An Espistemology of Dynamic Geometry

要了解学生如何在“动态几何”环境(如几何画板和CABRI等工具)中构建数学思想，需要清楚地描述：(1)软件中包含的数学“原材料”；(2)学生如何使用这些“原材料”。数学对象和允许的变换是什么？他们注意和注意到了哪些？他们如何解读他们注意到的东西？通过对开发人员的采访和我们的Won分析，我们将调查这些工具的数学和教学潜力。对学生的实验和临床采访很好地导致了对与该软件的定义功能相关的概念的初步认识论：动态“拖拽”。然后，聚焦实验将重新检查这些结果，并对其进行改进，以得出对学习和教学以及材料设计的启示。因此，该项目将为动态几何的认识论奠定经验和理论基础。

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.