Abstract:

In terms of mathematics education at secondary schools, there has yet to be a detailed assessment of augmented reality (AR) from the perspective of mathematics didactics. This paper seeks to redress the balance by taking key teaching-related aspects such as an appropriate image of mathematics, modeling, concept acquisition, and the open task format as the starting point for its investigation. As well as providing confirmation of certain established aspects and pinpointing additional possibilities, it also notes the limitations of AR within secondary-level mathematics education. The aspects confirmed here include the special potential of AR for visualization – notably in the field of geometry and above all in analytic geometry – along with the importance of AR in the context of interactive textbooks, worksheets, and Padlet learning environments, in which digital content such as photos, videos, 3D models, and audio files can be accessed with ease by each individual pupil via trackers/triggers and thus integrated into the learning process. This investigation also identifies modeling as a particular strength of AR, given that this technology can enable a slower transition from the real-world object to the idealized model and promote a subsequent period of reflection. While this can inspire the first step towards a mathematical model, there are clear limits to its usefulness for mathematization and working within the mathematical model itself; it would also be more of a hindrance than a help when seeking to communicate an appropriate image of mathematics in these areas. For a specific slate of topics, however, AR can promote the dynamic and static side of mathematics as well as the aesthetic and functional side and enables discovery learning and interdisciplinary settings. Yet while other publications have highlighted the particular importance of AR for abstract concepts, this must always be assessed on a case-by-case basis. This paper notes the limits of AR regarding the acquisition of abstract and complex mathematical concepts, with the discussion centering on the concepts of limit value and function. Crucially, AR can promote individual learning processes in diverse learning groups and also boost communication and collaboration – not least given that it supports the open task format within mathematics education in a variety of ways.

Keywords:

Augmented reality, digital tools in mathematics education, secondary level.