In this paper we describe a simple software system that allows students to practise their critical thinking skills by constructing argument maps of natural language arguments. As the students construct their maps of an argument, the system provides automatic, real time feedback on their progress. We outline the background and theoretical framework that led to the development of the system and then give a detailed example of how a student would work through a particular argument mapping exercise using the software. We then describe how the system was used in a single semester undergraduate critical thinking course. We evaluated the course using a standardised critical thinking test and measured an improvement in critical thinking skills of 0.45 standard deviations from pre-test to post-test; a modest, but encouraging result for a single semester course. We compare these results to those obtained in a number of other critical thinking courses, incorporating a variety of teaching methods. We conclude the paper with some comments on the limitations of the system and ways in which it might be improved and extended. (Contains 3 tables and 12 figures.)