Abstracts Mathematics

Linguagem científica de Thomas Kuhn e a matemática em livros didáticos da educação básica e manual de ensino superior de física: o caso da 1ª lei da termodinâmica

by William Borella

Abstract: This paper's main purpose is to approach mathematics while teaching physics, having the First Law of Thermodynamics as the empirical grounding from high school textbooks and from a manual of higher learning. Aiming to understand the relation that the teaching of mathematics presents in the teaching of physics and its educational role in the conception of physics. Thomas Kuhn?s epistemology was adopted as a theoretical frame. Its notion of the scientific language, which emcompases the lexicon and the diciplinary matrix?s elements, as symbolic generalizations, exemplary and models, has a huge analytical potential to think about mathematics functioning in physics and its teaching. A comparative analysis is carried from two books, PNLD 2018 and a higher education manual. Through Khun?s approach, and based on the analyzed material it is understood that the First Law of Thermodynamics is intrinsically related to mathematics? role in physics as scientific education, in basic education as in the physician formation. Differences are observed in the way the symbolic generalizations (verbal and equational language) regarding the First Law of Thermodynamics are presented in different textbooks, the way they are understood, in the relation with the exemplary and the relation to the models. Simultaneously, it was possible to observe that mathematics has a fundamental role in physics's scientific language according to Thomas Kuhn?s concept. It appears in the symbolic generalizations, related to the lexicon, exemplary and models. It is concluded that physics?s learning of the scientific language happens among the relation between the elements of the disciplinary matrix among each other, elements that establish a relation amid the lexicon and the world through its use; these elements can present and establish different relations in different textbooks. This relation between mathematics and the scientific language suggested by Kuhn shows in the textbooks in structures in higher and basic education. With variations regarding mathematics's profundity implied in higher education?s textbook and the goal presented by each one. It was possible to observe that similar characteristics involved in different levels and the learning objectives of the scientific language of the First Law of Thermodynamics can be an obstacle in the triad student-scientific language- mathematics. Meaning that by using the disciplinary matrix?s elements in a classroom with the basic education?s textbook the student is led to replicate the same path traced in a physicist?s education, where in reality the objective is otherwise.