Individual differences in the development of children's arithmetic fluency from grades 2 to 3

Chang Xu*, Jo-Anne LeFevre, Sheri Lynn Skwarchuk, Sabrina Di Lonardo Burr, Anne Lafay, Judith Wylie, Helena P. Osana, Heather Douglas, Erin A. Maloney, Victoria Simms

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
23 Downloads (Pure)


In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 – 3 = 2), and multiplication (e.g., 5 x 3 = 15). Canadian children were assessed twice, in grade 2 and grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in grade 3, whereas addition fluency did not. In grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network.
Original languageEnglish
Pages (from-to)1067–1079
Number of pages13
JournalDevelopmental Psychology
Issue number7
Publication statusPublished - 01 Jul 2021

Bibliographical note

Funding Information:
Support for project was provided by the Social Sciences and Humanities Research Council (SSHRC) of Canada through an Insight Grant to Jo-Anne LeFevre, Erin A. Maloney, Helena P. Osana, and Sheri-Lynn Skwarchuk.

Publisher Copyright:
© 2021 American Psychological Association


  • Addition
  • Mathematics
  • Multiplication
  • Subtraction
  • Symbolic integration

ASJC Scopus subject areas

  • Demography
  • Developmental and Educational Psychology
  • Life-span and Life-course Studies


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