In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In…

Studies of knowledge constructing often focus on the analysis of a single episode, without considering enough the history of the learners, or the future learners' trajectories with regard to the concepts learned. This paper presents an example of knowledge constructing within the context of peer learning. We show how the design of the task and the…

Presents a teaching approach related to the concept of function that lead students working within a graphic milieu to producing, discussing, and testing the validity of mathematical statements and theorems. Indicates that students experimenting with the approach became able to think of functions as objects and engage in questions of the validity…

Learning environment that facilitated the acquisition and expression of procedural skills in LOGO was set up for children in the 10- to 12-year range. Ten participants were placed in a series of situations that required them to manipulate programing procedures in LOGO. Analysis of children's behavior revealed their competence in manipulating…

Examples from related case studies illustrate possible consequences of a social constructivist approach to learning and teaching mathematics. Discusses student tasks that promote flexibility in mathematizing subject matter; constructive versus Euclidean geometry approaches; working with real-life mathematics problems; and product versus process…