Reasoning strategies with rational numbers revealed by eye tracking

Abstract

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), 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.

Children’s discrete proportional reasoning is related to inhibitory control and enhanced by priming continuous representations

“…In the context of discrete proportional reasoning, one possible intuitive response strategy is counting the segments. At least in adulthood, eye-tracking studies have shown that when proportions are presented in a discrete format, they elicit counting strategies (Plummer et al, 2017). Since performance on the H&F task shows a moderate relationship with the Discrete adjacent Counting misleading trials of the Spinners task that might elicit a counting strategy, we suggest that the role of inhibitory control in proportional reasoning is to help children avoid using this strategy and instead, focus on the proportional information.…”

“…This bias is especially problematic when discrete and proportional information are at odds with each other. Children's performance plummets when counting information contradicts proportional information (Jeong, Levine, & Huttenlocher, 2007), and even adults resort to counting strategies in these cases (Plummer, DeWolf, Bassok, Gordon, & Holyoak, 2017). Thus, a critical step in correctly accessing non-symbolic proportional information is inhibiting misleading discrete information, suggesting that individuals who are better at resolving interferences in general, may show enhanced proportional reasoning abilities.…”

Quantifying Scientific Thinking Using Multichannel Data With Crystal Island: Implications for Individualized Game-Learning Analytics

“…The retina determines if and how much visual information is available for processing and discloses the learners' foci of attention and thus what information is being processed (van Zoest et al, 2017(van Zoest et al, , p. 1555. A number of studies provide empirical evidence supporting this perspective, such that where participants look is indicative of their reasoning behaviors such as scientific thinking (Plummer et al, 2017(Plummer et al, , p. 1426Miller Singley and Bunge, 2018, p. 445). For instance, Vendetti et al (2017) showed that participants' saccades and fixations data were indicative of reasoning.…”

An investigation of the effects of n-gram length in scanpath analysis for eye-tracking research

“…The authors acknowledge the importance and novelty of using eye tracking methods for understanding reasoning processes; nevertheless, they also highlight the lack of breadth in eye tracking research in this area, suggesting that future research should investigate diverse reasoning processes in different domains [Blondon et al 2015]. A recent study investigating numerical reasoning employed an ad-hoc transition analysis technique specifically developed for exposing how people reason about rational numbers [Plummer et al 2017]. In this study, n-grams of fixations were compared to identify whether the reasoner was counting or comparing pieces of numerical information.…”

“…Three or more consecutive fixations on a single AOI were seen as an indicator of counting behavior; conversely, two or more transitions between different AOIs within three fixations were seen as an indication of comparing behavior. Although effective for its purpose, this method of analysis is domain-specific and does not transfer to reasoning tasks in general [Plummer et al 2017]. Transition analysis can, however, be used in more general terms, especially when a number of dissimilar pieces of information are provided and when the aim of the experimenter is to discover how and in which order these pieces of information are combined during a reasoning process.…”