Incidence of George Polya's Problem Solving Approach in the Variational Thinking’s Development DOI:

Abstract

Problem-solving has been a fundamental part of teaching mathematics, allowing it to satisfy the requirements when facing an everyday event. The objective of this study was to analyze the impact of George Pólya's approach to solving mathematical problems on the development of variational thinking, seen as one of the most recurrent problems in mathematics teaching. The application of a methodology under the naturalistic paradigm, Action Research method, qualitative approach, and interpretive type that allowed us to describe this difficulty in the sixth-grade students of the José Odel Lizarazo Villamaga educational institution, based on specific data taken from the plan proposed in the Pólya method. In this process, the phenomenon was approached from diagnosis and direct observation, the understanding and conception of problems through collaborative and cooperative work actions, and the implementation of mathematical resources and concepts to propose resolution options and reach a process of verification of the results. Once Pólya's proposal was executed, an evolution of variational thinking was evident in the key informants from its preoperational stage, where the initial difficulties in understanding the mathematical situations presented the weaknesses in the mathematical reading and writing process were recognized. Leading students to delve deeper into the inquiry, explore hypotheses, and propose solutions to the identified unknowns.