The Hierarchical Symbol Integration Model of Individual Differences in Mathematical Skill


  • Chang Xu
  • Feng Gu
  • Katherine Newman
  • Jo-Anne LeFevre


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.