Randomness Learning and Associated Concepts: a Secondary Study with Geogebra Support Aprendizaje de la Aleatoriedad y Conceptos Asociados: un Estudio en Secundaria con Apoyo de Geogebra

Abstract

In this paper we present the results of a study conducted during the 1st semester of the school year of 2017 in the context of a teaching experiment supported by ICTs, particularly Geogebra,  aimed at the learning of Probability in the 10th grade of the Costa Rican context. We present, in particular, one of the five tasks of the learning sequence that supports the teaching  experiment, aiming to understand how 10th grade students of Costa Rica learn the basic concepts associated with random experiments (randomness, favorable cases, total cases and random event) when working on exploratory tasks supported by Geogebra, and what is the role of this software as a  didactic resource for learning these concepts. The methodology used was qualitative and interpretative and data collection included: participant observation and the students? answers to the tasks. The results show that the majority of students have a notion of randomness, associating the concept with
their real life experiences. However, they have difficulties in using this concept to make decisions involving probabilities. The concepts of favorable cases, total cases and events are unknown to most students. Regarding the contributions of technology, working with Geogebra allowed some students to be able to correctly infer relations associated with the concepts of favorable cases, total cases and events as they simulate the experience of throwing two dice several times. In addition, when they do a small number of simulations for an experience, it was possible to observe that a large part of the students have wrong beliefs about randomness, due to an inadequate use of classical probability. In this way, the results obtained allow us to make a positive evaluation of the use of exploratory tasks with Geogebra for the teaching and learning of Probability concepts in secondary school. During the presentation of the work, we seek to present these results and show the simulation of Geogebra used in the task.