Mathematics and Physics at Work: The Study of Cosmological Functions in a High School

This paper presents a pedagogical approach developed within the Liceo Matematico (LM) project at the University of Salerno, focusing on an interdisciplinary lesson for final-year high school students. Drawing on principles of constructivist learning and inquiry-based teaching, we address a common student misconception that arises from the traditional textbook’s depiction of distance in a static universe, versus the reality of cosmic expansion. Specifically, we present a structured method for introducing and differentiating between key cosmological distance concepts: proper distance, luminosity distance, angular diameter distance, and light-travel distance. This approach is grounded in the pedagogical principle of leveraging student-initiated questions as a starting point for deeper learning. By modeling these distances as mathematical functions, we aim to clarify counterintuitive phenomena, such as the behavior of distance over time in an expanding universe. This lesson helps students better grasp fundamental cosmological concepts like redshift and the observable universe, illustrating how mathematics can be a powerful tool for modeling complex physical realities. To our knowledge, no previous high-school level activity has explicitly combined the formal study of mathematical functions with the exploration of cosmological distance measures, making this approach a novel contribution to the existing educational literature.