The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in R[superscript 3]. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The…

Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even…

For more than 14 years, the National Council of Teachers of Mathematics (1989, 2000) has advocated that teachers of mathematics facilitate that students make connections of various kinds, in their learning of mathematics. Semiotic theories, including those of Peirce and those of Saussure and Lacan (each for different purposes), provide useful…

Acknowledging the complex relationships which the field of didactics of mathematics has with other research fields (e.g. mathematics, educational sciences, epistemology, history, psychology, semiotics, sociology, cognitive science), the authors analyze in this paper some cases of fruitful and some of failed dialogue between experts of the…

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…