Abstract: Based on the constraint logic programming system BPU-CLP, the authors developed an intelligent tutoring system named BPU-ITS-Math, which is a student-oriented ITS aiming at high school mathematics tutoring. Here the authors introduce the method for designing and implementing the automatic reasoning module of BPU-ITS-Math. In BPU-ITS-Math, rules are represented with classical strips operators, and the exercise base, the knowledge base and the general reasoning machine are all implemented with the program of BPU-CLP. The technique of the rule design and expression is presented with the examples of calculating the mathematical function domains of high school. The backward reasoning algorithm of the general reasoning machine is also given. Currently, BPU-ITS-Math has solved successfully more than 200 exercises of calculating domains of mathematical functions. Now the authors are applying our achievments to extending the knowledge base for the purpose of making BPU-ITS-Math solve exercises of other mathematics domains.