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.
Keith Weber and Juan Pablo Mejía-Ramos
Kristen Lew and Juan Pablo Mejía-Ramos
This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.
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.