Conceptualizing functional relationships in an augmented reality environment: connecting real and virtual worlds

This paper describes how students conceptualize real-life phenomena in which two or more quantities are covarying in an augmented reality environment. With this technology, real-world phenomena and virtual representations may be connected simultaneously. We aim to investigate how students connect elements of the two worlds when conceptualizing functional relationships. We relied on Zindel's conceptual facet model for functional relationships to achieve this goal, specifically focusing on the covariational approach. Three 11th-grade students participated in two real-life experiments (Galileo and Hooke's law experiments) at the heart of this study. The qualitative analysis of selected episodes revealed how students relate the two worlds and how covariational reasoning is reflected in such connections. The findings show that students frequently related elements of the real and virtual worlds while engaging in several forms of covariational reasoning. The theoretical contribution resulting from this study is expanding Zindel's model to address the conceptualization of families of functions indexed by a parameter.