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This paper presents the design of an Intelligent Tutoring System (ITS) MathEH, that is a coached problem solving system, also called "Electronic Homework". In describing the main modules of the system, we emphasize its novel aspects: (1). Using Constraint Logic Programming (CLP) as the domain knowledge representation and automatic reasoning mechanism. (2). A method for probability propagation in Bayesian networks to achieve two adversary requirements: exact probability computation and real-time response. (3). The design decisions about how to deploy MathEH on the WWW.