School of Mathematical & Statistical Sciences Faculty Publications
Document Type
Article
Publication Date
3-16-2026
Abstract
The study is part of an instructional design project focused on introductory real analysis. The goal of the project is to develop a theoretically grounded and empirically supported instructional approach that builds on students’ experiences in the calculus sequence to engage them in the reinvention of the rigorous foundations of the calculus. An essential aspect of this foundation is the completeness of the real numbers. Drawing on the didactical phenomenology heuristic from the theory of Realistic Mathematics Education (RME), we conducted an iterative instructional design study focused on the completeness axiom. The work proceeded in two phases. First, we conducted an a priori phenomenological analysis to identify a context that would be experientially real to the students and that could be productively mathematized using the least upper bound concept and to develop a conjectured trajectory for the mathematization process. Second, we conducted a series of design experiments to develop a didactical phenomenology for completeness. The purpose of this empirical work was to test the viability of the design suggested by our a priori analysis and inform refinements to our design. The purpose of this paper is to share our design process, describe the resulting didactical phenomenology, and illustrate the corresponding reinvention process with examples from our empirical studies.
Recommended Citation
Larsen, Sean, Tenchita Alzaga Elizondo, Kristen Vroom, and Stephen Strand. "Toward a didactical phenomenology for the completeness axiom: Larsen et al." Educational Studies in Mathematics (2026): 1-17. https://doi.org/10.1007/s10649-026-10494-5
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Educational Studies in Mathematics
DOI
10.1007/s10649-026-10494-5
Comments
This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it.