Abstract:

The study of probabilities assumes a high importance in our daily lives, as probabilistic thinking justifies decision-making in different situations and professions. The study of this theme allows students to develop the ability to accept the existence of chance and hypothesis in nature and allows them to acquire strategies and structure reasoning that allow them to make the correct decision. decision.

The teaching of the concepts of conditioned probability, joint probability, total probability theorem and the Bayes rule only occurs in secondary education. However, several studies state that it would be more appropriate to start teaching them earlier. In Portugal, the results reported by some authors on intuitions on conditioned probabilities in 9th graders (ages 14-15), are encouraging as to the possibility of introducing the study of this concept in the 9th grade of Basic Education. Some Portuguese authors already studied the semiotic conflicts of the secondary students in these probabilistic topics.

Several authors have identified that students have misconceptions about some content on the subject of probabilities. There is a wide range of technological tools that are relevant to the teaching of mathematics in the classroom. The use of applets due to their dynamic and interactive character has changed the perspective and the way in which some mathematical content, namely that of probabilities, can be learned. Applets facilitate the visualization and simulation of specific concepts and are among the most powerful and sophisticated ways to obtain interactivity in the teaching of probabilities.

In this work, the didactic suitability of a teaching intervention on learning the topic of probabilities was analyzed in particular the contents of conditioned probability, joint probability, theorem of total probability and Bayes' rule, as a branch of mathematics taught in secondary education. In the first stage, their difficulties were identified and understood and, in the second stage, a didactic intervention was implemented using the applets in order to contemplate the semiotic conflicts found. In this second phase, a class of Mathematics Applied to Social Sciences (ages 15 and 16) participated and a case study was used in order to understand which elements of the use of the applets stood out in the learning of the probabilities. The theoretical framework used was the ontosemiotic approach of Godino and colleagues. In the second phase, analysis of the suitability of the instructional process was characterized, a priori and a posteriori, of the didactic intervention performed. As a result of the analysis there was a high didactic suitability a priori and a posteriori, and the mediational suitability was considered average.

Keywords:

Applets, probabilities, ontosemiotic approach, didactic suitability.