Reasoning strategies with rational numbers revealed by eye tracking

Recent research has begun to investigate the impact of different formats for rational numbers on the processes by which people make relational judgments about quantitative relations. DeWolf, Bassok, and Holyoak ( Journal of Experimental Psychology: General, 144 (1), 127–150, 2015) found that accuracy on a relation identification task was highest when fractions were presented with countable sets, whereas accuracy was relatively low for all conditions where decimals were presented. However, it is unclear what processing strategies underlie these disparities in accuracy. We report an experiment that used eye-tracking methods to externalize the strategies that are evoked by different types of rational numbers for different types of quantities (discrete vs. continuous). Results showed that eye-movement behavior during the task was jointly determined by image and number format. Discrete images elicited a counting strategy for both fractions and decimals, but this strategy led to higher accuracy only for fractions. Continuous images encouraged magnitude estimation and comparison, but to a greater degree for decimals than fractions. This strategy led to decreased accuracy for both number formats. By analyzing participants’ eye movements when they viewed a relational context and made decisions, we were able to obtain an externalized representation of the strategic choices evoked by different ontological types of entities and different types of rational numbers. Our findings using eye-tracking measures enable us to go beyond previous studies based on accuracy data alone, demonstrating that quantitative properties of images and the different formats for rational numbers jointly influence strategies that generate eye-movement behavior.