Logic classes need to satisfy students with widely different goals and needs. At one extreme are those who anticipate going on to careers in mathematics, computer science, or one of the other sciences or engineering disciplines. At the other are students who foresee no such career, but who want to be able to reason coherently in the problems that come up in every day life, with its increasing technical demands. Somewhere in-between are students who anticipate careers in something like law or political science where clear, logical reasoning is clearly required, but not necessarily at a formal level. Furthermore, within each group, students may have different reasoning styles: some people seem better at algebraic sorts of reasoning, while others are better at more geometric thought. There is much anecdotal evidence of this dichotomy within mathematics circles, and the results of Stenning et. al. [5] [4] begin to suggest that these reasoning styles may have a cognitive basis.
In planning and teaching logic courses, we need to bear these differences in mind. A course well-suited to someone with the skills and interests to become a mathematician or scientist might well be disastrous for someone with a different set of objectives; a course that might be wonderful for someone of an algebraic bent might be a nightmare for a more visual thinker. Finding techniques for teaching reasoning that bridge these various groups of students, however, is difficult.
Hyperproof, a courseware tool for teaching reasoning and first-order logic, has been designed for this purpose [1]. The system contains a proof checker for a logic containing two distinct forms of syntactic representations: a diagrammatic blocks world and standard, sentential, first-order predicate logic. Section 2 presents more details on the system and discusses the pedagogical benefits to the use of diagrammatic information. Section 3 discusses our experiences using Hyperproof in the classroom.