Dynamic Haptic Geometry in Elementary and Undergraduate Classrooms

该项目将the Geometer’s Sketchpad®的动态几何环境与触觉技术，特别是力反馈设备相结合。该项目创造了一系列几何活动，特别关注2D图形和形状，以及一些简单的3D表面和实体，使不同年龄的用户能够用不同的感官探索这些物体的属性。该项目将这些技术目标与学习目标结合起来，旨在为更广泛的学生提供更好的机会，包括科学、工程和数学领域的代表性不足的群体。首席研究员（PI）将在James J. Kaput数学教育研究与创新中心进行一系列非正式的课后实验，然后与当地学校的小学生一起制定正式的课堂干预措施。PI还将把这些活动扩展到马萨诸塞大学的工程和数学本科课堂。该项目将使用从技术环境和其他工具收集的数据，记录学生如何在新环境中发现数学对象的属性并发展正式论证，这在不同年龄组之间如何变化，以及如何将其整合到正式的课堂环境中。这些数据还将用于改进系统的设计。该项目的目的是发现在吸引不同年龄的学生探索几何概念方面，将感觉与视觉的第二模态输入融合在一起的影响，并观察可以设计哪些类型的数学活动与使用传统教学形式的数学活动有显著不同。它将评估整合这种技术的实用性和教育效益。该项目在The Geometer的Sketchpad®软件的基础上建立了一个新的功能，并且由于Sketchpad在世界各地的教室中产生了巨大的影响和采用，因此有可能改变数学，特别是几何概念，如何被学生理解。

This project combines the dynamic geometry environment of The Geometer's Sketchpad® with haptic technology, particularly force feedback devices. The project is creating a series of geometric activities specifically focused on 2D figures and shapes as well as some simple 3D surfaces and solids, to enable users of various ages to explore the properties of these objects with various senses. The project combines these technology goals with learning goals that aim to provide better access to a wider variety of students, including underrepresented groups, in science, engineering, and mathematics. The Principal Investigator (PI) will conduct a series of informal after-school experiments at the James J. Kaput Center for Research and Innovation in Mathematics Education and then develop formal classroom interventions with primary school students in local schools. The PI will also extend these activities to engineering and mathematics undergraduate classrooms at the University of Massachusetts. The project will document, using data collected from the technological environment and other instruments, how students discover properties of mathematical objects within this new environment and develop formal argumentation, how this varies across age group, and how it can be integrated into formal classroom settings. The data will also be used to refine the design of the system. The aim of the project is to discover what impact fusing a second modal input of feel to sight achieves in terms of engaging students of a variety of ages into exploring geometric concepts, and observe what kinds of mathematical activities can be designed that are significantly different to those using traditional forms of instruction. It will evaluate the practicality and educational benefits of integrating such technology. The project builds a new functionality on top of The Geometer's Sketchpad® software, and because of Sketchpad's huge impact and adoption by classrooms across the world holds the promise a potentially transformation of how mathematics, in particular geometric concepts, are understood by students.