Maximum and minimum: approaches to these concepts in Portuguese textbooks

Abstract

The approach in Portuguese textbooks to the concepts of maximum and minimum has undergone alterations over the years. These changes were influenced by the official curriculum and more recently by the introduction of the graphic calculator in high schools. The concept of the derivative was first mentioned in the national curriculum in 1905 (Aires, 2006; Santiago, 2008). However, not until 1954, with the change of the program, the official curriculum began to make reference to the application of derivatives in the study of the variation of functions. In this study we will begin by examining the first national curriculum, which makes reference to the concepts of maximum and minimum of a function. We will, then, continue analyzing how the concept was shown in Portuguese textbooks, comparing two textbooks and identifying differences and similarities.