We present a model to analyze the students' activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin's structural description of arguments, Peirce's notions of sign, diagrammatic reasoning and abduction, and Habermas' model for rational behavior.…

Discusses the role of context problems as they are used in the Dutch approach known as realistic mathematics education (RME). Uses an RME design for a calculus course to illustrate that theory based on the design heuristic using context problems and modeling, which was developed for primary school mathematics, also fits advanced topics such as…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…