SGER: Eye Tracking for the Study of Seeing and Imagining

“运动中的数学”项目的一个中心主题是数学学习中的视觉和想象之间的关系;通过我们的工作，我们对基于眼球运动的研究产生了浓厚的兴趣。 该SGER提案在利用正在进行的项目的意义上实现了机会成本，该项目将为拟议的工作提供及时的概念背景和实际需求。 它将允许我们对高中生进行采访，在采访中，他们将解释并绘制一个假想物体的运动曲线图。 我们将分析眼动仪收集的数据，并结合访谈录像及其转录。 我们将研究当被采访者试图看到和想象由图所象征的运动的不同方面时，她的扫描路径是如何变化的。 这些探索性研究将阐明运动中的数学提案中包括的项目的以下研究问题：“身体动作/感知如何成为想象数学实体的mothion和形状的一部分？学生对属性的理解如何塑造他们的身体行为/感知？“据我们所知，现有的数学教育跟踪眼动的研究集中在确定专家和新手如何注意录像片段的不同方面或验证信息处理的正式模型。 我们的目标是不同的，更多的是在传统的雅布斯（1967年）：进行个案研究分析模式的个人canpaths取决于观众的问题和她试图想象。

A central theme of the "Math in Motion project is the relationship between seeing and imaging in mathematics learning; through our work we have become deeply interested in conducting studies based on eye movements. This SGER proposal fulfills an opportunity cost in the sense of taking advantage of an ongoing prjoect that will provide a timely conceptual background and practical need for the proposed work. I t will allow us to conduct interviews with high school students in whichg they will interpret and draw graphs for the motion of an imaginary object. We will analyze the data collected with an eye tracker in conjunctions with the videotaped interview and its transcription. We will examine how thte interviewee's scanpaths change as she tries to see and imagine different aspects of the motion symbolized by the graph. These exploratory studies will illuminate the following research questions of the project included in the Math in Motion proposal: "How does bodily action/perception become part of imagining the mothion and shape of mathematical enitities? In which ways do students' understanding of properties come to mold their bodily action/perception?" As far as we know, the existing studies in mathematics education tracking eye motion have focused on ascertaining how experts and novices pay atteention to different aspect of videotaped episodes or to validate formal models of information processing. Our aim is different and more in the tradition of Yarbus (1967): the conduction of case studies analyzing patterns of indivi8dual canpaths depending on the viewer's questions and what she is trying to imagine.