Dynamic Haptic Geometry in Elementary and Undergraduate Classrooms

该项目将几何仪SketchPad®的动态几何环境与触觉技术相结合，特别是力反馈设备。该项目正在创建一系列专门针对2D图形和形状以及一些简单的3D表面和实体的几何活动，以使不同年龄的用户能够探索这些具有不同感官的对象的属性。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，包括在科学、工程和数学领域代表不足的群体。首席调查员(PI)将在詹姆斯·J·卡普特数学教育研究和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进行正式课堂干预。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生课堂。该项目将使用从技术环境和其他工具收集的数据，记录学生如何在这个新环境中发现数学对象的性质并发展正式的辩论，这在不同年龄段之间是如何变化的，以及如何将其融入正式的课堂环境。这些数据还将用于改进系统的设计。该项目的目的是发现融合感觉到视觉的第二种模式输入在吸引不同年龄的学生探索几何概念方面产生了什么影响，并观察可以设计出哪些类型的数学活动与使用传统教学形式的活动有显著不同。它将评估整合这些技术的实用性和教育效益。该项目在几何仪的SketchPad®软件的基础上构建了一项新功能，由于SketchPad的巨大影响和世界各地教室的采用，有望改变学生理解数学，特别是几何概念的方式。

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.