Generating examples: an intriguing problem-solving activity

Generating examples of mathematical objects can be very difficult for students and it can be considered a problem solving activity. In literature, some potentialities of such activity are suggested, from different points of view and for different reasons. Our investigation aims to better identify the characteristics and the potentialities of the processes of constructing examples. The analysis, carried out by observing students’ processes, reveals a high complexity of examples generation tasks. In particular, giving an example requires continuous integrations between semiotic activities on mathematical objects and argumentation, between concept image and concept definition, between cognitive and metacognitive resources. The study on these processes highlights the potentialities of generating examples activity as a tool for researchers in investigating many aspects of students’ thinking and for teachers in promoting students’ understanding and conceptualization.