The social and cultural approach to forming geometric concepts among schoolchildren

  • Natalia G. Podayeva Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia
  • Mikhail V. Podayev Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia.
  • Pavel A. Agafonov SBEI GES No. 2070, Moscow, Russia
Keywords: Geometric concepts; generalized ability to prove; integral units of thinking; real cognitive operations; plane of sign form.

Abstract

In line with the social and cultural approach, the problem of forming mathematical concepts among schoolchildren as the system of judgments is considered. Concepts at the verbal and logical level are formed through teaching to prove theorems and solve proof problems. Objective: To provide elements of the method of forming geometric concepts by means of specially organized learning activities of schoolchildren to develop the generalized ability to prove with the access to the value-oriented learning. Methods: Theoretical provisions on the laws of the concept formation process are developed. During the experiment forming stage the methodology to teach geometry to pupils of the 7th grade of secondary education institutions is developed. The basis is the activity to develop skills to prove. Relying on instrument-oriented, subject-oriented and value-oriented types of learning is assumed. Findings: During the quantitative and qualitative evaluation of results, the following independent characteristics have been taken into account: the form of action, the level of generalization, the level of expansion, the level of mastering, and the value relation. The results of analyzing the statistical data hav e confirmed the hypothesis about the significant influence of the following factors on the success of mastering geometric concepts by pupils: the mathematical training (significance level 0,003), the effect of electronic educational environment in combination with the evaluated method (significance level 0,001), the duration of training using the evaluated method (significance level 0,01). Conclusions: The hypothesis is substantiated and proved in practice: the process of forming concepts is regularly ensured by the following psychodidactic conditions: the formation of main components of conceptual psychic structures; the formation of declarative, procedural and evaluative knowledge; the gradual formation of the subjective image of the concept content; the gradual development of the entire psychic structure; the gradual development of the activity component of geometric concepts.

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Author Biographies

Natalia G. Podayeva, Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia

Doctor of Pedagogical Sciences, Professor, Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia

Mikhail V. Podayev, Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia.

Candidate of Pedagogical Sciences, associate professor of the Department of Mathematics and Methods of its Teaching, Yelets State University named after I.A. Bunin, Yelets, Lipetsk region, Russia.

Pavel A. Agafonov, SBEI GES No. 2070, Moscow, Russia

Teacher at SBEI GES No. 2070, Moscow, Russia

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Published
2019-06-25
How to Cite
Podayeva, N., Podayev, M., & Agafonov, P. (2019). The social and cultural approach to forming geometric concepts among schoolchildren. Amazonia Investiga, 8(20), 459-467. Retrieved from https://amazoniainvestiga.info/index.php/amazonia/article/view/175
Section
Articles
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