Abstract In this work, we show the results from a research made in a curricular innovation situation, whose main focus was to assess the performance of a teacher which implemented a teaching sequence on the concept of mass. This process began by a revision of the concept of mass in three different frameworks, namely classical mechanics, electromagnetism and relativity, with the purpose of addressing the epistemological changes of the subject from Newtonian mechanics to relativity. This revision yielded a written material about the theme and was employed in the development of the teaching sequence, which had as main methodology the Design Based Research. Our main research focus concerns the performance of the implementer teacher and his appropriation of the underlying didactic intention. In order to assess how effectively this teacher did absorb the intentions of the course he delivered, we relied on Chevallard’s Didactic Transposition Theory. Data were extracted from recordings of the teacher’s classes and the subsequent analysis has shown that there may be a relation between the difficulties he had in conveying the didactic intention and the innovative character of the contents involved. Our results indicate that these difficulties are directly related with the very nature of scientific knowledge and, in fact, belong to the realm of epistemology.

Abstract In this work, we discuss transformations in the meaning of the concept of mass, which are important to physics teaching, by means of three conceptual schemes, which emphasize visual patterns of knowledge organization. We begin by discussing how the meaning of a physical concept is constructed, through its relations with others. In physical theories, these connections usually involve mathematical operations. We focus on the concept of mass and its changes in three different contexts, namely classical mechanics, electromagnetism and relativity. Modifications are displayed as shifts in its relative position in conceptual schemes. These schemes enforce visual knowledge and may be used as didactical tools for teaching the subject, since they stress both the signification of mass in classical mechanics and its re-signification in relativity. This paves the way for a discussion of different approaches adopted for teaching the mass-energy relation in relativity, expressed by the famous formula E = m c 2. As the terms rest mass, relativistic mass and invariant mass, which have different ontological and epistemological contents, are part of this discussion, we consider the main approaches to mass present in both relativity textbooks and discourses by some influential physicists.

A física é uma maneira peculiar de raciocinar sobre o mundo que muitas vezes torna visível o invisível. Se é objetivo compreender o que a física é, reconhecer como as medições experimentais e o raciocínio matemático estão interligados é fundamental. Neste trabalho exemplificamos tal entrelaçamento por meio da análise de três estudos de caso. No primeiro, a explicação do efeito de Hall é enfatizada sobre o como se pode penetrar indiretamente na estrutura microscópica de um fio e avaliar o número de partículas carregadas por unidade de volume no seu interior, a partir de um conjunto de medidas macroscópicas. O segundo caso mostra como o nosso raciocínio nos permite determinar o raio do átomo de hidrogênio, através da medida experimental da energia de ligação do átomo. O terceiro exemplo vem da teoria cinética dos gases e ilustra como é possível calcular o número de partículas por unidade de volume de gás a partir dos valores experimentais de pressão e temperatura. Estes três estudos de caso mostram que o sinal de igual de certas equações pode ser visto como uma ponte (buraco de fechadura), que liga as dimensões empírica e teórica. Argumentamos que estas reflexões epistemológicas devem ser uma parte essencial da ensino da física, se pretendemos entregar uma imagem autêntica da natureza da física.

Physics is a peculiar way to reason about the world that often makes the invisible visible. If one aims at understanding what physics is about, recognise how experimental measurements and mathematical reasoning are intertwined is essential. In this work we exemplify such entanglement by analysing three case studies. In the first one, the explanation of the Hall effect underlines how we indirectly penetrate into the microscopic structure of a wire and manage to evaluate the number of charged particles per unit volume inside it from a set of macroscopic measurements. The second case shows how our reasoning allows us to determine the radius of a hydrogen atom from the experimental measure of the atom's binding energy. The third example comes from kinetic gas theory and illustrates how it is possible to estimate the number of gas particles per unit volume from the experimental values of pressure and temperature. These three case studies show that the equal sign of certain equations can be seen as a bridge (keyhole) connecting the empirical and theoretical dimensions. We argue that epistemological reflections should be an essential part of science education if we aim at delivering an authentic picture of the nature of physics.