Abstract

This article addresses how the concept of finding the area of a quadrilateral has been traditionally taught to student teachers majoring in Middle School Mathematics Education at the Catholic University of Santísima Concepción (UCSC) in Chile. It is important to note that Education Majors already possess a notion as to how to teach the concept of finding the area of a quadrilateral which we refer to here as their didactic cultural heritage. This study observes didactic cultural heritage as a product of the Chilean Educational School System and proposes a baseline to monitor and compare results among these students at UCSC and compare student views with fundamental elements of Didactic Theoretical Situations (DTS) according to Guy Brousseau (1986). Current teaching strategies are based on axiomatic structures and reproductive problem resolution and consider teaching as based on a traditional organizational method. However, students have also proposed more practical teaching methods applicable to real-life scenarios which involve increased teacher-student interaction and additional ways of representing diverse geometric objects, reflexive type exercises and active “devolution” alluding to a more conceptual mastery of area. The results conclude that teaching methods tend to be repeated and Education Majors, in this case, focusing on Middle School Math, will ultimately teach a concept according to how they were taught that same concept in the classroom when they were students in Middle School.

Keywords Mathematics Teacher Education; Mathematics Teaching Methodology; Theory of Didactical Situations; Didactic Cultural Heritage