Creating and Evaluating Interactive Formal Courseware for Mathematics and Computing

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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".