La competencia matemática. Caracterización de actividades de aprendizaje y de evaluación en la resolución de problemas en la enseñanza obligatoria

Abstract

Problem solving is agreed to be a fundamental mathematical competence. In Catalonia, it is expected that students acquire the problem solving competence during the compulsory education. Throughout this last decade, Catalan administration has been working in the identification of the aims of this mathematical competence. However, it is difficult to determine how to put this competence into practice in a properly way as well as to evaluate its effects in the educational community. The present thesis arises in this context. It aims to go more deeply into how to improve the management of the problem solving competence in the compulsory education with two intentions. On the one hand, as a research study, contribute evidences and significant arguments to the research community regarding mathematical education and, specifically, problem solving. On the other hand, share the instruments elaborated and used for the study and the corresponding analysis with the educational community, with the purpose that they will be useful in the teaching practice. Problem solving activates most of the mathematical aspects developed within the mathematics education. In this sense, problem solving is understood as the core of any teaching and learning mathematical process (Kilpatrcik, 1978; Lester, 1994; Luelmo, 1996; Ponte, 2007; Schoenfeld, 1992). Beyond this, we understand that the learning focus of the problem solving competence lies on the resolution process itself, in learning how to become aware of the process of solving problems and to act accordingly. In short, it aims to students learn how to manage mathematical skills and attitudes involved in the resolution processes in order to increasingly solve different mathematical problems more efficiently. We notice that regulation has a key role both in problem solving process as well as for the self-assessment of learning. According to this double and key role of regulation in the competence view of the mathematical education, we elaborated a set of problem solving instruments for the students who are in the transition from the Primary School to the Secondary School. This set of instruments consists of a collection of mathematical problems and two regulation tools, tagged as performance rubric and orientation basis (Sanmartí, 2010). Its aim is to improve the student’s mathematical competence in problem solving. This problem solving-related set of instruments were implemented in the last year of Primary School and first year of Secondary School at various schools in Barcelona. Based on the obtained data, we focus our study on the collection of problems and the generation process and use of problem solving-related orientation basis. The students solved the suggested problems using a problem solving-related orientation basis. We analyse students’ resolutions according to the used orientation basis and the comments from the teachers and students involved in the study. Although with nuances, analysed data inform of a positive impact that this set of instruments, as classroom activities, can play in students for the acquisition of problem solving competence. Moreover, the analyses inform about key aspects regarding the generation and the implementation processes of these instruments entailed with the teaching practice. Finally, we highlight that this is a qualitative study. However, in order to measure the impact of one of the orientation basis as a scaffolding resource, we use a recommended tool for small quantitative analyses: the Fisher's Exact Test. This small quantitative study, in turn, consolidates and enhances some of the evidences analyzed qualitatively.

Date of Award	18 Oct 2017
Original language	Spanish
Supervisor	Jordi Deulofeu Piquet (Director)