Resolución de problemas como estrategia para el fortalecimiento de las competencias matemáticas en estudiantes de grado noveno de la Institución Educativa Colegio Juan Atalaya del municipio de Cúcuta (Norte de Santander)
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Fecha
2022
Autores
Contreras Gelves, Sandra
Osorio Alvarez, Carmen Alicia
Otálora Salazar, Solangela
Título de la revista
ISSN de la revista
Título del volumen
Editor
Ediciones Universidad Simón Bolívar
Facultad de Ciencias Jurídicas y Sociales
Facultad de Ciencias Jurídicas y Sociales
Resumen
Antecedentes
Tras consultar estudios previos y agrupados por origen y conceptos se encuentran: A nivel internacional por Comprensión lectora y resolución de problemas: a Collantes A (2021), Gutarra C (2018), Pardavé C. (2018) y por Métodos de resolución de problemas a Díaz y Díaz (2018). A nivel Nacional por Comprensión Lectora y Resolución de Problemas a: Marriaga M y Páez P. (2018), por Resolución de Problemas a Vesga y Escobar (2018) y por Estrategias a Díaz, Natera, y Pérez (2017), Cuello, Mestra y Robles (2020) A nivel local por Resolución de problemas a Páez (2017), López y Chávez (2017), por Estrategia Aprendizaje por retos, Díaz-Guecha, L.Y., Izarra Vielma, D.A. y Pabón Rodríguez (2021).
Objetivo
Objetivo general
Analizar la resolución de problemas como estrategia didáctica para el fortalecimiento de la competencia matemática en estudiantes de grado noveno de la Institución Educativa Integrada Juan Atalaya del Municipio de Cúcuta (Norte de Santander).
Objetivos específicos
Identificar los niveles de desempeño en el área de matemáticas que presentan los estudiantes de noveno grado.
Determinar los procesos en la resolución de problemas que requieren mayor refuerzo en estudiantes de noveno grado.
Diseñar una estrategia didáctica basada en la resolución de problemas para fortalecer las habilidades matemáticas.
Materiales y métodos
La investigación se identifica con el paradigma positivista (Ramos, 2015, p10) y cuyo enfoque es cuantitativo ya que se basa en datos numéricos y la aplicación de instrumentos estandarizados, orientados en variables medibles, que busca la verificación de la hipótesis y teoría, cuyo propósito es la representatividad y generalización de los resultados Hernández y Mendoza (2018).
El diseño en esta investigación es no experimental, transaccional y descriptivo ya que se investiga la incidencia de los niveles de una variable en una población en este caso estudiantil. Hernández y Mendoza (2018).
Con una muestra de 92 estudiantes de noveno grado y tipo muestreo intencional, se aplicó una prueba estandarizada, elaborada con seis problemas los cuales fueron tomados de las pruebas Evaluar para avanzar y del libro Vamos Aprender Matemáticas, problemas que fueron adaptados y validados por expertos; cada situación problema presenta cuatro opciones de respuesta cerrada y el estudiante tuvo que resolver y justificar el procedimiento matemático para cada respuesta.
Resultados:
Niveles de desempeño por competencias
Competencia comunicativa: 33% nivel bajo, 25% nivel básico, 27% nivel alto y 15% nivel alto. Concluyendo que el 67% de los estudiantes participantes interpretan y utilizan los conceptos de media, mediana y moda, además demostraron la capacidad de encontrar diferencias en distribuciones de diferente dispersión y asimetría; también utilizan conceptos básicos de probabilidad (espacio muestral, evento, independencia, etc.).
Competencia de resolución de problemas: el 94% son de nivel bajo, y solo el 6% de los estudiantes aprobaron la competencia de resolución de problemas. Concluyendo que los estudiantes tienen dificultad para resolver problemas y simplificar cálculos utilizando las propiedades, relaciones y operaciones de los números reales.
Competencia de razonamiento y argumentación: El 100% de los estudiantes se encuentran en un nivel bajo, por lo que es posible concluir que tienen dificultad para interpretar enunciados, procesos, operaciones y estrategias para argumentar y comunicar sus pensamientos a través de las diferentes representaciones en matemáticas.
Análisis de procesos de resolución de problemas.
Comprensión del problema: el 82% en promedio son de nivel bajo, aspecto que está fallando en el desempeño para resolver problemas, este proceso es elemental y requiere que el estudiante lea, analice y recopile los datos proporcionados en el enunciado, además, identificar la incógnita a resolver.
Crear un plan: el 93% en promedio se encuentran en un nivel bajo, lo que indica que los estudiantes no tienen una estrategia holística para resolver una situación problema, no relacionan la información del enunciado con un plan de solución, según Villacis (2020) en este proceso es importante que el estudiante busque establecer similitud con otro problema visto anteriormente para elegir estrategias y operaciones; un 7% en promedio propuso una estrategia matemática, pero el procedimiento de desarrollo fue inadecuado.
Ejecutar un plan: el 93% en promedio de los estudiantes se encuentran en un nivel bajo, evidenciándose que los estudiantes participantes no planificaron una estrategia de solución, luego existió un vacío para su desarrollo, otros también propusieron operaciones pero con desarrollo inadecuado o erróneo, observándose operaciones o cálculos mal realizados o procesos incompletos; El 7% realizó algunas operaciones correctas, pero faltó orden en el desarrollo del problema, pero se evidencia que no siguen un proceso claro.
Verificar: el 76% en promedio se encuentran en nivel bajo y el 24% en nivel básico, evidenciando que los estudiantes desconocen o no realizan procesos de verificación de operaciones y resultados, o en su efecto algunos realizaron proceso de verificación, pero erróneamente, acaba de seleccionar la opción correcta al azar.
Conclusiones:
Nivel bajo en competencias: 94% en resolución de problemas: Dificultad para resolver problemas y simplificar cálculos usando las propiedades, relaciones y operaciones de los números reales y 100% en razonamiento y argumentación: Dificultad para interpretar enunciados, procesos, operaciones y usar estrategias.
Nivel bajo en procesos de solución de problemas
82% poco uso de sus conocimientos previos, 93% carecen de una estrategia holística y por lo tanto no siguen lo propuesto o no ejecutan correctamente y76% omite verificar los resultados
Verificación de la hipótesis: La no apropiación de una estrategia de resolución de problemas por parte del estudiante influye en el bajo desarrollo de competencias matemáticas.
Background: After consulting previous studies and grouped by origin and concepts are: An international level by Reading comprehension and problem solving: to Collantes A (2021), Gutarra C (2018), Pardavé C. (2018) and by Problem Solving Methods to Diaz and Diaz (2018). A National level by Reading comprehension and problem-solving to: Marriaga M and Páez P. (2018), for Problem-solving to Vesga and Escobar (2018) and Strategies to Diaz, Natera, and Pérez (2017), Neck, Mestra and Robles (2020) A local level by Solving problems to Páez (2017), López and Chávez (2017), for Strategy Learning by challenges, Díaz-Guecha, L.Y., Izarra Vielma, D.A. and Pabón Rodríguez (2021). General objective To analyze problem-solving as a didactic strategy the strengthening mathematical competence in ninth-grade students of the Juan Atalaya Integrated Educational Institution of the Municipality of Cúcuta (Norte de Santander). Specific objectives Identify the levels of performance in the area of mathematics presented by ninth-grade students. Determine the processes in solving problems that require greater reinforcement in ninth-grade students. Design a teaching strategy based on problem-solving to strengthen mathematical skills. Materials and methods: The research is identified with the positivist paradigm (Ramos, 2015, p10) and whose approach is quantitative since it is based on numerical data and the application of standardized instruments, oriented on measurable variables, which seeks verification of the hypothesis and theory, whose the purpose is the representativeness and generalization of the results Hernández and Mendoza (2018. The design in this research is non-experimental, transactional, and descriptive since the incidence of the levels of a variable in a population in this student case is investigated. Hernandez and Mendoza (2018). With a sample of 92 ninth-grade students and intentional sampling type, a standardized test was applied, elaborated with six problems which were taken from the Evaluate to advance tests and from the book Let's learn mathematics, problems that were adapted and validated by experts; each problem situation presents four closed response options and the student had to solve and justify the mathematical procedure for each response. Results: Performance levels by competencies Communication competence: 33% are a low level, 25% a basic level, 27% a high level, and 15% a high level. Concluding that 67% of the participating students interpret and use concepts of mean, median, and mode, they also demonstrated the ability to find differences in distributions of different dispersion and asymmetry; they also use basic probability concepts (sample space, event, independence, etc.). Problem-solving competition: 94% are low level, and only 6% of the students passed the problem-solving competition. Concluding that students have difficulty solving problems and simplifying calculations using the properties, relationships, and operations of real numbers. Reasoning and argumentation competence: 100% of the students are at a low level, which is possible to conclude that they have difficulty interpreting statements, processes, operations, and strategies to argue and communicate their thoughts through the different representations in mathematics. Analysis of problem-solving processes Understanding of the problem: 82% on average are low level, an aspect that is failing in the performance to solve problems, this process is elementary and requires the student to read, analyze and collect the data provided in the statement, in addition, identify the unknown to be solved. Create a plan: 93% on average are at a low level, indicating that the students do not have a holistic strategy to solve a problem situation, they do not relate the information of the statement with a solution plan, according to Villacis (2020) in this process it is important that the student seeks to establish similarity with another previously seen problem to choose strategies and operations; an 7% on average proposed a mathematical strategy, but the development procedure was inadequate. Execute a plan: 93% on average of the students are at a low level, evidencing that the participating students did not plan a solution strategy, then there was a vacuum for its development, others also proposed operations but with inadequate development or erroneous, observing poorly performed operations or calculations or incomplete processes; 7% carried out some correct operations but lacked order in the development of the problem, but it is evident that they do not follow a clear process. Verify: the 76% on average are low level and 24% at the basic level, evidencing that the students do not know or do not carry out verification processes of operations and results, or in its effect, some did verification process, but erroneously, they just selected the correct option at random. Conclusions: Low level of competencies: 94% in problem-solving: Difficulty in solving problems and simplifying calculations using the properties, relationships, and operations of real numbers and 100% in reasoning and argumentation: Difficulty in interpreting statements, processes, operations, and using strategies. Low level in problem-solving processes: 82% make little use of their previous knowledge, 93% lack a holistic strategy and therefore do not follow what is proposed or do not execute correctly, and 76% omit to verify the results Verification of the hypothesis: The non-appropriation of a problem-solving strategy by the student influences the low development of mathematical skills.
Background: After consulting previous studies and grouped by origin and concepts are: An international level by Reading comprehension and problem solving: to Collantes A (2021), Gutarra C (2018), Pardavé C. (2018) and by Problem Solving Methods to Diaz and Diaz (2018). A National level by Reading comprehension and problem-solving to: Marriaga M and Páez P. (2018), for Problem-solving to Vesga and Escobar (2018) and Strategies to Diaz, Natera, and Pérez (2017), Neck, Mestra and Robles (2020) A local level by Solving problems to Páez (2017), López and Chávez (2017), for Strategy Learning by challenges, Díaz-Guecha, L.Y., Izarra Vielma, D.A. and Pabón Rodríguez (2021). General objective To analyze problem-solving as a didactic strategy the strengthening mathematical competence in ninth-grade students of the Juan Atalaya Integrated Educational Institution of the Municipality of Cúcuta (Norte de Santander). Specific objectives Identify the levels of performance in the area of mathematics presented by ninth-grade students. Determine the processes in solving problems that require greater reinforcement in ninth-grade students. Design a teaching strategy based on problem-solving to strengthen mathematical skills. Materials and methods: The research is identified with the positivist paradigm (Ramos, 2015, p10) and whose approach is quantitative since it is based on numerical data and the application of standardized instruments, oriented on measurable variables, which seeks verification of the hypothesis and theory, whose the purpose is the representativeness and generalization of the results Hernández and Mendoza (2018. The design in this research is non-experimental, transactional, and descriptive since the incidence of the levels of a variable in a population in this student case is investigated. Hernandez and Mendoza (2018). With a sample of 92 ninth-grade students and intentional sampling type, a standardized test was applied, elaborated with six problems which were taken from the Evaluate to advance tests and from the book Let's learn mathematics, problems that were adapted and validated by experts; each problem situation presents four closed response options and the student had to solve and justify the mathematical procedure for each response. Results: Performance levels by competencies Communication competence: 33% are a low level, 25% a basic level, 27% a high level, and 15% a high level. Concluding that 67% of the participating students interpret and use concepts of mean, median, and mode, they also demonstrated the ability to find differences in distributions of different dispersion and asymmetry; they also use basic probability concepts (sample space, event, independence, etc.). Problem-solving competition: 94% are low level, and only 6% of the students passed the problem-solving competition. Concluding that students have difficulty solving problems and simplifying calculations using the properties, relationships, and operations of real numbers. Reasoning and argumentation competence: 100% of the students are at a low level, which is possible to conclude that they have difficulty interpreting statements, processes, operations, and strategies to argue and communicate their thoughts through the different representations in mathematics. Analysis of problem-solving processes Understanding of the problem: 82% on average are low level, an aspect that is failing in the performance to solve problems, this process is elementary and requires the student to read, analyze and collect the data provided in the statement, in addition, identify the unknown to be solved. Create a plan: 93% on average are at a low level, indicating that the students do not have a holistic strategy to solve a problem situation, they do not relate the information of the statement with a solution plan, according to Villacis (2020) in this process it is important that the student seeks to establish similarity with another previously seen problem to choose strategies and operations; an 7% on average proposed a mathematical strategy, but the development procedure was inadequate. Execute a plan: 93% on average of the students are at a low level, evidencing that the participating students did not plan a solution strategy, then there was a vacuum for its development, others also proposed operations but with inadequate development or erroneous, observing poorly performed operations or calculations or incomplete processes; 7% carried out some correct operations but lacked order in the development of the problem, but it is evident that they do not follow a clear process. Verify: the 76% on average are low level and 24% at the basic level, evidencing that the students do not know or do not carry out verification processes of operations and results, or in its effect, some did verification process, but erroneously, they just selected the correct option at random. Conclusions: Low level of competencies: 94% in problem-solving: Difficulty in solving problems and simplifying calculations using the properties, relationships, and operations of real numbers and 100% in reasoning and argumentation: Difficulty in interpreting statements, processes, operations, and using strategies. Low level in problem-solving processes: 82% make little use of their previous knowledge, 93% lack a holistic strategy and therefore do not follow what is proposed or do not execute correctly, and 76% omit to verify the results Verification of the hypothesis: The non-appropriation of a problem-solving strategy by the student influences the low development of mathematical skills.
Descripción
Palabras clave
Competencias matemáticas, Resolución de problemas, Estrategia didáctica método de Pólya, Mathematical skills, Problem solving, Pólya method didactic strategy