Touch the Derivative: Learning Mathematics with Augmented Reality

Abstract This editorial introduces a Special Issue devoted to the role of Augmented Reality (AR) in mathematics education, with a particular focus on the teaching and learning of calculus. While AR has been widely studied for its motivational and visualization benefits, much less is known about how it shapes mathematical activity and meaning-making. The six contributions in this volume address this gap by analysing a single, richly documented learning episode with the Touch the Derivative application, which enables learners to explore function–derivative relationships through embodied tracing and real-time graphical feedback. Each paper applies a distinct theoretical lens: Theory of Knowledge Objectification, Simondon’s notions of technicity and affectivity, semiotic bundle and conceptual blending, spatial–rhythmic framings, AR manipulatives through design affordances and feedback analysis. Complementing these contributions, a concluding postscript paper offers programmatic reflections on task design, curriculum integration, affordances, and memory, weaving together insights from the five studies and outlining directions for future research. Taken together, these perspectives illuminate the cognitive, embodied, affective, and spatial processes that unfold in an AR environment and highlight their implications for both research and educational practice. The Special Issue thus advances theoretical understandings of learning in AR environments, and provides practical insights for task design, curriculum development, and fostering collaboration between researchers and teachers in mathematics education.