Current Trends in Eye Tracking Research in Mathematics Education: A PME Literature Review
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paper_title: Eye Fixations and Cognitive Processes

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Abstract This paper presents a theoretical account of the sequence and duration of eye fixation during a number of simple cognitive tasks, such as mental rotation, sentence verification, and quantitative comparison. In each case, the eye fixation behavior is linked to a processing model for the task by assuming that the eye fixates the referent of the symbol being operated on.
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paper_title: A Theory of Reading: From Eye Fixations to Comprehension

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This article presents a model of reading comprehension that accounts for the allocation of eye fixations of college students reading scientific passages. The model deals with processing at the level of words, clauses, and text units. Readers make longer pauses at points where processing loads are greater. Greater loads occur while readers are accessing infrequent words, integrating information from important clauses, and making inferences at the ends of sentences. The model accounts forthe gaze duration on each word of text as a function of the involvement of the various levels of processing. The model is embedded in a theoretical framework capable of accommodating the flexibility of reading.
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paper_title: Spatial biases during mental arithmetic: evidence from eye movements on a blank screen

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While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the "mental number line"), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8-3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.
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paper_title: Eye Tracking: A comprehensive guide to methods and measures

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Holmqvist, K., Nystrom, N., Andersson, R., Dewhurst, R., Jarodzka, H., & Van de Weijer, J. (Eds.) (2011). Eye tracking: a comprehensive guide to methods and measures, Oxford, UK: Oxford University Press.
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paper_title: Human gaze control during real-world scene perception

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In human vision, acuity and color sensitivity are best at the point of fixation, and the visual-cognitive system exploits this fact by actively controlling gaze to direct fixation towards important and informative scene regions in real time as needed. How gaze control operates over complex real-world scenes has recently become of central concern in several core cognitive science disciplines including cognitive psychology, visual neuroscience, and machine vision. This article reviews current approaches and empirical findings in human gaze control during real-world scene perception.
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paper_title: Eye Tracking in Human-Computer Interaction and Usability Research: Ready to Deliver the Promises

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Publisher Summary ::: This chapter discusses the application of eye movements to user interfaces, both for analyzing interfaces (measuring usability) and as an actual control medium within a human–computer dialogue. For usability analysis, the user's eye movements are recorded during system use and later analyzed retrospectively; however, the eye movements do not affect the interface in real time. As a direct control medium, the eye movements are obtained and used in real time as an input to the user–computer dialogue. The eye movements might be the sole input, typically for disabled users or hands-busy applications, or might be used as one of several inputs, combining with mouse, keyboard, sensors, or other devices. From the perspective of mainstream eye-movement research, human–computer interaction, together with related work in the broader field of communications and media research, appears as a new and very promising area of applied work. Both basic and applied work can profit from integration within a unified field of eye­-movement research. Application of eye tracking in human–computer interaction remains a very promising approach; its technological and market barriers are finally being reduced.
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paper_title: Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry

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Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in mathematics even though they may not apply in this domain. This article investigates to what extent the EMH applies in mathematics—geometry in particular—and aims to lift the discussion of what inferences can be validly made from eye-tracking data. We use a case study to investigate the need for a refinement of the use of the EMH. In a stimulated recall interview, a student described his original thoughts perusing a gaze-overlaid video recorded when he was working on a geometry problem. Our findings contribute to better a understanding of when and how the EMH applies in the subdomain of geometry. In particular, we identify patterns of eye movements that provide valuable information on students’ geometry problem solving: certain patterns where the eye fixates on what the student is processing and others where the EMH does not hold. Identifying such patterns may contribute to an interpretation theory for students’ eye movements in geometry—exemplifying a domain-specific theory that may reduce the inherent ambiguity and uncertainty that eye tracking data analysis has.
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paper_title: Creativity in the eye of the student : Refining investigations of mathematical creativity using eye-tracking goggles

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Mathematical creativity is increasingly important for improved innovation and problem-solving. In this paper, we address the question of how to best investigate mathematical creativity and critical ...
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paper_title: Probabilistic approach to robust wearable gaze tracking

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This paper presents a method for computing the gaze point using camera data captured with a wearable gaze tracking device. The method utilizes a physical model of the human eye, advanced Bayesian computer vision algorithms, and Kalman filtering, resulting in high accuracy and low noise. Our C++ implementation can process camera streams with 30 frames per second in realtime. The performance of the system is validated in an exhaustive experimental setup with 19 participants, using a self-made device. Due to the used eye model and binocular cameras, the system is accurate for all distances and invariant to device movement. We also test our system against a best-in-class commercial device which is outperformed for spatial accuracy and precision. The software and hardware instructions as well as the experimental data are published as open source.
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paper_title: Watching mathematicians read mathematics

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This report contributes to the debate about whether expert mathematicians skim-read ::: mathematical proofs before engaging in detailed line-by-line reading. It reviews the conflicting introspective and behavioural evidence, then reports a new study of expert mathematicians' eye movements as they read both entire research-level mathematics papers and individual proofs within those papers. Our analysis reveals no evidence of skimming, and we discuss the implications of this for research and pedagogy.
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paper_title: Watching mathematicians read mathematics

paper_content:

This report contributes to the debate about whether expert mathematicians skim-read ::: mathematical proofs before engaging in detailed line-by-line reading. It reviews the conflicting introspective and behavioural evidence, then reports a new study of expert mathematicians' eye movements as they read both entire research-level mathematics papers and individual proofs within those papers. Our analysis reveals no evidence of skimming, and we discuss the implications of this for research and pedagogy.
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Title: Current Trends in Eye Tracking Research in Mathematics Education: A PME Literature Review

Section 1: Introduction
Description 1: Introduce the topic of eye tracking in mathematics education research, explaining the significance and context.

Section 2: Full keyword search
Description 2: Describe the methodology used for identifying relevant papers through keyword searches in PME proceedings.

Section 3: Analysis and coding of articles
Description 3: Explain the process of reading and coding the identified articles with respect to the research questions.

Section 4: RQ1: How did the number of ET related papers evolve over time?
Description 4: Analyze and present the evolution of the number of eye tracking-related papers over the years.

Section 5: RQ2: What ET equipment is used in the MER community?
Description 5: Discuss the types of eye tracking equipment used in the mathematics education research community.

Section 6: RQ3: What analysis and (result) presentation methods are used in MER?
Description 6: Describe the various methods of analysis and result presentation used in studies involving eye tracking.

Section 7: Discussion and Outlook
Description 7: Summarize the findings, discuss trends observed, and provide an outlook on future research directions and potential developments in the field.