What modes of use does the mathematics teacher propose in initial training to teach the Pythagorean theorem in secondary education?

Abstract

This article presents a case study on the meanings that beginning students of mathematics teaching assign to the Pythagorean theorem. In this study, emphasis was placed on one of the most important elements used for structuring a curriculum: the ways in which students of mathematics teaching make use of a mathematical concept. Twenty (20) students of Mathematics Teaching from the four public universities of Costa Rica that offer this career participated in the study. A questionnaire was designed and applied for collecting information, which consisted of 7 items which presented and solved tasks based on the use of the Pythagorean theorem. Answers to two of these items stand out, which are associated with the phenomenology of a mathematical concept. Content analysis, one of the components of didactic analysis, was used to examine and characterize teaching situations, together with the contexts proposed by this group of students for the statement and solution of mathematics tasks associated with the theorem. The results show that this theorem was mainly seen as a tool for solving mathematical tasks related to the calculation of lengths. Additionally, participants experienced some difficulties in proposing tasks based on non-mathematical situations, and the quality of the tasks proposed varies.