An Espistemology of Dynamic Geometry

要了解学生如何在“动态几何”环境（如Geometer's Sketchpad和Cabri等工具）中构建数学思想，需要明确描述：(1)软件中包含的数学“原材料”；(2)学生如何使用这些“原材料”。数学对象和允许的转换是什么？他们会注意并关注哪些？他们如何解释他们所注意到的？通过对开发人员的采访和我们的分析，我们将调查这些工具的数学和教学潜力。与学生的实验和临床访谈很好地导致了与该软件定义特征相关的概念的初步认识论：动态“拖拽”集中的实验将重新检查这些结果并磨练它们，从而得出学习和教学以及材料设计的含义。因此，该项目将为动态几何的认识论建立经验和理论基础。

To understand how students constructs mathematical ideas in "Dynamic Geometry" environments (tools like Geometer's Sketchpad and Cabri), one needs clear characterizations of : (1) the mathematical "raw materials" embodied in the software and (2) how students use these "raw materials." What are the mathematical objects and allowable transformations? Which do they notice and attend to? How do they interpret what they notice? Through interviews with developers, and through our won analyses, we will investigate the tools' mathematical and pedagogical potential. Experiments and clinical interviews with students well lead to a preliminary epistemology of concepts related to the defining feature of this software: dynamic "dragging." focussed experiments will then reexamine these results and hone them, to derive implications for learning and teaching, and for the design of materials. Thus the project will establish empirical and theoretical foundations for an epistemology of dynamic geometry.