Riding, Katherine;
Yang, Yang;
Clark-Wilson, Alison;
Mavrikis, Manolis;
Geraniou, Eirini;
Crisan, Cosette;
(2025)
Rethinking Affordances and Feedback in AR Environments to Foster Richer Mathematical Inquiry: Lessons from Touch the Derivative.
Digital Experiences in Mathematics Education
10.1007/s40751-025-00179-8.
(In press).
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Abstract
Augmented reality (AR) technologies offer unique opportunities to explore fundamental ideas in calculus by blending digital and physical worlds, yet realising the full potential of this hybrid reality requires a degree of creativity as we grapple with existing theoretical constructs and seek new ones. This study centres on a single-participant case: Karim, a 15-year-old secondary-school student who used an AR prototype “Touch the Derivative” to investigate relationships between functions and their derivatives. In this paper, we examine how AR technologies can support rich mathematical inquiry by rethinking two interconnected elements: affordances and feedback. We analyse the crucial role of the physical world within AR environments through two intersecting perspectives: the spatial affordances enabled by six degrees of freedom (6DoF), and the physical, cognitive, and contextual dimensions of AR. We then examine how AR facilitates various forms of feedback—through Karim’s interactions with both the researcher and the AR environment itself—highlighting the role of feedback to support understanding and engagement. We conclude by exploring how intentionally designed feedback mechanisms—enabled by analytics and automation—can amplify the affordances of AR and provide more impactful, inquiry-based learning experiences.
| Type: | Article |
|---|---|
| Title: | Rethinking Affordances and Feedback in AR Environments to Foster Richer Mathematical Inquiry: Lessons from Touch the Derivative |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40751-025-00179-8 |
| Publisher version: | https://doi.org/10.1007/s40751-025-00179-8 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Augmented reality, Inquiry-based learning, Design affordances, Feedback, Calculus education |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Education UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education > IOE - Culture, Communication and Media UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education > IOE - Curriculum, Pedagogy and Assessment |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10214113 |
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