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J Learn Disabil. 2017 Nov/Dec;50(6):614-620. doi: 10.1177/0022219416662032. Epub 2016 Aug 4.

Fractions Learning in Children With Mathematics Difficulties.

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1 Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA.
2 Siegler Center for Innovative Learning, Beijing Normal University, China.


Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.


cross-national differences; fraction learning; mathematics difficulties

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