Adaptive instruction, inquiry-based mathematical learning, and the Galileo experiment: Some historical reflections

A simulation of the Galileo experiment establishing the quadratic law of falling bodies, namely, that the distance a body falls is proportional to the square of the time, was the source of the research collected in this volume on adaptive instruction and inquiry-based mathematical learning. The variety of theoretical frameworks in these papers as well as the methodological approaches adopted for reflecting on the classroom discussion of the Galileo experiment demonstrates the variety of ways one can see adaptive instruction and inquiry even in a single case study. This is perhaps not surprising where teaching takes the form of dialog and discussion rather than dictation: a certain measure of adaptation is inevitably present according to individual differences among students and in teachers’ educational goals. Galileo's own presentation of the law of falling bodies is in dialog form and manifests its own set of adaptive strategies. Of course it is a constructed dialog, but it may be for that very reason one can see these strategies more clearly than in a spontaneous discussion, particularly those connected to mathematical discourse and to metalevel discourse. As a postscript to the papers in this special issue, this paper takes a close look at the original Galileo dialog with these adaptive strategies in mind.