This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

Dynamic Geometry Environments (DGEs) are popular tools in the exploration of geometry. This research is designed to explore the confidence of undergraduate mathematics students as they make mathematical statements when completing geometric tasks using DGEs. Students completed two series of tasks in both Euclidean and hyperbolic geometry. The first…

Common arguments for integrating the arts into mathematics courses include the arts fostering student creativity, improving academic achievement, and encouraging transfer between subjects. Research supporting these arguments is limited and carries layered complexities--such as what constitutes creativity and transfer, and whether they can be…

The emergence of non-Euclidean geometries in the 19th century rocked the foundations of mathematical knowledge and certainty. The tremors can still be felt in undergraduate mathematics today where encounters with non-Euclidean geometry are novel and often shocking to students. Because of its divergence from ordinary and comfortable notions of…

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate…