Learning Second-order Covariation with GeoGebra and Augmented Reality

Abstract

Second-order covariation is a form of mathematical reasoning that needs to be characterized both concerning students' cognitive processes and the design of tasks that promote it. This contribution aims to shed light on these two issues by comparing data related to the same learning experiment performed in two different learning environments: GeoGebra and augmented reality. The data analysis focuses on a characterization of the forms of second-order covariation emerging from students' learning process. Findings reveal how the two environments enable students to engage in second-order covariation: in the GeoGebra environment the students engaged in second-order covariation while using the digital tool; in the augmented reality environment, secondorder covariation fully emerged only after the students performed the experiment. Possible interpretations for this result are discussed.