This paper discusses the simple open student models used in two of our constraint-based tutors, SQL-Tutor and KERMIT, and their effects on self-assessment. The systems present a high-level abstraction of the detailed information contained in the student model, in terms of skill meters representing the student's progress on domain concepts. SQL-Tutor presents the open student model when the student requires it, or when selecting new problems. KERMIT, on the other hand, continuously displays a high-level summary of the student's progress, while more detailed information is available on request. Our results show that even simple open student models can have important positive effects on learning and students' meta-cognitive skills. Students appreciated having access to their models, and they felt this feature contributed to their understanding of the domain. Performance of less able students becomes significantly better than that of their peers of similar abilities without access to their models. We have also seen that open student models can help students learn to select better problems.