Grafos como herramienta didáctica en el reconocimiento de patrones gráficos y numéricos.
Autores
Rodríguez Cardenas, Carol Ximena
Director
Tipo de contenido
Trabajo de grado - Maestría
Idioma del documento
EspañolFecha de publicación
2017-03-13
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Resumen
En este trabajo se diseñó, aplicó y evaluó una secuencia de cuatro actividades relacionadas con la teoría de grafos que permitió el reconocimiento de patrones gráficos y numéricos. La propuesta estuvo dirigida a jóvenes de sexto grado de la I.E.D. Técnico Comercial de Tibacuy, del municipio de Tibacuy (Cundinamarca). Se plantearon las actividades con el propósito que los estudiantes establecieran patrones y conjeturaran algunos resultados de la teoría de grafos como: relación entre la suma de los grados de los vértices y la cantidad de aristas del grafo; relación de Euler para regiones, vértices y aristas en un grafo plano (R + V - 2 = A); condiciones para que un grafo sea recorrible o no y, la cantidad mínima de veces que se debe levantar el lápiz en un grafo no recorrible. Se realizó una descripción de los resultados encontrados en la aplicación de la secuencia de actividades, y se establecieron 13 categorías de análisis. Los resultados evidencian que los grafos son un recurso didáctico que permite que los estudiantes se motiven y reconozcan patrones, al mismo tiempo que hacen matemáticas.
Abstract. In this work, a sequence of four activities related to the theory of graphs was designed, applied and evaluated that allowed the recognition of graphic and numerical patterns. The proposal was addressed to sixth-grade youth from the I.E.D. Técnico Comercial de Tibacuy, of the municipality of Tibacuy (Cundinamarca). The activities were designed with the purpose that the students establish patterns and will conjecture some results of the theory of graphs like: relation between the sum of the degrees of the vertices and the amount of edges of the graph; Euler relation for regions, vertices and edges in a at graph (R + V - 2 = A); conditions for a graph to be recursive or not, and the minimum number of times to lift the pencil in a non-recursive graph. A description of the results found in the application of the sequence of activities was made, and 13 categories of analysis were established. The results show that graphs are a didactic resource that allows students to motivate and recognize patterns, while doing mathematics..
Abstract. In this work, a sequence of four activities related to the theory of graphs was designed, applied and evaluated that allowed the recognition of graphic and numerical patterns. The proposal was addressed to sixth-grade youth from the I.E.D. Técnico Comercial de Tibacuy, of the municipality of Tibacuy (Cundinamarca). The activities were designed with the purpose that the students establish patterns and will conjecture some results of the theory of graphs like: relation between the sum of the degrees of the vertices and the amount of edges of the graph; Euler relation for regions, vertices and edges in a at graph (R + V - 2 = A); conditions for a graph to be recursive or not, and the minimum number of times to lift the pencil in a non-recursive graph. A description of the results found in the application of the sequence of activities was made, and 13 categories of analysis were established. The results show that graphs are a didactic resource that allows students to motivate and recognize patterns, while doing mathematics..