One of the most useful ways to enhance collaboration is to create scenarios where learners are able to interact more effectively. Nevertheless, the design of pedagogically sound and well-thought-out collaborative learning scenarios is a complex issue. This is due to the context of group learning where the synergy among learners' interactions…

This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and…

The culture of the young may, in fact, be a harbinger enticing us to follow a pathway from which will emerge the re-conceptualized educational practices of this new century. The culture of those older will, no doubt, strive to maintain the more golden aspects of their now historical learning experiences. One of the tasks of all educators, but…

The d'Arbeloff Interactive Mathematics Project or d'AIMP is an initiative that seeks to enhance and ultimately transform the teaching and learning of introductory mathematics at the Massachusetts Institute of Technology. A result of this project is a suite of "mathlets," a carefully developed set of dynamic computer applets for use in the…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

Develops properties of tasks that are pedagogically efficient and allow students to discover mathematical concepts for themselves. Illustrates the structure and philosophy of powerful tasks for the concept of angle. Presents seven examples of powerful tasks, including two involving two-dimensional graphic systems. (Contains 39 references.)…

Frequently writing is now no longer the central mode of representation in learning materials--textbooks, Web-based resources, teacher-produced materials. Still (as well as moving) images are increasingly prominent as carriers of meaning. Uses and forms of writing have undergone profound changes over the last decades, which calls for a social,…