Adaptive instruction strategies to foster covariational reasoning in a digitally rich environment

This paper explores the strategies used by a senior teacher to adapt her instruction about covariation among quantities to her students and their learning processes. It analyses data from a teaching experiment conducted in Turin with twenty 15-year-old students. They used a digital simulation of the so-called Galileo experiment – a ball rolling along an inclined plane – to model the quadratic law of its motion. The adaptive instruction of the teacher is examined via a multimodal lens, analysing the semiotic productions active in the classroom: the teacher and her students' utterances, gestures, inscriptions, and the role of instruments within the development of the teaching design. The analysis highlights the primary strategies employed by the teacher during her instruction process and how these strategies support the students in reaching different levels of covariational reasoning, as defined by an extension of the Thompson and Carlson framework. Finally, some pedagogical implications are sketched.