Transforming Linear Algebra Education with GeoGebra Applets

这个项目正在开发12个交互式小程序，使用二维和三维动画来帮助学生可视化线性代数中的概念（例如向量、向量空间、线性变换、特征值、特征向量、行列式和正交性）。该项目使用的是GeoGebra，这是一个免费的、易于访问和使用的软件包，可兼容多种平台，包括手机和电脑平板电脑，在全国范围内广泛使用。每个applet都附有使用说明和教学模块，其中包含示例和学习练习，可在正式课程中使用，也可由学生和教师独立使用。每个模块还包括一个示例stem应用程序，为使用相应的applet提供上下文。这个项目的智力价值是基于研究表明，帮助学生可视化数学过程可以促进对相关概念的更好理解。此外，通过关注线性代数及其在化学、物理、工程和类似领域的广泛应用，该项目填补了促进数学概念学习的更大教育小程序集合中的空白。一组beta测试者和评论者的观点正在为开发工作提供信息，并且正在使用经过深思熟虑的实验设计来评估applet对学生学习的影响。在更广泛的影响方面，该项目正在使用积极的传播计划，包括会议研讨会和迷你课程，用于探索和下载小程序的专用web服务器，以及促进开发人员和用户之间互动的GeoGebraWiki。GeoGebra软件的灵活性及其在包括移动设备在内的多种平台上使用的适应性也有助于该项目具有广泛影响的潜力，并得到日益增长的GeoGebra开发人员社区的支持。

This project is developing twelve interactive applets that use 2-D and 3-D animation to help students visualize concepts in linear algebra (e.g. vectors, vector spaces, linear transformations, eigenvalues, eigenvectors, determinants, and orthogonality). The project is using GeoGebra, a free, easy to access and use software package that is compatible with multiple platforms including mobile phones and computer tablets, and has wide use nationally. Accompanying each applet are directions for use and an instructional module with examples and learning exercises usable both in formal classes and independently by students and teachers. Each module also includes an example STEM-application to provide context for the use of the corresponding applet. The intellectual merit of this project is grounded in research that indicates helping students visualize mathematical processes promotes better understanding of the concepts involved. Moreover, by focusing on linear algebra with its extensive applications in chemistry, physics, engineering and similar fields, the project is filling a gap within the larger collection of educational applets that promote learning of mathematical concepts. The perspectives of a set of beta testers and reviewers are informing the development work, and a well-considered experimental design is being used to assess the applets' impact on student learning. With respect to broader impacts, the project is using an aggressive dissemination plan featuring conference workshops and mini-courses, a dedicated web server for exploring and downloading the applets, plus the GeoGebraWiki to facilitate interactions among developers and users. The flexibility of the GeoGebra software and its adaptability for use on multiple platforms including mobile devices also contribute to the project's potential for broad impact and support from a growing community of GeoGebra developers.