This study deals with students' construction of mathematical objects. The basic claim is that the need for communication—any attempt to evoke certain actions by others—is the primary driving force behind all human cognitive processes. Effectiveness of verbal communication is seen as a function of the quality of its focus. Material objects may serve as a basis for creation of such a focus, but in some discourses, focus-engendering objects must be created. Such discursive construction is observed in analysis of one classroom episode. Special attention is given to metaphor, which is the point of departure for the construction process, and to the subsequent dialectical process of closing the gap between the metaphor-induced expectations and the need for a well-defined construction procedure to ensure effective communication.
Anna Sierpinska, Jeremy Kilpatrick, Nicolas Balacheff, A. Geoffrey Howson, Anna Sfard and Heinz Steinbring
As mathematics education has become better established as a domain of scienti fic research (if not as a scientific discipline), exactly what this research is and what its results are have become less clear. The hi story of the past three International Congresses on Mathematical Education demonstrates the need for greater clarity. At the Budapest congress in 1988, in particular, there was a general feeling that mathematics educators from different parts of the world. countries, or even areas of the same country often talk past one another. There seems to be a lack of consensus on what it means to be a mathematics educator. Standards of scientific quality and the criteria for accepting a paper vary considerably among the more than 250 journals on mathematics education published throughout the world.
Miriam Ben-Yehuda, Ilana Lavy, Liora Linchevski and Anna Sfard
To investigate mechanisms of failure in mathematics, we adopt the communicational approach to cognition, which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine the arithmetical discourses of two 18-year-old girls with long histories of learning difficulties. The resulting arithmetical discourse profiles of the two students help us substantiate the following two claims: (1) Almost any person may become a skillful participant of arithmetical discourse, provided, first, that a discursive mode is found that makes the best of this person's special strengths and second, that in the process of teaching, the general sociocultural context of learning is taken into account as having a central role in enabling or barring one's access to literate discourses; (2) if the potential for successful participation remains often unrealized, it is mainly because of certain widely practiced abuses of literate mathematical discourse.