Designing technology-based tasks for enhancing mathematical understanding through problem solving

Abstract

In this paper, we propose some organizing principles that can be useful for high schools or bachelor mathematics teachers when designing technology-based instructional tasks. It is widely accepted that tasks are the most important aspect to promote students’ mathematical understanding, since tasks offer opportunities to attain relevant sensorial experiences fostering the construction of mental images as sources of meanings for mathematical concepts. In this vein, we reflect on the work developed by three bachelor mathematics teachers who participated in a problem solving seminar. The main points identified during task design involved recognizing how mathematical concepts are structured around the task, and which are needed to approach it, and proposing a hypothetical learning trajectory in which technology plays a role as amplifier and reorganizer of cognitive processes.