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Keith Weber and Juan Pablo Mejía-Ramos

In a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their initial reading of a proof took half as long as their total time spent reading that proof. Authors Keith Weber and Juan Pablo Mejía-Ramos present an analysis of Inglis and Alcock's data that suggests that mathematicians frequently used an initial skimming strategy when engaging in proof validation tasks.

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Nicholas H. Wasserman, Keith Weber, Timothy Fukawa-Connelly and Juan Pablo Mejía-Ramos

A 2D version of Cavalieri's Principle is productive for the teaching of area. In this manuscript, we consider an area-preserving transformation, “segment-skewing,” which provides alternative justification methods for area formulas, conceptual insights into statements about area, and foreshadows transitions about area in calculus via the Riemann integral.