What do errors reveal about the mathematical mind? Intriguingly, errors are often logically consistent and rule based rather than being random. Investigating errors, therefore, presents an opportunity for uncovering the mental representations underlying mathematical reasoning. A useful question is whether errors break down into different categories or types. If this were the case, then one could explain a variety of seemingly different problem-solving behaviors by using only a few principles. The aim of this article is to provide a taxonomy of rule-based errors in mathematical reasoning that illustrates how a few basic mental processes may be responsible for generating myriad different errors. Implications for general processes of reasoning and problem solving are discussed.
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