Cross-notation knowledge of rational numbers predicts fraction arithmetic.

Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered.

Aims: To examine the extent to which children's earlier knowledge of cross-notation magnitude predicted subsequent performance in fraction addition and subtraction as well as fraction multiplication and division longitudinally.

Sample: Three hundred and fifty-four Chinese children (M = 112.1 months).

Methods: During the first wave of assessment, a range of cognitive abilities of children were measured, including within-notation fraction and decimal magnitude comparisons, whole-number arithmetic fluency, non-verbal intelligence, attentive behaviours, counting recall, word-level reading, and phonological awareness. Twelve months later, the same children were assessed again with two tasks of fraction arithmetic: fraction addition and subtraction as well as fraction multiplication and division.

Results And Conclusions: Multiple linear regressions showed that within-notation fraction and decimal magnitude knowledge predicted fraction addition and subtraction longitudinally, after the effects of working memory, nonverbal intelligence, language skills, attentive behaviour, and whole-number arithmetic were controlled. Cross-notation magnitude knowledge made independent contributions to fraction addition and subtraction longitudinally beyond the influence of within-notation fraction and decimal magnitude knowledge and other covariates. However, within-notation fraction and decimal magnitude knowledge were not associated with fraction multiplication and division, whereas cross-notation magnitude knowledge remained a unique predictor. These findings suggest that it may be useful to incorporate cross-notation knowledge in the assessments of children's mathematics abilities and teaching.