Individual differences in fraction arithmetic learning.

Published on Aug 1, 2019in Cognitive Psychology3.029
· DOI :10.1016/J.COGPSYCH.2019.04.002
David W. Braithwaite7
Estimated H-index: 7
(FSU: Florida State University),
Elena R. Leib2
Estimated H-index: 2
(University of California, Berkeley)
+ 1 AuthorsJake McMullen13
Estimated H-index: 13
(UTU: University of Turku)
Abstract Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA ( F raction A rithmetic R eflects R ules and A ssociations; Braithwaite, Pyke, and Siegler, 2017), to investigate individual differences in children’s fraction arithmetic. FARRA predicted four qualitatively distinct patterns of performance, as well as differences in math achievement among the four patterns. These predictions were confirmed in analyses of two datasets using two methods to classify children’s performance—a theory-based method and a data-driven method, Latent Profile Analysis. The findings highlight three dimensions of individual differences that may affect learning in fraction arithmetic, and perhaps other domains as well: effective learning after committing errors, behavioral consistency versus variability, and presence or absence of initial bias. Methodological and educational implications of the findings are discussed.
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