Cognitive Basis of Conditional Reasoning: Insight Through Eye Movements

The current study used eye movements to investigate the cognitive processes underlying deductive reasoning. Connections were made between eye-tracking research on problem-solving and existing accounts of deductive reasoning. Eighteen college students solved conditional reasoning problems using three valid inference rules from propositional logic: modus ponens, modus tollens, and hypothetical syllogism. Their eye movements during the task were analyzed for insights toward the nature of the deductive reasoning process: specifically, whether it is driven by mental models or syntax-based, domain-independent inference rules. Findings suggest that the reversal of propositional terms between modus ponens and modus tollens problems had a significant effect on the accuracy of participants’ responses. Despite this, general eye movement patterns during those two problem types remained similar. Although these findings do not entirely dismiss the role played by syntax-based rules, they offer potential evidence toward the mental model account of reasoning. COGNITIVE BASIS OF CONDITIONAL REASONING 3 Cognitive Basis of Conditional Reasoning: Insight Through Eye Movements Since the midto late 20th century, eye-tracking has become an increasingly popular method for studying cognitive processes, particularly during visual search, scene perception, decision-making, reading, and various types of problem-solving. This is likely because eye movements can inform us on a detailed level about the online processes (i.e., processes occurring during the course of a given task) driving these activities. This type of information typically cannot be gained through traditional measures such as reaction time and error rate. Moreover, eye movements are good measures of overt attention and precise indices of mental processing. Finally, eye-tracking data can be combined with those gathered using traditional measures for a more comprehensive understanding (see Rayner, 2009, for a review of research on eye movements during reading, scene perception, and visual search). The present study investigates the largely unexplored intersection between eye movements and deductive reasoning, specifically conditional reasoning (i.e., reasoning based on “if...then...” statements). The sections below provide an overview of how eye movements have been used to study various types of reasoning tasks, including diagram-based problem-solving (Grant & Spivey, 2003; Hegarty & Just, 1993; Just & Carpenter, 1985), arithmetic problems and number line estimation tasks (Green, Lemaire, & Dufau, 2007; Hegarty, Mayer, & Monk, 1995; Schneider et al., 2008; Sullivan, Juhasz, Slattery, & Barth, 2011; Verschaffel, De Corte, & Pauwels, 1992;), and deductive reasoning (Aaron & Spivey, 1999; Espino, Santamaría, Meseguer, & Carreiras, 2005; Halberda, 2006; Johnson-Laird & Bara, 1984). Then, the argument forms modus ponens, modus tollens, and hypothetical COGNITIVE BASIS OF CONDITIONAL REASONING 4 syllogism are briefly described. Finally, existing theories of deductive reasoning and their relationships to biases in human logical inference are discussed (Ball, Phillips, Wade, & Quayle, 2006; Johnson-Laird & Wason, 1970; Oberauer, Hörnig, Weidenfeld, & Wilhelm, 2005; Wason & Shapiro, 1971). Together, these studies demonstrate that eye movements are a valid medium through which insights about reasoning processes may be obtained. Eye Movements and Problem Solving Existing literature documents eye movements during various problem-solving tasks. Several studies on the subject have focused on diagram-based problems. For example, Just and Carpenter (1985) made use of eye movements to study spatial reasoning ability, particularly the mental rotation of visual stimuli. The study used the Cube Comparison test, in which participants were asked to determine whether two drawings of differently oriented cubes could depict the same object. The researchers also looked at performance in the Shepard-Metzler task, which required participants to compare two images of 3-dimensional, asymmetrical objects. Differences between individuals with high and low spatial reasoning skills were examined. Also investigated were different mental rotation strategies. These entail the encoding of objects with respect to various cognitive coordinate systems, in which mental representations of said objects are rotated. In both tasks, eye movements helped to indicate that subjects with low spatial reasoning ability took longer to mentally rotate the given object, and that they were less efficient than their counterparts with high spatial reasoning ability at keeping track of multiple aspects of the object. In addition, COGNITIVE BASIS OF CONDITIONAL REASONING 5 in the Cube Comparison task, subjects with high spatial reasoning skills were found to be more flexible with their mental rotation strategies. Hegarty and Just (1993) examined eye movements of people as they constructed mental models of simple machines based on written descriptions and diagrams. A preliminary experiment showed that people tend to understand mechanical systems better through a combination of text and diagrams than through either alone. A second experiment investigated the process of integrating information from these two media. Subjects’ eye movement patterns suggested that they had read the descriptions incrementally, rereading relevant sections prior to the construction of mental models. In addition, they had engaged the diagrams first on a local level, as individual components, and later on a global level, as connected systems of many parts. It was suggested that subjects had used the diagrams as external representations of their mental models. In doing so, they had freed up cognitive resources to mentally integrate the individual parts into a whole. More recently, eye movements have been used to examine and even actively influence the process of solving insight problems, the answers to which cannot be merely deduced using logic. Grant and Spivey (2003) demonstrated that guiding eye movements can increase the likelihood of success in an insightand diagram-based problem known as Duncker's radiation problem. Participants were given a diagram representing a tumor surrounded by healthy tissue. The diagram contained four regions of interest: an oval “tumor” at the center, a larger surrounding oval representing skin, a white region of “healthy tissue” between the tumor and the skin, and the region outside of the skin. Participants were then asked to think of a way, COGNITIVE BASIS OF CONDITIONAL REASONING 6 using hypothetical lasers that destroy tissue at a sufficient intensity, to cure the tumor without damaging the healthy tissue. The solution is to fire multiple low-intensity lasers from outside the healthy region so that they converge at the tumor at a sufficient combined intensity. Perhaps surprisingly, it was found that the successful problem solvers spent a significantly higher percentage of time looking at the “skin” than the unsuccessful ones did. Moreover, in a follow-up experiment, the researchers were able to significantly increase the success rate by subtly animating the skin region. It was suggested that, in the successful problem solvers, the numerous fixations on the skin region were a side effect of frequent eye movements from the tumor to the outside region and back, and that these movements simulated the process of directing of multiple lasers at the tumor. In conclusion, the study showed that eye movements may actively direct cognition rather than solely being directed by cognition. Eye Movements and Mathematical Reasoning While it may be intuitive to use eye movements to study diagram-based problem solving, which clearly involves spatial cognition, eye movements have also been informative of cognitive processes involved in seemingly abstract problemsolving tasks requiring mathematical skill, such as number line estimations and arithmetic problems. An eye-tracking study by Sullivan et al. (2011) examined the numerical-spatial translation skills of adults using number line estimation tasks, as well as the effect of the initial number’s size on their performance. Participants were asked to estimate, using mouse clicks, the positions of pseudo-randomly generated numbers on a number line. It was found that adults’ numerical-spatial translation COGNITIVE BASIS OF CONDITIONAL REASONING 7 skills were rapid and accurate, and that the size of the target number influenced the location of the first fixation. In addition, because the size of the initial number affected both looking behavior and estimation performance, it was suggested that participants had used on-line calibration. That is, they had calibrated their estimates in real-time as they were completing the task as opposed to relying on memorized number-to-location correspondences. Finally, patterns of estimation error suggested bias caused by a proportional-reasoning strategy, wherein participants made biased judgments of numerical magnitude by considering the part (the number whose location is to be estimated) in relation to the whole (the number line). This was reflected by participants’ tendencies to fixate on the midpoint as a central reference point. Schneider et al. (2008) conducted a similar study, in which the number-line estimation task was presented to children. The study also used both eye-tracking and behavioral methods. Specifically, participants indicated their answers with fixations as well as mouse clicks. It was concluded that elementary school children’s number sense, as indicated by the number-line estimation task, increases with grade level; that eye fixations on the number line are closely related to mouse clicks on the same; that in Grade 2, fixations are related to the ability to solve addition problems; and that children also use the midpoint of the line as a reference. Green et al. (2007) conducted a study using eye movements as reflections of complex addition s