Year: 2025
Type: article
Abstract: The article has two sections. The first one introduces the conceptual framework to the psychogenetic theory of cognitive processes exposed by Piaget and Szeminska [1] and Piaget and Inhelder [2], the proposal of the first educational program in this perspective by Beauverd [3], the demonstration that learning to count does not imply a cardinal meaning by Sophian [4] and, the proposal that the learning of symmetric relations precedes cardinality by Rivera [5]. The second section contains the development of an educational program whose objective is to master the mathematical concept of cardinal quantity in sets of discrete objects. Piaget postulated three stages in the understanding of cardinal quantity whose characteristics in summary are: First stage, non-conservation of quantities due to only perceptual capture of the figural properties of the collections to be compared (between two collections of the same cardinal number, the one that occupies more space is considered the most numerous by the child). Second stage, of transition, in which a conflict emerges between the figural properties and the term-to-term correspondence of the collections. Third stage, the child is no longer guided by perceptual or figural configurations, and we see the presence of spontaneous control operations, made through dissociations of the totalities (collections) and formation of series, thus arriving at the notion of cardinal equivalence between collections. The program, in accordance with its objective, contains the cognitive characteristics of the stages from which exercises-problems are proposed to be solved by the child and a strategy to achieve mastery of the notion of counting in base ten. Keywords: psychogenetic theory, understanding of cardinal quantity, figural properties, cardinal equivalence, notion of counting in base ten.
Source: Revista ECIPeru
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
SDG: Quality education
Open Access status: diamond
OpenAlex ID: W4411787685