Comprensión de la representatividad y variabilidad muestral por estudiantes de Educación Secundaria

Abstract

El objetivo del trabajo fue analizar la mejora con el curso escolar de la comprensión de la representatividad y variabilidad muestral en estudiantes de secundaria. Para ello se analizan las respuestas dadas por una muestra de 536 estudiantes de tres cursos (segundo y cuarto curso de Educación Secundaria Obligatoria y segundo curso de Bachillerato) a una tarea en que se piden cuatro valores de una distribución binomial. Se analizan la media y rango de dichos valores, que constituyen una muestra de cuatro resultados de la citada distribución, comparando con los valores teóricos de la distribución muestral de la media y el rango. Los resultados sugieren que los estudiantes tienen una percepción aceptable del valor esperado, pero que la percepción de la variabilidad es incorrecta y no mejora con la edad. Se observan también el sesgo de equiprobabilidad y la heurística de la representatividad en una parte de los estudiantes, mejorando los resultados según avanza el curso.

Future math teachers ‘knowledge about fair games

“…the player loses, to decide if the game was fair or not. 27,30 That is, the strategies they used to identify if the game is fair or not, when comparing the probabilities of winning or losing, using the corresponding prizes, were adequate, the difficulties arose was trying to make the game fair. Well, contrary to the solution given by P1, the difficulties were related to the calculation of the probabilities of winning, since they found solutions with non-composite basic probabilities, but in the case of the probability of a sum, they did not conceive that they should use two or more point probabilities to form the overall probability of the event.…”

“…However, "the analysis of comprehension difficulties about probabilistic reasoning when faced with a task that involves uncertainty", 20 that are very difficult to deal with. Therefore, if you want future mathematics teachers to explore sociocultural contexts, where they can identify and use for didactic purposes, situations in which there is uncertainty, which lead them to make appropriate decisions for their teaching, it is necessary to put them to analyze the contradictions that may result from their own beliefs and conceptions, with formal aspects of probability, which help to enhance their probabilistic reasoning, 30 as well as in the ways of teaching it. In addition, interaction with peers is always important in this type of activity, so collaborative work between teachers in training could be a complementary alternative to what was said above.…”

“…In their solutions, the future teachers prioritized the classical approach, and although in some solutions they obtained data, with which they could make inferences using the frequentist approach, their solutions were oriented to the formal calculation of a priori probabilities, obviating the need to use different approaches to probability, which make it easier for their future students to become aware of their intrinsic limits. The presence of correct intuitive ideas about expected value is evident in this group of future teachers, 30 since they take into account both the probability of winning the game and the value that is won or lost, to decide whether a game is fair or not. In addition, they use appropriate strategies to compare the probabilities of winning or losing a game, but have difficulty transforming an unfair game into a fair one.…”