In this paper, we report our first experiment in teaching the theory of computability in the problem-based way. As far as we know, this is the first experiment of applying the problem-based method to a purely theoretical course of computer science. Performing the course consisted of three parts: First, the new subjects were learnt according to the classical seven step method, which contains both individual and group work, and problem reports were written. Second, the students participated in a

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... raditional exercise session, in which the new techniques were practised in details. And third, the students kept a learning diary, in which they processed the subjects further, tried to construct an overall schema of things learnt, and supervised their own learning. The results were really successful: the students committed themselves well and the drop out percentage was very small; they achieved very deep understanding of the subjects measured by their grades and quality of learning diaries; the experience was enjoyable for both the students and the teachers; and finally, the method supported different kinds of learners very well. Index terms -theory of computation, problem-based learning. S1H-1