Basic components in the scienctific didactical training of the secondary school mathematics teachers

Secondary mathematics teacher training in Spain is currently the subject of a heated revision debate. The speed of social, cultural, scientific and economic changes have left a hundred years old teacher training model well behind. However, academical inertia and professional interests are impeding a real new training of the mathematics teacher as an autonomous mathematical educator. Teachers of Didactic of Mathematics and the Spanish Associations of mathematics teachers have recently been discussing the issue. Their conclusions are included here.

Analyzing and selecting tasks for mathematics teaching: a heuristic

In planning units and lessons every day, teachers face the problem of designing a sequence of activities to promote learning. In particular, they are expected to foster the development of learning goals in their students. Based on the idea of learning path of a task, we describe a heuristic procedure to enable teachers to characterize a learning goal in terms of its cognitive requirements and to analyze and select tasks based on this characterization. We then present an example of how a group of future teachers used this heuristic in a preservice teachers training course and discuss its contributions and constraints.

Characterizing mentors’ performance in mathematics teacher education

This study describes the performance of the mentors in a blended graduate-level training program of teachers in the field of secondary school mathematics. We codified and analyzed the mentors’ comments on the projects presented by the groups of in-service teachers for whom they (the mentors) were responsible. To do this, we developed a structure of categories and codes based on a combination of a literature review, a model of teacher learning, and a cyclical review of the data. We performed two types of analysis: frequency and cluster. The first analysis permitted us to characterize the common actions shared by most of the mentors. From the second, we established three profiles of the mentors’ actions.