Working together with introductory situations of proportional reasoning in primary school. Analysis of a teaching experience centered on the teacher, the student and the content

Abstract Although there is a fairly generalized consensus in mathematics education in favour of constructivist-type instructional models, their pertinence is controversial. Between the extreme centered models, either on the student or on the teacher, we find other mixed type models, where both educational process agents play a leading role, depending on the intended content and the students’ previous knowledge. In this article, we describe and base the implementation of a three stages mixed-type instructional model: In a first phase, the teacher acquires the leading role by introducing the theme; in a second phase of collaborative work between teacher and students, they jointly solve a situation-problem, and in a third phase the students work autonomously. This model has been experimented with 5th grade primary school students, with the objective of creating a first encounter with direct proportionality problems. Although this is a case study that does not allow the generalization of results, the evaluation of the learning achieved serves to formulate hypotheses about the influence of the instructional mixed model on student learning, which can be tested in new research cycles on this subject and in similar contexts.