic for children in Grades 3 through 6, whereas in Grades 1 and 2, number comparison was the best predictor. These results suggest that the ordinal judgment task captures an even more critical set of individual differences in symbolic number knowledge than does the number comparison task (Lyons, Vogel, & Ansari, 2016)
We proposed a Hierarchical Symbol Integration (HSI) model for numerical associations and tested the model by contrasting mathematical performance of more- and less-skilled adults
Summary
Symbolic number knowledge is strongly related to mathematical performance for both children and adults. The underlying assumption of the HSI model is that various symbolic number associations become progressively more integrated as mathematical skill increases (Deacon, 1997; Hiebert, 1988; Werner, 1957) Such number integration can be viewed as a process of combining subsets of associations (e.g., cardinal and ordinal knowledge) to construct a higher-level understanding of number (Siegler & Chen, 2008). We evaluated this prediction by comparing two groups of adults who vary substantially in their arithmetic performance (i.e., Chineseversus Canadian-educated university students). Vanbinst et al (2016; see Rousselle & Noël, 2007) concluded that performance on the symbolic number comparison task is a central individual difference that can be used to understand children’s arithmetic learning; as important as phonological awareness is for understanding individual differences in reading (cf. Gillon, 2017)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
