Las ideas fundamentales de probabilidad en el razonamiento de estudiantes de bachillerato

• Ernesto Alonso, Sánchez, Sánchez ^[1] ; Julio César, Valdez, Monroy ^[1]
  1. [1] Centro de Investigación y de Estudios Avanzados del IPN
• Localización: Avances de investigación en educación matemática: AIEM, ISSN-e 2254-4313, Nº. 11, 2017, págs. 127-145
• Idioma: español
• DOI: 10.35763/aiem.v1i11.180
• Enlaces
  • Texto completo (pdf)
• Dialnet Métricas: 1 Cita
• Resumen
  • español

    El objetivo de este trabajo es explorar las inferencias que los estudiantes de bachillerato formulan a partir de su conocimiento de las interpretaciones frecuencial y clásica de probabilidad. Se describen y analizan los razonamientos de 30 estudiantes del 12º grado, quienes cursaban la materia de Probabilidad y Estadística II. La recolección de datos se lleva a cabo mediante tres versiones de un cuestionario en los que se pide hacer predicciones y estimar probabilidades. El análisis de las respuestas revela la tendencia de los estudiantes al cálculo de probabilidades, mayormente apoyados en razonamientos inadecuados en los que intervienen las ideas de variabilidad, aleatoriedad e independencia. Dichos razonamientos son descritos en una jerarquía con la finalidad de informar sobre las trayectorias de los estudiantes. Con base en este resultado, se sugiere que el primer objetivo en la enseñanza de la probabilidad debe ser el desarrollo de un razonamiento adecuado sobre estas ideas.

  • English

    The aim of this paper is to explore the inferences made by high school students from their knowledge of the frequentist and classical interpretations of probability. The reasoning of 30 12th grade students who were studying the subject of Probability and Statistics II is described and analyzed. Data were collected through three versions of a questionnaire in which students were asked to make predictions and assess probabilities. The analysis of the responses reveals the students’ tendency to the calculation of probabilities, mostly supported by inadequate reasoning in which the ideas of variability, randomness and independence are involved. This reasoning is described in a hierarchy for the purpose of reporting on the trajectories of the students. Based on this result, it is suggested that the first objective in the teaching of probability should be developing of an adequate reasoning about these ideas.

  • français

    Le but de cet article est d'explorer les inférences faites par des élèves du secondaire sur la base de leur connaissance de les interprétations fréquentiste et classique de la probabilité. Le raisonnement de 30 élèves de 12e année qui étudiaient le sujet de la probabilité et de la statistique II est décrit et analysée. La collecte des données a été par le biais trois versions d'un questionnaire qui demande de faire des prévisions et d'évaluer les probabilités. L'analyse des réponses révèle la tendance des élèves per le calcul des probabilités, la plupart du temps pris en charge par un raisonnement inadéquat dans laquelle les idées de la variabilité, le hasard et l'indépendance sont impliqués. De tels arguments sont décrits dans une hiérarchie afin de faire rapport sur les progrès des élèves. Sur la base de ce résultat, il est suggéré que le premier objectif de l'enseignement des probabilités doit être le développement d'un raisonnement informel sur ces idées.

  • português

    O objetivo deste artigo é explorar as inferências feitas por estudantes do ensino médio através de seus conhecimentos sobre interpretações frequentista e clássica da probabilidade. O raciocínio de 30 alunos do 12º ano que estavam estudando o assunto de Probabilidade e Estatística II é descrito e analisado. A coleta de dados foi através de três versões de um questionário, no qual se pediu para fazer previsões e avaliar probabilidades. A análise das respostas revela a tendência dos alunos para o cálculo de probabilidades, em sua maioria apoiados por insuficiente raciocínio em que estão envolvidas as idéias de variabilidade, aleatoriedade e independência. Tais argumentos são descritos em uma hierarquia, a fim de apresentar um relatório sobre o progresso dos alunos. Com base neste resultado, sugere-se que o primeiro objectivo do ensinamento de probabilidade deve ser o desenvolvimento de um raciocínio informal sobre estas ideias.

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