La resolución de problemas matemáticos a través del análisis secuencial de procesos

Introduction. The macroscopic perspective is one of the approaches to tackled research on problem solving. Our study , from this perspective, is focused in the thinking stages when solving mathematical problems, offering an innovative standpoint because we apply the sequential analysis process and the polar coordinate technique to study the sequential relationships and the global interrelationships between the different stages of mathematical problem solving. Method. This study is based on observational methodology, using as unit of analysis the set of processes that we can observe from a pair of students when solving a mathematical problem. The quality of the information (reability intra and inter-observer and the Chi-squared independent test) is guaranteed, so it is allowed to apply the sequential analisys and also the polar coordinates technique. Results. We present two precision levels, one per each student, and the other for each pair. We then obtain the set of basic statistics; the periods of collaborative work and parallel work; the transition probabilities, the signifivative sequences or chains, the traslations of realisations and the set of maps that includes the global relationships between different stages. These results allow to describe and analyse the behabiour of students and pair when solving mathematical problems and the collaborative work performed. Discussion. This paper reflects a new approach to research the interrelationships that arise between the stages of problem solving and the collaborative work from a macroscopic viewpoint. This fact constitutes a new methodology in mathematics education. The two precision levels allow to obtain results that describe the individual influence in the whole process of problem solving, describing more deeply the interrelationships emerged between students and the collaborative work performed. Also this paper shows the potential of this kind of analysis for studying the learning difficulties in solving mathematical problems