A model of eye movements and visual working memory during problem solving in geometry

Abstract

The Oculomotor Geometry Reasoning Engine (OGRE) was proposed to model eye movements and visual working memory during problem solving in geometry. OGRE postulates that geometrical elements from diagrams are added to visual working memory when they are scanned. Newly-added elements overwrite elements already in memory. The model was applied to eye-movement patterns of three subjects: two geometry experts and one non-expert. Their eye movements and verbal protocols were recorded as they solved geometry problems posed with diagrams. Subjects used highly redundant eye-movement patterns with multiple rescans of the same geometrical elements. OGRE's model of visual memory provided a good fit for the distribution of times between rescans. The model was used to estimate the size of visual working memory used in geometry. The estimates varied as a function of both problems and subjects, with means and standard deviations for each subject being: 5.3+/-1.4, 4.0+/-0.9 and 4.7+/-1.6.

Linking attentional processes and conceptual problem solving: visual cues facilitate the automaticity of extracting relevant information from diagrams

“…Prior research on eye movements and problem solving has shown that overt attention can illuminate the cognitive processes involved in problem solving (Epelboim and Suppes, 2001; Knoblich et al, 2001, 2005; Grant and Spivey, 2003; Jones, 2003; Thomas and Lleras, 2007, 2009; Bilalić et al, 2008; Eivazi and Bednarik, 2010, 2011; Madsen et al, 2012, 2013a,b; Lin and Lin, 2014; Susac et al, 2014). However, we are particularly interested in two directions of causal relationships between overt attentional selection and the higher-level cognitive processes involved in problem solving: (1) the causal relationship starting from higher-level cognitive processes involved in problem solving and ending with attentional selection; and (2) the reverse causal relationship starting from attentional selection and ending with the higher-level cognitive processes involved in problem solving.…”

“…However, we are particularly interested in two directions of causal relationships between overt attentional selection and the higher-level cognitive processes involved in problem solving: (1) the causal relationship starting from higher-level cognitive processes involved in problem solving and ending with attentional selection; and (2) the reverse causal relationship starting from attentional selection and ending with the higher-level cognitive processes involved in problem solving. A relatively small number of studies have investigated each of these relationships, with some speaking more to the effect of higher-level cognitive processes in problem solving on attentional selection (Epelboim and Suppes, 2001; Knoblich et al, 2001; Madsen et al, 2012), and others speaking more to the effect of attentional selection on higher-level cognitive processes in problem solving (Epelboim and Suppes, 2001; Cameron et al, 2002; Grant and Spivey, 2003; Tai et al, 2006; Thomas and Lleras, 2007, 2009; Lin and Lin, 2014; Susac et al, 2014). …”

“…Research on the effect of the cognitive processes involved in problem solving on overt attentional selection has shown that mandatory top-down processes based on prior knowledge can enable solvers to rapidly attend to relevant information when solving a problem (Epelboim and Suppes, 2001; Madsen et al, 2012). In the most extreme cases, based on prior knowledge, an expert may attend to the relevant information in a problem within the time frame of a single eye fixation, while a novice may instead take much more time while attending to various sources of irrelevant information (Charness et al, 2001; Reingold et al, 2001).…”

Influence of visual cueing on students' eye movements while solving physics problems

“…Eye movements of problem solvers have been studied [e.g. Epelboim & Suppes, 2001;Madsen et. al, 2012].…”

High Regularities in Eye‐Movement Patterns Reveal the Dynamics of the Visual Working Memory Allocation Mechanism

“…For over a decade, considerable effort had been devoted to investigating the relationship between VWM and eye movements (Bays & Husain, 2008;Epelboim & Suppes, 2001;Hodgson, Dittrich, Henderson, & Kennard, 1999;Postle, Idzikowski, Sala, Logie, & Baddeley, 2006;Soto, Humphreys, & Rotshtein, 2007). Our eye-tracking experiment results for the first time demonstrate a strong correlation between individual VWM capacity and eye-movement patterns in a nontrivial problem-solving scenario.…”