Orchestrating the discovery of the Greatest Common Divisor and the Least Common Multiple hidden in a digital spirograph

This paper focuses on good practices in technology-rich mathematics education, and in particular, on the principles and heuristics that may guide the teacher’s orchestration of fruitful activities. We present a teaching activity, framed by the Method of Varied Inquiry (MVI), which involved a small group of 10th grade students, with the aim to let them discover the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) as objects that mathematize a digital spirograph. Results are analysed and discussed to show how students’ learning can be supported by the teacher’s orchestration of the activity.