Feeling the Slope with Augmented Reality Technology: Movements of Consciousness in the Learning of the Derivative

In this article, we explore how the concept of derivative is learned through a joint activity involving a tenth-grade student, an instructor, and an augmented reality application. This application, Touch the Derivative, allows users to trace a function graph with their hands and simultaneously displays the derivative function graph as they move their hands on the graph. This study is guided by the theory of knowledge objectification, which considers learning as a social, reflexive, and creative meaning-making dialectical process. The joint activity was qualitatively analyzed to answer the two research questions about the meaning of the derivative concept appearing in the joint activity and the role of contradictions. Focusing on the creative, embodied, and materialist process of becoming conscious of the function–derivative mathematical relations, in the results section we discuss the tenth-grader student’s movement of consciousness and the emerging contradictions outlining the semiotic means involved. The meaning-making process of the student progressed through four interrelated layers of consciousness, which evolved dynamically through the contradictions arising as a movement beyond the opposite perspectives of the student and the instructor. We conclude the article by emphasizing the need to understand the pedagogical potential of augmented reality in terms of the activity in which it is used.