Designing example-generating tasks for a technology-rich mathematical environment

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students’ mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined use of a dynamic mathematics software environment and a computer-aided assessment system. In example-generating tasks, students are asked to generate examples that fulfil certain conditions. Based on data in terms of examples generated by 491 first-year engineering students, taking a first course in calculus, the paper examines patterns of student response to three example-generating tasks. As a theoretical lens, the notions of dimensions of possible variation and associated ranges of permissible change are used. In light of the observed patterns, the paper provides some guiding principles for designing example-generating tasks and associated formative feedback to foster students’ mathematical understanding by enriching their example spaces. For example, this paper illustrates occasions where it might be instructive to start by asking for two examples, followed by adapted feedback before requesting a third example.