Pathways to fraction learning

Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge

Ai Ye, Ilyse Resnick, Nicole Hansen, Jessica Rodrigues, Luke Rinne, Nancy C. Jordan

Research output: Contribution to journalArticle

10 Citations (Scopus)


The current study investigated the mediating role of number-related skills in the developmental relationship between early cognitive competencies and later fraction knowledge using structural equation modeling. Fifth-grade numerical skills (i.e., whole number line estimation, non-symbolic proportional reasoning, multiplication, and long division skills) mapped onto two distinct factors: magnitude reasoning and calculation. Controlling for participants’ (N = 536) demographic characteristics, these two factors fully mediated relationships between third-grade general cognitive competencies (attentive behavior, verbal and nonverbal intellectual abilities, and working memory) and sixth-grade fraction knowledge (concepts and procedures combined). However, specific developmental pathways differed by type of fraction knowledge. Magnitude reasoning ability fully mediated paths from all four cognitive competencies to knowledge of fraction concepts, whereas calculation ability fully mediated paths from attentive behavior and verbal ability to knowledge of fraction procedures (all with medium to large effect sizes). These findings suggest that there are partly overlapping, yet distinct, developmental pathways from cognitive competencies to general fraction knowledge, fraction concepts, and fraction procedures.

Original languageEnglish
Pages (from-to)242-263
Number of pages22
JournalJournal of Experimental Child Psychology
Publication statusPublished - 1 Dec 2016
Externally publishedYes


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