8. april 2025

The Mathematics of Map Projections

The Mathematics of Map Projections
An Analysis and Design of Teaching Material for an Interdisciplinary Lesson

IND's Studenterserie nr. 128, 2025, Speciale i Matematik & Didaktik

Josefine Dixen Zwisler

Vejleder: Carl Winsløw

Abstract: 

This is a theoretical thesis in Mathematics Education which examines how map projections, as an interdisciplinary topic between mathematics and geography, can be communicated to Danish upper secondary students. Given the limited literature on teaching map projections in Danish upper secondary schools, the thesis focuses on transposing scholarly knowledge on the subject into actual teaching material. To do so, Didactical Engineering is used as the methodology, with emphasis on its preliminary analyses as the foundation of the design. The analyses include an epistemological analysis of the mathematics at stake, an institutional analysis identifying potential conditions and constrains affecting the development of the teaching material, as well as an didactical analysis about existing didactic literature, which relates to the thesis. Based on these analyses, the Theory of Didactical Situations is used as a framework for the design process.

The thesis demonstrates, through the example of the teaching material, how and what aspects of the theory of map projections can be communicated. It suggests that as an interdisciplinary topic, the geographical aspects of map projection and the use of maps, can serve as a meaningful way to present the theory of map projections, as a transition to the mathematics of map projections. In addition to this, the design suggests that most of the scholarly knowledge about map projections, especially the mathematics, has the potential to be transposed into concepts mentioned in the curricula and textbooks, and provides an example hereof. However, the analyses also suggest that there might be some limitations to how much that can be transposed. The designed teaching material then provides an example on how these limitations can be addressed differently.

Emner