Abstract:

Numerous authors highlight the importance of starting the teaching of probability from the earliest levels of education, building on the intuitions of schoolchildren and moving towards the expression, quantification and modelling of uncertainty through probability. This need has motivated curricula in various countries to incorporate the study of probability in primary education, admitting that probabilistic knowledge should form part of the objectives of mathematical literacy for citizens.

Despite its importance, there is still little research on children's intuitions about the idea of fair play, their strategies for deciding whether a game is fair or not, intuitions about mathematical hope and the influence of out-of-school experiences on the development of the idea of fairness and its relationship with that of probability.

The study is based on the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction. The OSA assumes an ontological formulation of mathematical objects, whose primitive notion is that of problem-situation, from which the theoretical concepts of practice, object (personal and institutional) and meaning (personal and institutional) are defined.

In this paper, we evaluate the responses of a group of 6th grade primary school students to a task in which they must decide which results must be favourable to one player or the other for the game to be fair. For the study, the mathematical practices carried out by the sample of students when solving the problem are analysed (cognitive analysis) and compared with the expert practices (epistemic analysis). The results allow us to observe which are the intuitions and strategies followed by the students to transform the game, identifying their difficulties in relating gain and probability in this decision.

Keywords:

Probability, Fair play tasks, Primary education, Ontosemiotic approach.