The observation that the human mind operates in two distinct thinking modes--intuitive and analytical- have occupied psychological and educational researchers for several decades now. Much of this research has focused on the explanatory power of intuitive thinking as source of errors and misconceptions, but in this article, in contrast, we view…

We analyze the role of generic proofs in helping students access difficult proofs more easily and naturally. We present three examples of generic proving--an elementary one on numbers, a more advanced one on permutations, and yet more advanced one on groups--and consider the affordances and pitfalls of the method by reflecting on these examples. A…

Explores (n=113) computer science majors' understanding of Lagrange's Theorem (the order of a subgroup divides the order of a finite group), its converse, and its applications. (SW)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…

The relation between mathematical and computational aspects of recursion are discussed and some examples analyzed. Definition, proof, and construction are considered, as well as their counterparts in computer languages (illustrated with Logo procedures). (MNS)