Meditations on Future Directions for AR Research in Mathematics Education: Postscript Paper for Touch the Derivative

Abstract The papers in this volume consider an instance of using AR technology for developing an idea of the derivative and derivative function, an experiment called “Touch the Derivative.” The analyses bring out not only the potential of AR for exploring the specific mathematical topic of the derivative but also general questions concerning AR that can and, perhaps, ought to be explored. On the basis of these papers and the Touch the Derivative experiment, this short postscript paper will, accordingly, consider some future directions for research. These future directions come under the following headings: Tasks and Task Design; Curriculum and AR—Tool-Content-Reciprocity; Defining the Affordances of AR; Interiority and AR Memory. While serving as a synthesis of some of the results and approaches presented in this special issue, some theoretical ideas diverging from those in the papers will be suggested, for example, tool-content reciprocity and AR memory.