Abstract
AbstractIn mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties.
Funder
Marcus and Amalia Wallenberg Foundation
Umeå Universitet
Umea University
Publisher
Springer Science and Business Media LLC
Subject
Education,General Mathematics
Reference68 articles.
1. Aaten, A. B., Deprez, J., Roorda, G., & Goedhart, M. (2017). Undergraduates’ reasoning while solving integration tasks: Discussion of a research framework. Paper presented at the CERME 10.
2. Andrá, C., Lindström, P., Arzarello, F., Holmqvist, K., Robutti, O., & Sabena, C. (2015). Reading mathematics representations: An eye-tracking study. International Journal of Science and Mathematics Education, 13(2), 237–259. https://doi.org/10.1007/s10763-013-9484-y
3. Bergqvist, T., & Lithner, J. (2012). Mathematical reasoning in teachers’ presentations. Journal of Mathematical Behavior, 31(2), 252–269. https://doi.org/10.1016/j.jmathb.2011.12.002
4. Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher, R. W. Pew, L. M. Hough, & J. R. Pomerantz (Eds.), Psychology and the real world: Essays illustrating fundamental contributions to society (pp. 56–64). Worth Publishers.
5. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning (Rev. and expanded ed.). L. Erlbaum.