Abstract
Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to isolate, a priori, the possibilities and limitations of computer-based tasks is thus desirable. In this paper I develop such a tool in the form of a framework. Key components of this framework are the mathematical focus of the task, its cognitive demands, its technical demands and the affordances of the technology that it exploits. I illustrate the use of this framework by analysing three tasks that were used in a content-based functions course for in-service teachers. This analysis illuminates important pedagogical aspects of these tasks. It also supports the notion that the use of technology in a task may afford the design of high-order thinking activities.
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