Case study on intra-mathematical connections when solving tasks associated with the classification of groups of prime order

• Erika Zubillaga-Guerrero ^[1] ; Flor Monserrat Rodríguez-Vásquez ^[2] ; Jesús Romero-Valencia ^[1]
  1. [1] Faculty of Mathematics, Autonomous University of Guerrero, México
  2. [2] Department of Mathematics Education, Autonomous University of Guerrero, México
• Localización: REDIMAT, ISSN-e 2014-3621, Vol. 10, Nº. 3, 2021, págs. 269-295
• Idioma: inglés
• Títulos paralelos:
  • Estudio de caso sobre conexiones intramatemáticas al resolver tareas asociadas a la clasificación de los grupos de orden primo
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El isomorfismo es un concepto difícil de entender para los estudiantes universitarios. En Educación Matemática, se plantea que es necesario promover conexiones matemáticas para favorecer su comprensión. En este artículo se presentan algunas conexiones intramatemáticas en la clasificación de grupos de orden primo, que emergieron en la resolución de tareas, las cuales, se fundamentaron en un análisis histórico y epistemológico del concepto de grupos isomorfos. La investigación muestra un estudio de caso. Se usó una entrevista para recoger los datos, y para analizarlos se realizó un análisis cualitativo de texto. Se identificaron catorce conexiones asociadas a los conceptos de grupo, subgrupo, grupos cíclicos, isomorfismo, grupos isomorfos y el teorema de Lagrange, implicados en la clasificación de grupos de orden primo. Se concluye que las tareasdiseñadas con una fundamentación histórica favorecen en una comprensión profunda a partir de la apreciación conectada de los conceptos, teoremas, métodos y algoritmos.

  • English

    IIsomorphism is a difficult concept to understand for undergraduate students. However, Mathematics Education suggests that it is necessary to promote mathematical connections to foster its understanding. This paper presents some intra-mathematical connections on the classification of groups of prime order that emerged solving task, which were based on a historical and epistemological analysis of the concept of isomorphic groups. This research is a case study. An interview was used for data collection, and qualitative text analysis was performed. Fourteen connections associated with the concepts of group, subgroup, cyclic groups, isomorphism, isomorphic groups, and the Lagrange theorem were identified, involved in the classification of prime order groups. We concluded that the tasks designed with a historical foundation enhance a deep understanding from the connected appreciation of concepts, theorems, methods, and algorithms.

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