La invención de problemas aritméticos por estudiantes con talento matemático
Fecha
2016
Autores
Espinoza González, Johan
Lupiáñez Gómez, José Luis
Segovia Alex, Isidoro
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ISSN de la revista
Título del volumen
Editor
Universidad de Almería
Resumen
Introducción. Se presenta el análisis de los problemas aritméticos planteados por un grupo de estudiantes considerados con talento matemático ante dos tareas de invención de problemas y su comparación con las actuaciones que presentan un grupo estándar de estudiantes de un colegio público ante las
mismas tareas. Este estudio se centró en caracterizar e identificar las diferencias entre las producciones de ambos grupos, con base en un esquema de análisis confeccionado en esta investigación.
Método. La muestra está conformada por dos grupos de estudiantes. El primero está compuesto por 21 estudiantes identificados con talento matemático y el segundo está formado por 19 estudiantes de segundo curso de Educación Secundaria de un colegio público. Ambos grupos contestaron dos tareas de invención de problemas aritméticos que fueron confeccionadas en este estudio. Los resultados se analizaron con base en tres categorías de análisis y algunas variables que están relacionadas con la estructura sintáctica, semántica y matemática de los mismos.
Resultados. Los problemas inventados por el grupo de estudiantes con talento en matemática presentan mayor riqueza que los del grupo del colegio público, ya que están conformados por una mayor cantidad de proposiciones, emplean diferentes tipos de números, requieren más pasos y procesos de cálculo distintos para ser resueltos y presentan una mayor cantidad de relaciones semánticas distintas.
Además, los resultados muestran algunos atributos que caracterizan a los estudiantes con talento en matemática cuando resuelven tareas de invención de problemas.
Conclusión. El instrumento de invención de problemas y el esquema analítico empleado permitieron describir y explorar la actuación de un grupo de estudiantes considerados con talento matemático. Además, las tres categorías de análisis y la solución de cada problema dan lugar a diez componentes cuyos valores caracterizan la riqueza de los problemas inventados por los sujetos. Por último, el análisis estadístico realizado refuerza las diferencias encontradas entre las producciones de ambos grupos en estudio.
Introduction. The analysis of the arithmetic problems posed by a group of mathematically talented students considered at two tasks of inventing problems and their comparison with the actions that have a standard group of students from a public school to the same tasks is presented. This study focused on characterizing and identifying the differences between the productions of both groups, based on a framework of analysis made in this study. Method. The sample consists of two groups of students. The first one consists of 21 students identified talented in math and the second one consists of 20 secondary students from a public school. Both groups completed two tasks of invention of arithmetic problems that were not made in this study. The results were analyzed based on three categories of analysis and some variables that are related to the syntactic, semantic and mathematical structure thereof. Results. The problems invented by a group of talented students in mathematics have greater value than the group of public school because they are composed of a greater number of propositions, use different types of numbers, require more steps and processes different calculation to be solved and have a greater number of different semantic relationships. Furthermore, the results show some attributes that characterize talented students in mathematics when solving tasks of inventing problems. Conclusion. The instrument of inventing problems and the analytical framework used to describe and explore allowed the performance of a group of students considered with mathematical talent. Moreover, the three categories of analysis employed and the solvability of every problem lead to ten components whose values characterize the wealth of problems invented by the subjects. Finally, statistical analysis reinforces the differences between the productions of both groups in the study.
Introduction. The analysis of the arithmetic problems posed by a group of mathematically talented students considered at two tasks of inventing problems and their comparison with the actions that have a standard group of students from a public school to the same tasks is presented. This study focused on characterizing and identifying the differences between the productions of both groups, based on a framework of analysis made in this study. Method. The sample consists of two groups of students. The first one consists of 21 students identified talented in math and the second one consists of 20 secondary students from a public school. Both groups completed two tasks of invention of arithmetic problems that were not made in this study. The results were analyzed based on three categories of analysis and some variables that are related to the syntactic, semantic and mathematical structure thereof. Results. The problems invented by a group of talented students in mathematics have greater value than the group of public school because they are composed of a greater number of propositions, use different types of numbers, require more steps and processes different calculation to be solved and have a greater number of different semantic relationships. Furthermore, the results show some attributes that characterize talented students in mathematics when solving tasks of inventing problems. Conclusion. The instrument of inventing problems and the analytical framework used to describe and explore allowed the performance of a group of students considered with mathematical talent. Moreover, the three categories of analysis employed and the solvability of every problem lead to ten components whose values characterize the wealth of problems invented by the subjects. Finally, statistical analysis reinforces the differences between the productions of both groups in the study.
Descripción
Palabras clave
ARITMÉTICA, PROBLEMAS, EJERCICIOS, ETC., MATEMÁTICAS, TALENTO, ESTUDIANTES, ENSEÑANZA DE LAS MATEMÁTICAS, ARITHMETICS, PROBLEMS, EXERCISES, ETC., MATHEMATICS, TALENT, STUDENTS, TEACHING MATHEMATICS