Probabilidade de acontecimentos envolvendo aspetos lógicos

In this article, we study the Probability's knowledge of prospective primary school teachers, when there are logical aspects involved in the formulation of events. Forty-six students participated in the study, from a University in Northern Portugal, who had to resolve a three-item task in the context of a formal evaluation: the first one, on the union probability (connective or), the second one, on the joint probability (connective and), and the third one, on the conditional probability, in which the conditioned event is, in turn, a joint probability (connective and). In terms of the main results of the study, it was found that the students showed a very limited performance, frequently changing the connectives and and or, the inclusive disjunction with the exclusive disjunction and in the disjunction considered as incompatible non-disjoint events.Neste artigo estuda-se o conhecimento de Probabilidades de futuros professores dos primeiros anos escolares, quando na formulação dos acontecimentos estão envolvidos aspetos lógicos. Participaram no estudo 46 alunos da Licenciatura em Educação Básica, de uma Universidade do Norte de Portugal, os quais resolveram uma tarefa, com três itens, em contexto de avaliação formal: o primeiro sobre a probabilidade da reunião (conetivo ), o segundo sobre a probabilidade conjunta (conetivo ) e o terceiro sobre a probabilidade condicionada, em que o acontecimento condicionado é, por sua vez, uma probabilidade conjunta (conetivo ). Em termos dos principais resultados do estudo, verificou-se que os alunos revelaram um desempenho muito limitado, trocando, frequentemente, os conetivos e , a disjunção inclusiva com a disjunção exclusiva e na disjunção consideraram como sendo incompatíveis acontecimentos não disjuntos.Este trabalho contou com o apoio de Fundos Nacionais através da FCT – Fundação para a Ciência e a Tecnologia no âmbito do projeto PEst-OE/CED/UI1661/2014, do CIEd-UM e do projeto UID/Multi/04016/2016

El Pensamiento Probabilístico de los Profesores de Biología en Formación

Los futuros profesores de secundaria requieren de una formación acorde a las demandas de la sociedad del siglo XXI. Ello impone el desarrollo de un pensamiento que le permita interpretar y abordar los fenómenos de naturaleza aleatoria. El objetivo de este trabajo es determinar las tendencias de pensamiento probabilístico de los estudiantes de los profesorados de Biología de la provincia de Mendoza, Argentina. Para ello se aplicó un cuestionario a los 325 estudiantes que cursan esta carrera. El mismo consta de tres partes; la primera trata sobre las variables demográficas de los estudiantes, la segunda corresponde al reconocimiento de la aleatoriedad; y la tercera a la estimación de la probabilidad de diferentes sucesos. Las respuestas se analizaron a partir de la aplicación de diferentes técnicas estadísticas; el test de independencia, el análisis de la varianza, el test de Tukey, análisis de clusters y análisis discriminante. En primer lugar, se encontraron diferencias significativas entre el reconocimiento de la aleatoriedad y el contexto del suceso, siendo mayor en el contexto de juego que en el físico natural. Mientras que, en el contexto físico natural se afirma la aleatoriedad desde la causalidad, en el de juego se afirma desde la incertidumbre. En segundo lugar, no se encontró relación de dependencia entre el reconocimiento de la aleatoriedad y la edad de los estudiantes, como así tampoco con el nivel académico de los mismos. Respecto a la estimación de la probabilidad, los estudiantes argumentan fundamentalmente desde la equiprobabilidad y desde la contingencia. El análisis de clusters y análisis discriminante permitieron encontrar cuatro tendencias de pensamiento: incertidumbre, determinista, contingente y personalista

Research on Teaching and Learning Probability

This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic views. It discusses their possible applications, philosophical problems, as well as their potential and the level of interest they enjoy at different educational levels. Next, the book describes the main features of probabilistic thinking and reasoning, including the contrast to classical logic, probability language features, the role of intuitions, as well as paradoxes and the relevance of modeling. It presents an analysis of the differences between conditioning and causation, the variability expression in data as a sum of random and causal variations, as well as those of probabilistic versus statistical thinking. This is followed by an analysis of probability’s role and main presence in school curricula and an outline of the central expectations in recent curricular guidelines at the primary, secondary and high school level in several countries. This book classifies and discusses in detail the three different research periods on students’ and people’s intuitions and difficulties concerning probability: early research focused on cognitive development, a period of heuristics and biases programs, and the current period marked by a multitude of foci, approaches and theoretical frameworks