What is it about?

We tested 3rd-5th graders’ estimation of integers and fractions on number lines and designed a training intervention to teach fractions by analogy to integers. We found that a short, online session of alignment between integers and fractions on number lines, for example, 3 on a 0 to 8 number line and 3/8 on a 0 to 1 number line, facilitates children’s knowledge of fractional magnitude to the level as good as college students. The training effect persisted when the analogical sources of integers desisted. Therefore, rather than being an obstacle to fraction learning, pre-existing integer knowledge can be a stepping stone to a better understanding of fractions with the power of good analogies.

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Why is it important?

Fractions are the gatekeeper to college-prep math courses, which are essential to educational and financial success. However, fractions are also notoriously difficult to learn. Our research showed that comparing integers and fractions on number lines helps children better understand fractions through a short session. Moreover, our intervention can be done from the comfort of children’s homes and can be easily scaled up to classroom settings. Theoretically, our results support the integrated theory of numerical development. The understanding of integers and fractions was not qualitatively different, rather, they interact with each other and become coherent over development.


This is my first paper with APA! And the process was not easy. When we were ready to launch the study, the pandemic hits, and schools were closed. We transited our training intervention to an online setting, and excitedly found that our short online training benefits children’s fraction learning! Thanks to my wonderful collaborators who made this project possible and were always so helpful and inspiring!

Shuyuan Yu
Ohio State University

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This page is a summary of: From integers to fractions: The role of analogy in developing a coherent understanding of proportional magnitude., Developmental Psychology, June 2022, American Psychological Association (APA), DOI: 10.1037/dev0001398.
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