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Using mathematics as a reasoning instrument in physics instruction: a theoretical tool for the analysis of didactic approaches

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Author(s):
Ricardo Avelar Sotomaior Karam
Total Authors: 1
Document type: Doctoral Thesis
Press: São Paulo.
Institution: Universidade de São Paulo (USP). Faculdade de Educação (FE/SBD)
Defense date:
Examining board members:
Mauricio Pietrocola Pinto de Oliveira; Olival Freire Junior; Michel Henri Lucien Georges Paty; Cibelle Celestino Silva; Sonia Krapas Teixeira
Advisor: Mauricio Pietrocola Pinto de Oliveira
Abstract

Physics is a highly mathematized science, so that its concepts and methods are profoundly influenced by the mathematical thinking. Nevertheless, in the context of physics education, mathematics tends to be seen as a mere tool to describe and operate physical quantities, preventing students from understanding the structural role of the mathematical formalism for the development of physical theories. Thus, it is essential to devote a systematic research effort to investigate how to enable students to reason mathematically about the physical world. Despite the existence of several studies that identify the main difficulties faced by students to understand the meaning of physics equations and to use mathematics to solve physics problems, this topic has not been sufficiently investigated from the perspective of instruction. Aiming at contributing to this effort, this work conducts a case study in relativity and electromagnetism lectures, which were taught by an experienced and distinguished professor. The analysis of these lectures with the software videograph, along with historical and epistemological studies, led us to proposing a theoretical framework with eight categories, which is intended to describe and evaluate teaching approaches regarding the emphasis on the multiple aspects of the relationship between physics and mathematics. This framework is used in the analysis of 19 teaching episodes extracted from the recordings of the electromagnetism course given by the case study professor. His approach focused on constructing mathematical representations of physical concepts, physically interpreting mathematical expressions, encouraging metacognition, among others. This allowed us to identify several criteria related to the didactical quality of the lectures analyzed. These criteria are later justified by the professor in semi-structured interviews. The use of this analytical tool to conduct comparative studies between different lecturers/teachers, to evaluate different conceptions about the role of mathematics in physics textbooks and as a didactic resource for teacher education, are some of the future perspectives of this research. (AU)

FAPESP's process: 10/19276-8 - The structural role of mathematics in physical thought and implications for the teaching and learning of physics
Grantee:Ricardo Avelar Sotomaior Karam
Support Opportunities: Scholarships in Brazil - Doctorate