Abstract:

There is currently a great interest in statistics education research on the possibility of teaching different contents from informal approaches in order to facilitate their transition to the understanding of formal ideas, taking into account the students' prior knowledge. This trend is part of the general concern for the planning of the study of mathematics with different degrees of abstraction and formalisation, in order to foster the understanding of the contents to be taught, taking into account the students' prior knowledge. This implies admitting the possibility of establishing different levels of formalisation, i.e., different degrees of implication and emergence of algebraic objects and processes, in terms of generalisation, symbolisation and analytical calculation.

The view of algebra as the use of unknowns, equations, functions, parameters, or abstract structures, whose properties allow to operate with symbols hides an essential feature of algebraic reasoning: the progressive expression of generality. From a broader point of view, algebraic reasoning arises in the mathematical activity that is carried out from the first educational levels, in the study of different mathematical contents (arithmetic, geometric or stochastic, among others).

The purpose of this work is to analyse the algebraic activity required in working with probability at primary and secondary school levels and to describe it through the levels proposed by the elementary algebraic reasoning model, developed by the Onto-Semiotic Approach framework. This will make it possible to define different degrees of formalisation in the study of probability, depending on the level of algebraization required at each level, and to propose a sequence for introducing the fundamental ideas of probability at these educational stages.

The levels of algebraization allow us to model the institutional knowledge that is put into play in the operative, discursive and normative practices involved in solving probability problems in the various approaches, describing mathematical activity from the perspective of objects and processes characteristic of algebra. In our case, we have focused on the classical or Laplacian meaning of probability, admitting that, within it, a given problem can be approached in different ways at any given time, involving different objects, degrees of generality and transformations, that is, different levels of algebraization.

Keywords:

Algebraic reasoning, Probability, Primary education, Ontosemiotic Approach.