Computer Use and Views of the Mind

Empirical and theoretical research on human cognition has provided a variety of insights and new approaches to mathematics learning and teaching. This research is guided by various different paradigms. In an eclectic way and without paying very much regard to the various research paradigms, in this chapter I will choose some especially interesting (to me) results and research orientations for the following purpose. After a - necessarily short - presentation of the respective basic ideas I will try to point out possible relations with, and applications to, the use of the computer for the learning and teaching of mathematics. These relations, for example, are hints as to which roles the computer could play and which functions it could fulfill in the learning/teaching process. Thereby ” computer” should always be understood as a synonym for the whole system consisting of hardware and software and possibly other audiovisual tools. The overall tendency which results is to view the computer as a tool and a means for our cognitive activity. Conditions and demands with regard to the structure and the properties of the computer systems to be used will follow implicitly from our considerations. I do not assert that the software available today can play all the learning activity. I am more generally interested in establishing a broad framework and a basic orientation for computer use in mathematics education which then has to be adapted specifically to various concrete situations.