The solving of mathematical problems and the factors that intervene in its teaching and learning

Abstract

One of the challenges in the teaching and learning of mathematics is problem solving, not only in the operational and motivational aspects, but also in the analysis and understanding of a situation, since it has been seen as a resolution of routine exercises that have more to do with mechanical or rote processes. This article investigates the factors that influence the teaching of mathematical problem solving. Several investigations have shown the influence of the teacher’s pedagogical practice, the affections that are promoted and generated in the classroom towards the subject and/or the teacher or the mathematical processes promoted in the classroom, among many others. As for the methodology adopted, it is adjusted to the characteristics of the quantitative approach, at a descriptive level with a field design. The members of the sample are a group of 80 teachers working in public or private institutions in Cúcuta and its metropolitan area. A validated questionnaire was applied, which consists of 54 items in total, where six mathematical processes are evaluated, of which 9 items correspond to the problem-solving process, all of them are evaluated by means of a five-level Likert scale. The results indicate that problem solving correlates significantly with the other mathematical processes and it is concluded that mathematical processes cannot function independently or in isolation from each other. An important aspect to highlight for future research is to identify what does the teacher understand by a problem? Do they really pose problem situations to their students or are they simply exercises in contextualized situations for which they have already defined a solution algorithm? These concerns arise as possible research complements to these results, since all mathematical processes should be associated with problem solving and it seems that some of them are not enhanced in classroom work.