Robert L. Smith
Abstract
EXCHECK is a system for developing mathematically-based CAI courses. It is currently being used at Stanford University to teach a college-credit course in axiomatic set theory
The design of this system had several goals. First, we wanted an instructional system that would provide a semantic base for our work on processing natural language and computer-generated audio. Axiomatic mathematics fits this description in that the underlying semantics is relatively well understood, but many of the interesting problems of natural language are also involved in the informal language of mathematics and the informal expression of mathematical proofs.
Second, we recognized that traditional proof checkers were inadequate for teaching mathematics, or for that matter, introductory logic. People understand mathematical concepts and arguments at a level much higher than the traditional formal systems of mathematical logic.
Finally, we designed the EXCHECK system to be an extensible system in which other curricula could be implemented with incrementally less work.
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Index Terms
- A generalized system for university mathematics instruction
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