Representation of Problem-Solving Procedures in MathCAL

Abstract

MathCAL is a network-based learning system for users to practice mathematical problem solving. Math knowledge is pre-analyzed to derive a set of macro functions for use in solving problems in a specific domain. Each macro function typically represents a math concept or rule which may be used to transform a math problem from a state into the next. Learners select problems to work on from the problem bank and proceed with problem solving step by step. The kernel of the system uses Petri nets to dynamically record a learner's problem-solving activities. The Petri-net representation allows the system to determine appropriateness of a user's application of a function at a certain step. It also enables the system to understand a user's thinking process when it is requested to offer guidance. MathCAL also supports synchronous and asynchronous network functions which may be used to establish a collaborative problem-solving environment. In addition, MathCAL allows users to add new problems and/or new solution paths to its databases.