QUANTIDADES EXTENSIVAS E QUANTIDADES INTENSIVAS: RELAÇÕES COM O ENSINO DE RESOLUÇÃO DE QUESTÕES MATEMÁTICAS

Abstract

Intensive quantities such as density, velocity, among others, have been relatively neglected in teaching, as studies are mostly carried out with extensive quantities. Therefore, the research's guiding question arises: What are the contributions that the understanding of intensive quantities and extensive quantities can bring to the teaching of solving mathematical questions? In response to this guiding question, this theoretical essay brings the results of a study whose objective was to analyze how extensive quantities and intensive quantities relate to the teaching of solving mathematical questions. The text discusses the implications for teaching solving mathematical questions, addressing factors that influence the difficulty of solving them, such as the semantic structure of the question, the number, the syntactic complexity and the position of the unknown quantity. Based on a bibliographic review, the theoretical essay presented the results of the analysis on how these two categories of quantities can be understood and used in mathematics teaching. The text also presents the challenge of ratio studies, which involve intensive quantities, a type of quantity conceptually more demanding than those that are evaluated by counting or measuring, called extensive. It is pointed out that current curricular approaches generally fail to promote students' thinking about intensive quantities.

Keywords: Teaching. Mathematics. Extensive Quantity. Intensive Quantity. Question Resolution.