Interplay between Mathematics and Physics to Catch the Nature of a Scientific Breakthrough: The Case of the Blackbody

This paper aims to provide a contribution to the research in physics education regarding the interplay between mathematics and physics in teaching and learning physics at the university level. The argument is developed through a study focused on the historical case study of the blackbody that led Planck to make one of the most significant scientific breakthroughs in physics: the introduction of discreteness and quantization into physical processes. The study is methodologically guided by the model that Udhen, Karam, Pietrocola, and Pospiech elaborated to highlight the interplay between physics and mathematics within teaching and learning practices [O. Uhden, R. Karam, M. Pietrocola, and G. Pospiech, Modelling mathematical reasoning in physics education, Sci. Educ. Netherlands 21, 485 (2012).]. The model emphasizes the distinction between the technical and structural roles of mathematics in physics, with the latter role being argued to correspond to processes of mathematization and interpretation. We used this model to analyze Planck's original papers and to reconstruct the reasoning that, thanks to the structural role played by mathematics, paved the way for the quantistic scientific breakthrough. The results of the analysis led us to design a teaching tutorial that we implemented with mathematics and physics university students. Students' reactions are reported to discuss the educational potential of the approach beyond the specific case and to argue for its potential general application to other similar physics topics.