FracVisET: Investigating Fraction Visualizations using Eye Tracking
FracVisET (Investigating Fraction Visualizations using Eye Tracking) is a research project at the intersection of cognitive psychology and mathematics education. It uses eye tracking to investigate the cognitive processes involved in comparing fraction visualizations.
Many learners struggle to develop a solid understanding of fractions - especially when it comes to estimating their numerical value. One reason is that fractions are different from natural numbers. Thinking about fractions is often influenced by the so-called natural number bias - the tendency to treat fractions as if they were natural numbers.
In this project, we explore how children and adults visually compare fractions using tape diagrams (narrow rectangular diagrams; see figure below). We are particularly interested in how different types of visualizations affect cognitive processing. We compare two types of tape diagrams:
- Continuous tape diagrams, in which the fraction is shown as a bar without visible subdivisions (see right-hand side of the figure),
- and discretized tape diagrams, in which the bar is divided into equal segments that can be counted (see left-hand side of the figure).
To understand how people approach the visual comparison of fractions, we use eye tracking. This method allows us to record where participants look while solving the tasks. Particularly insightful are so-called scanpaths, which show how the eyes move during problem solving (see figure below).
Our findings so far show:
- Both children and adults perform more accurately and respond more quickly when comparing continuous visualizations.
- In the continuous format, they use inefficient counting strategies less frequently, suggesting that they are more likely to process the fractions holistically rather than by counting.
- Some high-achieving children still rely on counting. While this strategy is less efficient (i.e., slower), it still can lead to high accuracy.
- Low-achieving children tend to compare absolute sizes of shaded areas rather than the proportions. This strategy can lead to incorrect answers and indicates a lack of conceptual understanding of fractions.
- A textbook analysis shows that despite the potential benefits of continuous visualizations, they are rarely used in instructional materials.
These findings make it clear: The way fractions are visually represented influences how they are cognitively processed.
Therefore, effective fraction instruction should not only focus on appropriate task selection, but also on the beneficial design of visual representations. Our project offers initial insights for the development of teaching materials and digital learning tools that can promote students' understanding of fractions more effectively.
Project-related publications and presentations
Obersteiner, A., Schwarzmeier, S., Alibali, M.W. & Marupudi, V. (2022). Adults' eye movements when comparing discretized or continuous fraction visualizations. In C. Fernández, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 384). PME.
Schwarzmeier, S., Obersteiner, A., Alibali, M. W., & Marupudi, V. (2023). Diskretisierte und kontinuierliche Visualisierungen von Brüchen: Eine Eye-Tracking Studie mit Erwachsenen. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik. WTM. DOI: 10.37626/GA9783959872089.0
Schwarzmeier, S., Obersteiner, A., Alibali, M. W., & Marupudi, V. (2023). Comparing Continuous and Discretized Tape Diagrams of Fractions: An Eye-Tracking Study with Adults. 20th Biennial EARLI Conference.
Schwarzmeier, S., Obersteiner, A., Alibali, M. W., & Marupudi, V. (2023). Why Continuous Tape Diagrams of Fractions are Easier to Process than Discretized ones: Evidence from Adults’ and Children’s Eye-Movements. WOG 2023.
Schwarzmeier, S., Obersteiner, A., Alibali, M. W., & Marupudi, V. (2024). How do people compare visualizations of fraction magnitudes? Evidence from adults’ and children’s eye movements with continuous and discretized tape diagrams. The Journal of Mathematical Behavior, 75, 101160. DOI: 10.1016/j.jmathb.2024.101160
Schwarzmeier, S., & Obersteiner, A. (2024). Is Students’ Ability of Visually Comparing Fraction Magnitudes Related to Their General Fraction Knowledge? An Eye-Tracking Study. MCLS Conference.
Schwarzmeier, S., Kober, A., & Obersteiner, A. (2024). Visualisierungen von Brüchen in Schulbüchern: Kontinuierlich, diskretisiert oder diskret? In P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht & P. Scherer (Eds.), Beiträge zum Mathematikunterricht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik. WTM. DOI: 10.37626/GA9783959872782.0
Schwarzmeier, S., & Obersteiner, A. (2025). Is counting a bad idea? Complex relations among children’s fraction knowledge, eye movements, and performance in visual fraction comparisons. Journal of Experimental Child Psychology, 252, 106181. DOI: 10.1016/j.jecp.2024.106181
Schwarzmeier, S., & Obersteiner, A. (2025). Visualisierungen von Brüchen in Schulbüchern: Diskret, diskretisiert oder kontinuierlich? GEBF Conference.