Abstract:

Problem posing is a fundamental competence that enhances the didactic-mathematical knowledge of the mathematics teacher, so it should be an objective in teacher education plans. The aim of this paper is to describe, by means of a case study, the design and implementation of a formative action with prospective primary school teachers, which aims to develop this competence. Some theoretical and methodological tools of the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction are used. The teacher’s Didactic-Mathematical Knowledge and Competence (DMKC) model proposed by the OSA interprets and extends other teacher’s knowledge models used in mathematics education, such as the MKT model. In the DMKC model, it is assumed that teachers should have a common mathematical knowledge regarding the educational level where they teach, and an extended mathematical knowledge that allows them to articulate it with higher levels. In addition, for each mathematical content, the teacher should have didactic-mathematical knowledge of the different facets that affect the educational process. This allows the teacher, when dealing with a certain mathematical situation, to recognize the diversity of meanings that are put into play, to be able to solve the task using different procedures and showing different justifications (epistemic facet), as well as to be competent to modify it according to the students’ learning needs (instructional and cognitive facets). In the task proposed to the participants, a situation is posed in a probabilistic context (fair play). Prospective teachers are asked to create a problem involving proportional reasoning, solve it, recognise the mathematical objects and processes involved and finally identify potential difficulties of the students. They must then modify the problem to create a new statement that places greater cognitive demand on potential learners, justifying why the new problem is more challenging than the original one.

Keywords:

Problem posing, Proportional reasoning, Probabilistic reasoning, Teacher training.