Didactic analysis of linear equation systems: A math teacher’s areas of expertise

Abstract

From a teaching perspective, mathematics is one of the disciplines that presents various difficulties in terms of comprehension, despite teachers’ thorough knowledge of the content to be taught. In these situations, didactic analysis plays a crucial role by providing a research methodology that allows for in-depth scrutiny of content, which helps teachers plan, considering all possible scenarios in a class. Therefore, the objective of this study is to demonstrate the usefulness of didactic analysis for teachers in training, focusing on the subject of Linear Equation Systems, taking as a reference its treatment in Secondary Education. It was carried out in the second semester of 2024. A documentary analysis was applied to the materials used to develop this topic: teaching unit, textbooks, teacher’s guide, and activity book. Based on these results, the knowledge that a mathematics teacher must possess to provide meaningful learning was explored in depth, analyzing, describing, and establishing the different meanings, representation systems, and phenomena that give meaning to this content. In addition, learning expectations, limitations, and opportunities were identified as key elements for teaching planning.