Abstract

Rather than being random deviation, student errors can be a source of insight into the nature of student difficulties. This paper reports on (and offers pedagogical advice concerning) many common student errors in the construction of proofs, in the application of inference and replacement rules, and in the choice of proof strategies. In addition, a detailed description of the bottom-up strategy for “working backwards” is supplied, along with a discussion of the main difficulties students face when trying to solve proofs in this fashion. Ultimately, it is argued that students can employ both top-down and bottom-up proofs strategies by making use of a graphic proof representation.