Creating and Evaluating Interactive Formal Courseware for Mathematics and Computing

这是一项为大学水平的数学和计算机教学创造一种新媒介的提议。这种媒介的基础是一个由超文本和正式参考材料组成的在线交互式数据库，该数据库是用现代证明开发系统（Nuprl1）构建的。这种由计算机系统动画的文本和正式材料的混合提供了一种全新的课件；它也为教授那些在教育文献中被认为是基本的数学问题解决技能提供了新的机会。通过将新媒介与新兴的信息基础设施连接起来，教育创新的可能性是前所未有的。要求提供资金以创建这种媒介的范例，探索其教育价值并加以传播。这些材料将首先用于离散数学课程（在数学系、计算机科学系和电子工程系提供）。在这些课程中，这些工具将使计算数学和日益复杂的软件工程数学的教学更加相关和有效——这两者对美国技术都至关重要。该建议包括一个详细的技术案例，说明所建议内容的可行性，以及一个基于研究者丰富的教学经验和先前的实验努力以及有限的媒介实例的教学案例。引言部分总结了整个案例，而随后的两节则进行了详细阐述。第二节详细介绍了新的研究技术，第三节详细介绍了本文提出的教学依据。读作“新珍珠”。

This is a proposal to produce a new medium for teaching college-level mathematics and computing. The basis for this medium is an on-line interactive data base of hypertext integrated with formal reference material built with a modern proof development system (Nuprl1). This hybrid of text and formal material animated by a computer system provides an entirely new kind of courseware; it also presents new opportunities for teaching those mathematical problem solving skills found to be fundamental in the educational literature. By connecting the new medium to the emerging information infrastructure, the possibilities for educational innovation are unprecedented. Funding is requested to create an example of this medium, explore its educational value, and disseminate it. The material will be deployed first in discrete mathematics courses (offered in Mathematics, Computer Science and Electrical Engineering departments). In such courses these tools will enable more relevant and effective teaching of computational mathematics and of the increasingly sophisticated mathematics of software engineering--both critical to U. S. technology. The proposal includes a detailed technical case for the feasibility of what is proposed and a pedagogical case based on the extensive teaching experience of the investigator and on prior experimental efforts with limited examples of the medium. The introduction summarizes the entire case whereas the subsequent two sections elaborate. Section two details the new research technology, and section three details the pedagogical basis for the proposal. Pronounced "new pearl".