Plenary Lecture

Tommy Dreyfus , Holon Academic Institute of Technology, Israel

The teaching and learning of algebra, whether elementary, linear or modern algebra, seems to virtually cry out for computer support, for several reasons: A large variety of multi-representational tools are available, the heavier calculations can easily be taken over by the computer, and most importantly, appropriate software can be used to bridge the existing gap between the concrete and the abstract (see, e.g., Schwarz & Dreyfus, 1995). Indeed, there are examples of success in using technology for students' construction of meaning for abstract algebraic concepts but there are also examples of failure. In the lecture, I will examine a number of possible reasons for failure, including inadequate task design (Sierpinska, Dreyfus & Hillel, 1999) and the ambiguity of representatives for mathematical objects (Dreyfus & Hillel, 1998; Schwarz & Hershkowitz, in press). I will conclude that there is no simple explanation. I will then make the point that in order to deepen our understanding of the relevant learning processes, a re-conceptualization of abstraction is in order, as well as a research program that allows describing processes of abstraction. Such a re-conceptualization will be proposed and a research program will be outlined (Hershkowitz, Schwarz & Dreyfus, in press).