La metacognición en la invención y resolución de problemas matemáticos

Abstract

The present monograph is located within the field of mathematics didactics. Through the review and bibliographic analysis, the aim was to theoretically support the intervention of metacognition in the invention and resolution of mathematical problems. First, the concept and classification of metacognition was addressed, to then see its relevance within the current educational system, its relationship with the constructivist theory, and its presence and contribution within mathematics. Secondly, the invention and problem solving were presented as central axes within the mathematical activity, for their contributions to the learning of this discipline, as well as the consubstantial relationship that these tasks share jointly in the mental processes that they require for its approach. Also, models proposed by several authors were described, among them Polya, models that showed the phases to follow for a successful approach to the problems. In the third place, it was analyzed how the metacognitive processes focused on knowledge and cognitive regulation are present and act within the work with problems. Finally, it was concluded that inventing and solving mathematical problems requires favorable emotions, knowledge of what is known (people, tasks and strategies), and mental processes such as reflecting, planning, questioning, evaluating, etc. Mental processes that agree with the models proposed to work on problems and that allow us to demonstrate the action of metacognition. In addition, it should be emphasized, the role of the teacher as a mediator to promote metacognitive processes during the activities of invention and problem solving