Playing Online as Preparation for Mathematics: The Cultural-Historical Approach as an Alternative to Constructivism.

Background: While the traditional method of teaching consists of repetition and memorization, the constructivist theory proposes independent discovery and free play. The cultural-historical approach, on the other hand, does not insist on the early introduction of formal mathematics as implicit or explicit knowledge. According to this outlook, important psychological developmental is necessary for the child before he/she can learn mathematics in primary school. Objective: To present a methodology for organizing the play activity of children of preschool age by introducing symbolic means on the materialized and perceptual levels as an essential aspect of preparation for learning mathematical concepts in primary school. Design: The experiment consisted in pedagogical work in the online modality by the authors at a private college in the city of Puebla, Mexico. Eighteen children from three levels of preschool education (from three to six years old) participated in 45-minute sessions three times per week. There were six children from each preschool level. Results: It was shown that playing with roles online allows children at least partially to include different symbolic means in their activity. This allows the children not only to satisfy their curiosity and be positively engaged in the topic of the play, but also to develop symbolic functions as preparation for intellectual actions with numerical content in primary school. Conclusion: The article shows a feasible way to organize preschool play with roles online and thus to scaffold the formation of children's imagination and ability to use symbolic means, which is important for future learning. The cultural-historical approach offers useful guidelines here, although more research is needed to support the development of children's symbolic function within math-specific activity, based on activity theory applied to learning.

The program for introduction of basic mathematical knowledge: the effects in six years old Mexican children.

Introduction: The process of teaching and learning mathematics in primary school represents an obstacle for both teachers and pupils. According to the historical-cultural conception of development and education, the way how intellectual concepts are initially introduced may radically affect a student's success in learning. The historical-cultural conception of development, together with activity theory, may serve as the basis for creating a novel methodology for pedagogical work on mathematical concepts with pre-school and school children. Methods: The goal of the present study was to show the effects of work with an original program for the initial introduction of mathematical concepts to young school children. The program included reflexive symbolic and logical actions on the materialized and perceptual level, which were introduced and performed collectively by six-year-old children under the guidance and assistance of a teacher. The pupils were tested before and after their work with the program. Results: The results showed important qualitative and quantitative progress by the children in solving the tasks of the assessment, together with an increment of reflection on their intellectual actions. Discussion: The study points to the necessity for more intensive and extensive research, involving specialists in psychology and pedagogy trained in cultural-historical methodology.

Corrigendum: The program for introduction of basic mathematical knowledge: the effects in six years old Mexican children.

[This corrects the article DOI: 10.3389/fpsyg.2023.1198675.].