Quod erat demonstrandum: Understanding and Explaining Equations in Physics Teacher Education

Abstract

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their master's degree in two European universities. The course had two main goals: (1) To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and (2) To expand students' repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students' views on the role of mathematics in physics, an increase in the participants' awareness of the difficulties faced by learners to understand physics equations and a broadening in the students' repertoire to answer ''Why?'' questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived.

Louis de Broglie's wave-particle duality: from textbooks’ blackboxes to a chain of reference presentation

“…Since the Scientific Revolution, mathematics play a crucial role in scientific theories, being considered a structural part of it [72]. In theoretical Physics, however, it plays an even more substantial role, since it is the main tool used to articulate knowledge [73].…”

“…It does not mean however that this is the only way to derive this equation. A mathematical equation may assume different epistemological status and meanings depending on the theoretical context in which it is developed [72].…”

“…The validity of his ideas is guaranteed by the network of theories and tools that he mobilized to speak about reality, i.e, his phenomenotechnique [67]. In this sense, all Physics concepts change through time and they can never be considered the final truth -their correctness is always relative to the network they mobilize [70] and the epistemological status of an equation is always dependent of the theoretical construction it belongs to [72]. Thus, by analyzing de Broglie original conceptions and how they changed we may have glimpses about how Theoretical Physics works and how it is possible to achieve important results through counter-inductive movements [74].…”

“…This means that the "practice" used by de Broglie to find the mathematical equation that expresses wave-particle duality is ignored. All textbooks only present the result p = h λ and some of them treat it as a postulate -which may be considered an epistemological misclassification [72] In the sequence, we searched whether textbooks, at least, mentioned the elements (theories and assumptions) that de Broglie used. Results are summarized in table 2.…”

“…We comprehend that a scientific formation encompasses not only the development of the capacity of manipulating equations but also the understanding of the articulation and of the meaning of these equations. Mathematics is a structural part of Physics [72] and it cannot be treated as a simple tool that we use when it is applicable. To derive an equation such as the wavelengthmomentum relation allows us to understand what it means and what it is speaking about.…”