Modelling Roles of Mathematics in Physics

Abstract

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in modelling and problem solving. In this article, we present a new characterisation of the roles mathematics plays in physics and physics education, taking as a premise that mathematics serves as a constitutive structure in physics analogous to language. In doing so, we aim to highlight how mathematics affects the way we conceptualise physical phenomena. To contextualise our characterisation, we examine some of the existing models and discuss aspects of the interplay between physics and mathematics that are missing in them. We then show how these aspects are incorporated in our characterisation in which mathematics serves as a foundation upon which physical theories are built, and on which we may build mathematical representations of physical information that in turn serve as a basis for further reasoning and modifications. Through reasoning processes mathematics also aids in generating new information and explanations. We have elucidated each of these roles with an example from the historical development of quantum physics. To conclude, we discuss how our new characterisation may aid the development of physics education and physics education research.

Exploration of physics teacher identity through life experience: A case study of science teacher with excellent achievement

“…This is because mathematics is closely related to physics. This is in line with the results of the research from Palmgren & Rasa (2022), which showed that mathematics has an important and even inseparable role in physics and also in physics education. They add an explanation that mathematics is closely related to the formation of physics knowledge and that the role of mathematics cannot be separated from learning physics.…”

How much is just maths? Investigating problem solving in chemical kinetics at the interface of chemistry and mathematics through the development of an extended mathematical modelling cycle

“…Over the past two decades, there has been a remarkable growth in the body of literature exploring the role of mathematics in scientific disciplines. Much of this work has focused on its role in physics education (Pospiech et al, 2019;Palmgren and Rasa, 2022). While traditionally, mathematics has been regarded primarily as a tool in physics, its role has lately been recognised to extend beyond these conventional notions, suggesting a twofold nature (Uhden et al, 2012).…”

Research hotspots and development trends of model and modelling education research: Bibliometric analysis based on CiteSpace

“…It is also necessary for teachers to master additional pedagogical knowledge about modelling [ 19 ]. The opportunities and forms of MM embedded in teaching are flexible, appearing in various learning stages [ [20] , [21] , [22] ], in different disciplines [ 23 , 24 ], with multiple carriers [ 25 , 26 ], and combined with other strategies [ 27 , 28 ]. To present the panorama of MMER, we included science education research related to modelling practice into the scope of analysis and tried to obtain the international hot spots and trends.…”