Knowledge to Teaching Linear Equations. A case study

David Alfonso PÁEZ – Daniel EUDAVE MUÑOZ

One of the current problems in Mathematics Education is the required knowledge to teach algebra. In several studies regarding teaching and learning of system of linear equations in two variables, it is reported that students have problems understanding and solving such systems. Several researchers consider that the teacher must create adequate environments for students to develop such kinds of thinking, so the students may move from one to the other, as well as to teach and promote reflection on the different mathematical methods to solve a system of equations in two variables, stressing the importance to the graphic method. The aim of this paper is to show the mathematical knowledge that a teacher reveals when solving systems of linear equations in two variables. We report a case study of a Mexican teacher, teaching mathematics even when his professional profile is not related. Two class sessions were videotaped in order to promote a reflection on his teaching practice. Results show this teacher has basic knowledge related to finding the values that satisfy a system of linear equations, which may produce conceptual and epistemological obstacles to students; results also show that he lacks mathematical arguments to determine and justify if a system of linear equations can be solved.