ISSN: 2073-2635
eISSN: 2949-270X
ISSN: 2073-2635
eISSN: 2949-270X
En Ru
On the Content of School Mathematics Education. From Content to Contents: Mathematics as a System of Mental Means

On the Content of School Mathematics Education. From Content to Contents: Mathematics as a System of Mental Means

Recieved: 04/23/2024

Accepted: 05/19/2024

Published: 05/22/2024

Keywords: content of school mathematical education; form, content and contents; mental means; symbolic and ideal means of thinking; concepts; mental operations and relationships; system; tempo-rhythm; change and development

Available in the on-line version with: 29.08.2024

To cite this article

Borovskikh A.V. On the Content of School Mathematics Education. From Content to Contents: Mathematics as a System of Mental Means. // Lomonosov Pedagogical Education Journal 2024. N 2. p.61-82

N 2, 2024

Abstract

Background. The need for reconstruction (and not modification, as it was previously done) of school mathematics education, due to the intensive development of information technology, requires the restoration of the foundations on which it is built. Discussions about what topic to include or exclude from a mathematics course based on arguments like “It is impossible to be an educated person without knowing...” on the one hand, or “Children cannot understand anything about...” on the other, clearly have no chance in obtaining productive solutions.

Objectives. This paper introduces a system of concepts and distinctions that provides the basis for solving the problem of constructing foundations for designing a school mathematics course.

Methods. The study involves problematization (transition from a problem situation to a problem formulation), methodological analysis of the problem, introduction of conceptual distinctions, construction of a system of relations between concepts.

Results. A distinction has been introduced between the content and contents of mathematical education — both as a process and as a result. It is shown that functionally (substantively) mathematics exists in culture as a system of mental means necessary to represent the relationships between conceivable entities in a particular science or field of activity. Accordingly, the content of the process of mathematical education is the mastery of these mental means and methods of applying them, and the content of mathematical education as a result is the possession of these mental means and methods for representing the relationships between entities of a particular nature.

Conclusions. It is shown that mathematics functionally acts as a system of mental means and therefore the design of school mathematical education should be carried out precisely in the logic of mastering mental means, and not “topics”, “objects”, “tasks”, “skills”, “knowledge”, etc.

In the second part of the article, a developed system of ideas will be used to specify, on the one hand, the tempo-rhythmic structure of the educational process, and on the other, to provide a logical justification for the initial part of mathematical education (arithmetic) as a process of mastering mathematical thinking tools.


References

Beba, D.N., Gureev, V.A. (2023). Methodological features of textbooks by A.P. Kiseleva. Uchenye Zapiski Orlovskogo Gosudarstvennogo Universiteta (Scientific Notes of Oryol State University), 3(100), 180–183. (In Russ.).

Boguslavsky, M.V., Sadovnikov, E.Yu. (2023). Content analysis of the general mathematics education program of the 1970s. Gumanitarnye Issledovaniya Central'noj Rossii (Humanitarian Studies of Central Russia), 3(28), 49–60. (In Russ.).

Gorbachev, V.I. (2011). The content of general mathematical education and the mathematical picture of the world. Vestnik Bryanskogo Gosudarstvennogo Universiteta (Bulletin of Bryansk State University), 1, 282–294. (In Russ.).

Gorev, P.M., Belova, O.Yu. (2016). Content and structure of the course of continuous additional mathematical education for students in grades 3–6 of secondary school. Nauchno-metodicheskij elektronnyj zhurnal "Koncept" (Scientific and Methodological Electronic Journal "Concept"), S1, 31–35. (In Russ.).

Iamblichus Chalcis. (2002). On the Pythagorean life. Per. from ancient Greek I.Yu. Melnikova. Moscow: Aletheia. (In Russ.).

Roslova, L.O., Alekseeva, E.E., Butsko, E.V. (2022). MATHEMATICS. Implementation of the requirements of the Federal State Educational Standard for basic general education: A manual for teachers. Moscow: Institute for Education Development Strategy RAO. (In Russ.).

Snegurova, V.I., Podkhodova, N.S., Orlov, V.V. (2018). Features of the selection and implementation of the content of a school mathematics course. Izvestiya Rossijskogo Gosudarstvennogo Pedagogicheskogo Universiteta im. A.I. Gercena (News of the Russian State Pedagogical University named after A.I. Herzen), 190, 175–182. (In Russ.).

Vygotsky, L.S. (1983). History of the development of higher mental functions. In: Collection. op. in 6 volumes. T. 3. Problems of mental development. Moscow: Pedagogy. (In Russ.).