Knowledge and Competencies of Prospective Teachers for the Creation of Proportionality Problems

Background: 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. Objectives: This paper describes and analyses a training intervention with prospective teachers to develop such competence using proportionality tasks. Design: This qualitative and interpretative study adopts a methodology characteristic of didactic design or engineering research. The design of the intervention and the content analysis of the participants’ answers use theoretical and methodological tools from the onto-semiotic approach to mathematical knowledge and instruction. Context and participants: The training action was carried out with 127 undergraduates attending a primary education teaching degree in the framework of the Design and Development of the Mathematics Curriculum in Primary Education subject in a Spanish university. Data collection and analysis: The prospective teachers, organised in 33 working teams, were asked to create two problems based on a given situation and to identify objects and difficulties, the solution of which was analysed by the research team. Results: The results show that the participants encounter difficulties in elaborating relevant proportionality problems from the given situation, identifying the associated level of complexity, recognising the mathematical objects interacting in the solution to their problems and the difficulties that these could cause to primary school pupils. Conclusions: It is mandatory to reinforce problem creation competence and proportional reasoning in teacher education