Didactic analysis in teacher training based on the onto-semiotic approach tools. The case of proportionality textbook lessons on proportionality

Abstract

A textbook lesson shows the instructional process planned by the author to promote the learning of   content by potential students. Assessing the suitability of a lesson requires an in-depth analysis that considers the sequence of operative and discursive practices proposed by the author for developing the mathematical content, how the required prior knowledge is managed, and identifying potentially conflictive elements that the teacher must consider. This paper describes the results of a training experience with students for primary school teacher aimed at fostering the competence of didactical analysis, using a proportionality textbook lesson. The aim is for students to analyse teaching situations by characterising objects and processes as constituent elements of the mathematical content (onto-semiotic analysis) to be learned and to identify their role in possible learning difficulties (identification of semiotic conflicts). The design, implementation, and evaluation of the experience are based on the application of theoretical-methodological tools of the Onto-semiotic Approach. The content analysis of the reports produced by the students for teacher reveals their difficulties in identifying the objects (mainly propositions and arguments) that are required or emerge from the practices, through the respective mathematical processes. Accordingly, the identification of conflicts, especially those referring to specific epistemic and cognitive aspects of proportionality or their treatment is not sufficiently satisfactory.