Measuring fraction comparison strategies with eye-tracking
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Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their strategies to the type of fraction pair. To extend previous research on simple fraction comparison, we used a highly controlled set of more complex fractions with two-digit components. In addition to response times, we recorded eye movements to assess how often the participants fixated on and alternated between specific fraction components. In line with previous studies, our data suggest that the participants preferred componential over holistic strategies for fraction pairs with common numerators or common denominators. Conversely, they preferred holistic over componential strategies for fraction pairs without common components. These results support the assumption that mathematically skilled adults adapt their strategies to the type of fraction pair even in complex fraction comparison. Our study also suggests that eye-tracking is a promising method for measuring strategy use in solving fraction problems.
KeywordsFraction processing Holistic strategies Componential strategies Eye movements
The authors would like to thank the university students for participating in our study. We also would like to thank the anonymous reviewers for their constructive comments on an earlier draft of this article.
- Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. (1981). Results from the second mathematics assessment of the National Assessment of Educational Progress. Washington, DC: National Council of Teachers of Mathematics.Google Scholar
- Carraher, D. W. (1996). Learning about fractions. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 241–266). New Jersey: Lawrence Erlbaum Associates.Google Scholar
- Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth- grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–144. doi: 10.2307/749646.CrossRefGoogle Scholar
- Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87, 215–251. doi: 10.1037/0033-295X.87.3.215.
- Green, H. J., Lemaire, P., & Dufau, S. (2007). Eye movement correlates of younger and older adults’ strategies for complex addition. Acta Psychologica, 125, 257–278. doi: 10.1016/j.actpsy.2006.08.001.
- Huber, S., Klein, E., Willmes, K., Nuerk, H.-C., & Moeller, K. (2014a). Decimal fraction representations are not distinct from natural number representations—evidence from a combined eye-tracking and computational modeling approach. Frontiers in Human Neuroscience, 8, 172. doi: 10.3389/fnhum.2014.00172.CrossRefGoogle Scholar
- Ischebeck, A., Weilharter, M., & Körner, C. (2015). Eye movements reflect and shape strategies in fraction comparison. The Quarterly Journal of Experimental Psychology. Advance online publication. doi: 10.1080/17470218.2015.1046464.
- Obersteiner, A., Dresler, T., Reiss, K., Vogel, C. M., Pekrun, R., & Fallgatter, A. J. (2010). Bringing brain imaging to the school to assess arithmetic problem solving. Chances and limitations in combining educational and neuroscientific research. ZDM—The International Journal on Mathematics Education, 42, 541–554. doi: 10.1007/s11858-010-0256-7.
- Obersteiner, A., Moll, G., Beitlich, J. T., Cui, C., Schmidt, M., Khmelivska, T., & Reiss, K. (2014). Expert mathematicians’ strategies for comparing the numerical values of fractions—evidence from eye movements. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 338–345). Vancouver: PME.Google Scholar
- Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., Jacobs, A. M., & Stern, E. (2008). A validation of eye movements as a measure of elementary school children’s developing number sense. Cognitive Development, 23, 409–422. doi: 10.1016/j.cogdev.2008.07.002.
- Sullivan, J. L., Juhasz, B. J., Slattery, T. J, & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin and Review, 18, 557–563. doi: 10.3758/s13423-011-0081-1.
- Tzelgov, J., Ganor-Stern, D., Kallai, A., & Pinhas, M. (2014). Primitives and non-primitives of numerical representations. Oxford Handbooks Online. Retrieved 24 July 2015. http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199642342.001.0001/oxfordhb-9780199642342-e-019.
- Vamvakoussi, X. (2015). The development of rational number knowledge: old topics, new insights. Learning and Instruction, 37, 50–55. doi: 10.1016/j.learninstruc.2015.01.002.