A Methodological Design for Teacher Conceptions about Students Production by Using Semiotic Representation and Dimensions of Teacher's Knowledge

Abstract

Our goal in this study is to present a methodological design for the analysis of empirical data in a qualitative research. To achieve that purpose, we used results of a previous research about mathematics problem solving, in which high school students were asked to solve a trigonometry question with two items. In the present work, questionnaires were answered by twenty high school teachers, who were asked to characterize the kind of the most representative errors found in that research, as well as to propose ways of intervention in mathematics teaching that could stimulate the students to critically think about their errors, in order to overcome them. The teachers’ answers were analysed upon the light of two theoretical frameworks: the first deals with mathematical learning by using semiotic analysis, as proposed by Duval, and the second one is related to the teacher's knowledge, according to Shulman. From this analysis, we proposed a methodological design to the qualitative analysis of teaching activities in the pedagogical approach of problem solving in mathematics.

Keywords:
Methodological design; Semiotics and mathematical learning; Discursive functions of language; Teacher's training