Abstract
Early knowledge of fractions can largely predict later mathematical performance, and a comprehensive and in-depth understanding of fractions is fundamental to learning more advanced mathematics. The study aimed to explore the influencing factors and age characteristics of magnitude representations of fractions by a fraction comparison task, using subjects’ eye-movement measures as direct evidence and the results of linear regression analyses as indirect evidence. The results found that the number of digits of fractions’ components and types of fraction pairs jointly influence the magnitude representations of fractions. For one-digit fraction pairs with and without common components, componential representation is favored; for two-digit fraction pairs with common components, componential representation is preferred, while for two-digit fraction pairs without common components, holistic representation is selected. The representation styles are consistent across university students, junior high school students and primary school students, and there are significant age differences in representation levels, with university students being more flexible in their use of representation strategies of fractions than the other two ages, and junior high school students showing the same level with the primary school students. These results suggest that not only Chinese university students, but also Chinese primary and junior high school students can select and adapt representation strategies of fractions according to the characteristics and complexity of fraction processing tasks. The eye-movement technique can largely compensate for the shortcomings of the regression analysis paradigm and better reveal the critical cognitive processes involved in the processing of fractions.
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Data Availability
The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
The study described in this report was Funded by an open grant from the Hubei Research Center for Quality Education in Primary and Secondary Schools (Project No.2020HBSZB13). The content is solely the responsibility of the authors and does not necessarily represent the official views of Normal College(Faculty of Education) of Hubei University. We are appreciative of the parents, children, and teachers who participated in our study and the many people who assisted in data collection.
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All authors have participated in the study and have read and approved the submitted version of the manuscript. Zhang Yuding conceived the idea and acquire the fund, Wu Hao performed the experiment, analyzed the data and wrote the manuscript, Luo Qiong reviewed and edited the manuscript. Zhu Zhengzhou is responsible for contacting and coordinating teachers and students in secondary and primary schools.
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Prior to conducting the study, Normal College(Faculty of Education), Hubei University Scientific Research Ethics Committee in China approved the research protocol, including the consent procedure.
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Wu, H., Zhang, Y., Luo, Q. et al. The magnitude representations of fractions of Chinese students: evidence from behavioral experiment and eye-tracking. Curr Psychol 43, 4113–4128 (2024). https://doi.org/10.1007/s12144-023-04627-9
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DOI: https://doi.org/10.1007/s12144-023-04627-9