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.

眼动追踪数据集，用于几何分类任务的抽象与非抽象思维研究。抽象过程之开发与评估一直是数学教育领域中的长期方法论难题。近年来，眼动追踪技术的出现引发了对眼动分析是否能够支持关于数学思维的合理推断的讨论。在本研究中，我们探讨了眼动追踪是否可用于推断个人是否使用抽象方法来解决几何分类任务。参与者被展示三种不同试验中的三角形或四边形（任务形状）的样本。随后，他们被要求从六个几何形状（响应形状）的阵列中选择所有属于同一类的其他形状。同时，我们对他们的眼动进行了追踪。最终，我们根据参与者是否通过口头报告（i）使用抽象概念或（ii）直接比较任务形状与响应形状以解决问题来对每个试验进行编码。我们发现，概念试验的特征是任务形状与响应形状之间连接较少，而响应形状之间的连接较多。非概念试验的特征是眼动将任务形状与响应形状连接起来，仿佛直接比较它们的相似性。基于眼动数据的逻辑回归模型在80.3%的情况下正确地将试验分类为概念或非概念。我们得出结论，眼动追踪有助于对数学思维过程进行推断，并促进抽象研究。