Eye-tracking data for classification of geometric shapes

Eye-tracking data for geometric classification tasks for abstract and non-abstract thinking. How to develop and assess abstraction processes are longstanding methodical problems in mathematics education. Recently, the advent of eye tracking technology has spurred a discussion about whether eye movement analysis can support valid inferences about mathematical thinking. In this study, we investigated whether eye tracking can be used to infer whether a person uses abstraction to solve a geometric classification task. The participants were shown three exemplars of either triangles or quadrilaterals (task shapes) in different trials. They were then asked to select all the other shapes belonging to the same class from an array of six geometric shapes (response shapes) while we tracked their eye movements. Finally, we coded each trial by whether participants verbally reported to (i) use an abstract concept or (ii) directly compare task shapes with response shapes to solve the task. We found that concept trials were characterised by eye movements that made few connections between the task shapes and the response shapes and more connections between the response shapes. Non-concept trials were characterised by eye movements that connected task shapes with response shapes as if to compare their similarity directly. A logistic regression model correctly classified the trials as concept or non-concept based on eye-tracking data in 80.3% of the cases. We conclude that eye tracking can contribute to making inferences about mathematical thought processes and facilitate research on abstraction.面向抽象与非抽象思维几何分类任务的眼动追踪数据。如何开发与评估抽象思维过程，是数学教育领域长期存在的方法论难题。近年来，眼动追踪技术的问世引发了学界关于眼动分析能否为数学思维的有效推断提供支撑的讨论。本研究旨在探究眼动追踪能否用于推断个体是否通过抽象思维完成几何分类任务。实验中，参与者在不同试次中会看到三角形或四边形的三类范例（任务刺激图形）；随后要求他们从包含六个几何图形的阵列（作答刺激图形）中选出所有与范例同类的图形，同时记录其眼动轨迹。最后，我们根据参与者的口头报告对每个试次进行编码：若其报告（i）使用抽象概念解题，或（ii）直接对比任务刺激图形与作答刺激图形以解题，则将该试次归入对应类别。研究结果显示，抽象概念类试次的眼动特征为：任务刺激图形与作答刺激图形间的关联较少，而作答刺激图形内部的关联更多；非抽象概念类试次的眼动特征则为：眼动轨迹会在任务刺激图形与作答刺激图形间建立关联，仿佛在直接比对二者的相似性。基于眼动追踪数据构建的逻辑回归模型，能够以80.3%的准确率将试次正确划分为抽象概念类与非抽象概念类。综上，眼动追踪技术可为数学思维过程的推断提供助力，并推动抽象思维相关研究的开展。