Abstract

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels: 7th grade in 2013 and 8th grade in 2014. With this aim, a training plan was designed, based on a Model of Professional Competences in Mathematics (MCPM) (Diaz & Poblete, 2004) which was validated and previously evaluated through the implementation of the national research Project Fondecyt N° 1010980, and was based on a strategy for teaching mathematics that considered the didactic approach to content and its assessment, considering the types of problems and types of mathematics competences (Diaz & Poblete, 2009). In this model, the mathematics teacher’s competences are defined as the effective and efficient skills acquired when teaching mathematics with quality, in order to ensure a good formative educational performance. The theoretical framework underlying this research was built on two pillars: the Anthropological Theory of Didactics (TAD) of Yves Chevallard (1991) and the Competence Approach as a scientific concept developed by a social science such as Didactics of Mathematics, aimed at the integral personal development oriented towards professional, social and civic skills, based on lifelong learning(Gascón, 2011). Due to the nature of this project, in which the process and the product are important, quantitativedescriptive and qualitative-interpretative methods were used. The population consisted of urban and rural schools in the regions of Los Rios and Los Lagos region of southern Chile. For the selection of the non-random sample, the school was considered as a unit, and the analysis was focused on the competences of teachers and the learning achievements of students. This project considered a total of 164 primary school teachers without expertise in mathematics and 6.700 students from 117 public schools in urban and rural areas of Chile. It is important to mention that all of the teachers did not have training on teaching mathematics. The results show that teachers’ performance in didactic-mathematic tasks improves substantially, thus improving their teaching performance. They also showed specific competences such as the ability to apply disciplinary knowledge, the ability to use different teaching strategies; ability to promote learning by problem-solving and the ability to use updated assessment methods. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions the country