The articulation of didactic engineering with the didactic situations theory: Examples of applications to the study of integer sequences

Abstract

According to the guidelines of the Didactic Engineering as a research methodology and in complementarity with the Didactic Situations Theory, we will show how Didactic Engineering and the Didactic Situations Theory can be articulated to study integer sequences. We will present two examples of applications of this articulation between Didactic Engineering and the Didactic Situations Theory to the study of numerical sequences and it is our intention to describe the main elements of two initial stages of Didactic Engineering, namely, Preliminary Analysis and Design and a priori Analysis. We will highlight the conception of didactic situations and the possible behaviors and resolution of the students before the problem situations, organized for purposes of experimentation.