La resolución de problemas matemáticos a la luz de la metodología Polya en la enseñanza del pensamiento numérico en estudiantes del grado 3º de la Institución Educativa de Yatí.

Abstract

The present research study done in the Institution Educative de Yatí, jurisdiction of the municipality of Magangué, in the department of Bolívar, aims to analyze how the resolution of mathematical problems influence the teaching of numerical thinking. This analysis aims to establish the main causes that originate the low levels of performance of 3rd grade students in the area of mathematics, specifically in problem solving skills with content of numerical thinking. We called the study as follows “The resolution of mathematical problems in the light of Polya methodology in the teaching of numerical thought”. The profiling of this investigation constitutes the search for concrete and precise answers to the following question: How does the resolution of mathematical problems affect the teaching of numerical thinking in 3rd grade students of the Yatí educational institution? On the other hand, at the time of referencing the background and theoretical bases that support the present investigation, we have cited similar studies of the local, national and international order related to the subject under study and that allow not only to show the globality of the problem but also to have A clearer vision of what is intended to be done by knowing the effects and results of the research object in other contexts. The theories on which we rely on the foundation of the concepts of the different categories willing to research and within which we cite: The resolution of problems, where the ideas of authors such as Shoenfeld and G. Polya are described, with the establishment of the steps that must be taken into account in the teaching of problem solving, and that allows, the incentive of reasoning in students. In addition, the different pedagogical approaches used throughout the times in the teaching of mathematics are described as: The Behavioral or traditional approach, the cognitive approach in this learning is not produced by the acquisition of new knowledge, nor by the decomposition of complex knowledge in simpler ones, but it goes further, being its intention to alter the cognitive structures of the student to give rise to other more extensive and finally current approach, work by competences. This is focused on reasoning and understanding; Students before solving a certain problem will have to reason. On the other hand and landing on the foundations that give legitimacy to this study and that allow us to strengthen our actions within a legally established academic field, we can say that we rely on the following normative guidelines: 1. Article, 20 of Law 115 of 1994. (General Law of Education), which establishes the general objectives of basic education, in its Literal C textually expresses the need to: Expand and deepen the logical and analytical reasoning for the interpretation and solution of the problems of science, technology and everyday life. In the methodological framework, the instruments and methods (Approach, design, technique, key informants, phases of the investigation) which have been used for the study, which are transcendental for the collection, are selected and defined in a descriptive way of the information and data that will allow obtaining a response to the matter under investigation. The stages of the case study design are also presented. Traditionally, the development of a case study is divided into five well-defined phases that are: 1. Case selection. 2. Development of an instrument to capture information. 3. Location of sources and data collection. 4. Analysis and interpretation of information and results. This study is not intended to measure the degree to which the qualities of events are found, but to discover as many qualities as possible, (in our case, all possible factors with negative effectson the teaching processes of problem solving problems In addition, and trying to maintain consistency with the selected approach, we chose to adopt the case study as a method of study. The informants in this study are all teachers and students of the Institución Educativa de Yatí, constituted by a headquarters administrative and 3 tax offices located in the rural sector For the selection of key informants, it was determined by the choice of a teacher and a third grade student for each one of the offices, in this sense four teachers and four students were selected. In the study three categories were determined, which constituted the cases of inquiry in the present study; these are: 1 Mathematical Problem Solving, 2. Problem Solving Teaching and 3. Numerical Thinking. Subdivided into their respective subcategories, as shown in the attached table. For the execution of this research work, two types of techniques have been taken into account as research instruments: “Test procedure” and “Observation,” trying to be consistent with the research design (Case study), and the type of qualitative research. In the end, the triangulation of the information was made for the purpose of the investigation, which consisted of conducting a thorough analysis of the characteristics observed in each of the categories under study by each of the individuals who participated in the present study as Key Informants and this is explicitly described in the main project document. In conclusion, the findings found reveal the great of the competence of problem solving in the teaching of numerical thinking and that its disuse by teachers in the planning and execution of classes remarkably influences the low performance of students in the contents related to numerical thinking.