Abstract
This paper describes the prototype of an Internet-based computer-assisted-learning system that allows learners to practice mathematical problem solving. Petri nets are used by the system as its knowledge representation model. Math knowledge within a chosen domain is pre-analyzed to derive a set of macro functions for use in solving problems. Each macro function typically embodies a math concept or rule that may be applied to transform a math problem from a state to another. The macro functions correspond to transitions in a Petri net graph, while the conditions for triggering those functions correspond to places. With Petri net graphs, the system can store experts’ static problem-solving knowledge as well as learners’ dynamic problem-solving procedures. The graphs may then be used effectively for diagnosing learners’ problem-solving difficulties and for offering guidance. The system also supports synchronous and asynchronous network communication functions that may be used by learners to solicit help from other system users. Users may add new problems to the problem bank with the system-provided editor. In addition, the system can automatically detect new solution paths to any old or new problem and augment the system’s knowledge base accordingly.
| Keywords: | object-oriented design; Petri nets; computer assisted learning; mathematical problem solving; relational database systems |
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