Aportes al Desarrollo del Pensamiento Matemático mediante la Modelación Geométrica y la Resolución de Problemas

Source abstract

The development of human mathematical thinking plays a crucial role in problem solving and contributes significantly to individual and social progress. This article socializes the results obtained from a research that aimed to contribute to the development of mathematical thinking through geometric modelling and problem solving in eighth grade students of a public institution in the department of Cundinamarca. The analysis of the background of the PISA and SABER tests showed the low performance of Colombian students in problem solving and modelling. In addition, the results obtained from the implementation of two exploratory activities show that there are scarce skills in these two processes. In this framework, eight didactic activities were designed and implemented with advanced mathematical content adapted to the age and educational level, where two fundamental processes were linked: geometric modelling and problem solving, and two processes intrinsic to the fundamental ones: mathematical visualisation and Sense Making. A qualitative approach was used with a participatory action design, eight rubrics, video and audio recordings, participant observation and a final survey. The results show that students made significant progress in the development of problem-solving skills in simulated or real contexts, relying on geometric modelling and mathematical visualisation, where they constructed robust mathematical concepts giving mathematical meaning and significance. It is concluded that the organisation and planning of the practical action of mathematics teaching under the four processes contributed significantly to the robust development of students’ mathematical thinking.