How do people compare visualizations of fraction magnitudes? Evidence from adults ' and children ' s eye movements with continuous and discretized tape diagrams

Adults and children are able to compare visually represented fractions. Past studies show that people are more efficient with continuous visualizations than with discretized ones, but the specific reasons are unclear. Presumably, continuous visualizations highlight magnitudes more directly, while discretized ones encourage less efficient strategies such as counting. In two experiments, adults and children compared the magnitudes of continuous and discretized tape diagrams of fractions. In both experiments, participants answered more accurately, faster, and with fewer eye saccades when the visualizations were continuous rather than discretized. Sequences of saccades indicated that participants used counting strategies less often with continuous than discretized diagrams. The results suggest that adults and children are more efficient with continuous than discretized visualizations because they use more efficient, magnitude-based strategies with continuous visualizations. The findings indicate that integrating continuous visualizations in classroom teaching more frequently could be beneficial for supporting students in developing fraction magnitude concepts.