Actualization of gifted schoolchildren’s intentional experience in the process of mastering geometric concepts: from support to activity mechanism

Natalia Georgievna Podaeva; Pavel Alexandrovich Agafonov

doi:10.22633/rpge.v25i2.15449

Authors

Natalia Georgievna Podaeva Bunin Yelets State University (BYSU), Yelets https://orcid.org/0000-0002-9491-5011
Pavel Alexandrovich Agafonov SBEI Secondary School No. 2070, Moscow https://orcid.org/0000-0002-8934-0233

DOI:

https://doi.org/10.22633/rpge.v25i2.15449

Keywords:

Geometry teaching, Intentional experience, Mental activity, Educational environment, Integral thinking units

Abstract

People’s intellectual abilities become a powerful civilization resource. Therefore, intellectually gifted schoolchildren’s development should be the focus of the state educational policy. Russian opinion leaders interpret the phenomenon of giftedness as a systemic quality that describes the child’s psyche as a whole. Such an approach turns into a priority to update and enrich the gifted schoolchildren’s intentional experience during geometry teaching. It assumes the development of a particular subjective state of orientation and selectivity of individual cognitive activity in preferences. This unique state becomes a mental activity mechanism, not just an accessory. The statistical data analysis confirms the hypothesis: the efficiency of actualizing gifted schoolchildren’s intentional experience in the form of their individual dispositions, beliefs, and emotional assessments while solving geometric problems during academic competitions is provided by specifically organized educational activities. It positively correlates with the level of mental activity development during mastering the activity methods with geometric concepts.

Downloads

Download data is not yet available.

Author Biographies

Natalia Georgievna Podaeva, Bunin Yelets State University (BYSU), Yelets

Professor of Department of Mathematics and its Teaching Methodics.

Pavel Alexandrovich Agafonov, SBEI Secondary School No. 2070, Moscow

Mathematics teacher.

References

ARBAIN, N.; SHUKOR, N. A. The effects of GeoGebra on Students achievement. Procedia-Social and Behavioral Sciences, v. 172, p. 208-214, 2015.

ARNOLD, V. I. Hard and soft mathematical models. Moscow: Moscow Center for Continuing Mathematical Education, 2000.

BOGOMOLNY, A. The Fifth Postulate. Attempts to Prove. Cut the Knot, 2018 Available: https://www.cut-the-knot.org/triangle/pythpar/Attempts.shtml Access: 10 May 2021.

BOGOYAVLENSKAYA, D. B.; SHADRIKOV, V. D. The working concept of giftedness. Moscow: Magistr, 2003.

DALINGER, V. A. Methods of teaching the proof of mathematical propositions to students. Moscow: Prosveshchenie, 2006.

DAVYDOV, V. V. Psychological theory of educational activity and methods of primary education based on meaningful generalization. Tomsk: “Peleng” Publishing House, 1992.

DOBRENKOV, V. I. Society and education. Moscow: INFRA-M, 2003.

FRIEDMAN, L. M.; TURETSKY, E. How to learn to solve problems. Moscow: Prosveshchenie, 1989.

GALPERIN, P. Y. Methods of teaching and mental development. Moscow: Prosveshchenie, 1985.

GRUDENOV, Y. I. Psycho-didactic fundamentals of teaching mathematics methods. Moscow: Pedagogika, 1987.

KABANOVA-MELLER, E. N. Psychology of knowledge and skills formation in students. Moscow: APN RSFSR, 1962.

KAIVO-OJA, J.; ROTH, S. The Technological Future of Work and Robotics. Econstor, 2015. Available: http://hdl.handle.net/10419/118693 Access: 10 May 2021.

LEGENDRE, A. M. Elements of Geometry. Baltimore: Kelly & Piet Publishers, 1867. Available: https://archive.org/details/cu31924001166341/page/n5/mode/2up Access: May 10, 2021.

LERNER, I. Y. Methodological problems of the didactic theory of textbook construction. In LERNER, I. Y.; SHAKHMAEV, N. M. What should a textbook be: Didactic structuring principles Part 1. Moscow: Publishing House of the Russian Academy of Sciences, 1992. p. 7-26.

METELSKY, N. V. Didactics of mathematics. Minsk: Belarus State University Publishing, 1982.

PASANI, C. F. Analyzing Elementary School Students Geometry Comprehension Based on Van Hiele’s Theory. Journal of Southwest Jiaotong University, v. 54, n. 5, p. 1-11, 2019. Available: http://jsju.org/index.php/journal/article/view/389. Access: 10 May 2021.

PETER, R. The game with infinity. Moscow: Progress, 1968.

PIAGET, J. How children form mathematical concepts. Psychology Issues, v. 4, p. 121-126, 1966.

PIAGET, J. Selected psychological works. Psychology of intelligence. Moscow: Prosveshchenie, 1969.

PISAREVSKY, B. M.; KHARIN, V. T. Talks about mathematics and mathematicians. Moscow: Fizmatlit, 2004.

PODAEVA, N. G.; PODAEV, M. V. Updating the content of school mathematical education: a sociocultural approach. St. Petersburg: “Lan’” Publishing House, 2014.

PODAEVA, N. G.; PODAEV, M. V.; AGAFONOV, A. P. Formation of concepts in the process of teaching geometry to students in e-learning environment. “Concept” Scientific Methodical Electronic Journal, n. 6, p. 10-25, 2019. Available: http://e-koncept.ru/2019/191040.htm Access: 10 May 2021.

PODAEVA, N. G.; PODAEV, M. V.; AGAFONOV, P. A. The social and cultural approach to forming geometric concepts among schoolchildren. Amazonia Investiga, v. 8, n. 20, 2019. Available: https://amazoniainvestiga.info/index.php/amazonia/article/view/175 Access: 10May 2021.

POINCARE, A. About science. Moscow: Nauka, 1983.

POINCARÉ, H.; HADAMARD, J. An essay on the psychology of invention in the mathematical field. Princeton: Princeton University Press, 1949.

POYA, D. Mathematics and plausible reasoning. Moscow: Nauka, 1975.

ROTENBERG. V. S. “I image” and behaviour. Tel Aviv, 2001.

ROTENBERG. V. S.; BONDARENKO, S. M. Brain. Training. Health: Teacher’s book. Moscow: Prosveshchenie, 1989.

RUBINSTEIN, S. L. Fundamentals of general psychology. St. Petersburg: “Peter” Publishing House, 1999.

SARANTSEV, G. I. Goals of teaching mathematics in secondary school in modern conditions. Mathematics at school, n. 6. p. 36-41, 1999.

SHARYGIN, I. F. Does the school of the XXI century need geometry? Mathematics at school, n. 4, p. 72-79, 2004.

SHCHEDROVITSKY, G. P. Processes and structures in thinking (a course of lectures). From the archive of G. P. Shchedrovitsky. Moscow, 2003. v. 6.

SHIRSHOV, I. E. Personality – Freedom – Creativity. In: Humanization of education process: personal motive and creative development. Report theses of scientific conference in Bobruisk, March 29-30 2001. Minsk: Belarus State Economic University Publishing, 2001.

SLEPKAN, Z. I. Psychological and pedagogical foundations of teaching mathematics. Kiev: Radianska shkola, 1983.

SOROKIN, P. A. Social and Cultural Dynamics. Volume IV: Basic Problems, Principles, and Methods. New York: Bedminster Press, 1941.

STEPIN, V. S. On the philosophical foundations of synergetics. Synergetic paradigm. Synergetics of education. Moscow: Progress-tradition, 2007. p. 97-102.

TAKACI, D.; STANKOV, G.; MILANOVIC, I. Efficiency of learning environment using GeoGebra when calculus contents are learned in collaborative groups. Computers & Education, v. 82, p. 421-431, 2015.

THAMBI, N.; EU, L. K. 2013 Effect of students’ achievement in fractions using GeoGebra. SAINSAB, v. 16, p. 97-106.

TOLMAN, E. C.; BRUNSWIK, E. The organism and the causal texture of the environment. Psychological Review, v. 42, n. 1, p. 43–77, 1935.

USTILOVSKAYA, A. A. Psychological mechanisms of overcoming the symbolic naturalization of the ideal content of geometric concepts. Moscow: Scientific research institute of secondary education development Innovative strategies, 2008.

YAKIMANSKAYA, I. S. Psychological foundations of mathematical education. Moscow: Akademia, 2004.

ZAKARIA, E.; LEE, L. S. Teacher’s perceptions toward the use of GeoGebra in the teaching and learning of Mathematics. Journal of Mathematics and Statistics, v. 8, n. 2, p. 253-257, 2012.

ZEMLIAKOV, A. N. Psychodidactic aspects in-depth mathematics study in senior grades of secondary school. Mathematics. The First of September, n. 5, p. 8-10, 2005.

ZENGIN, Y.; FURKAN, H.; KUTLUCA, T. The effect of dynamic mathematics software GeoGebra on student achievement in teaching of trigonometry. Procedia: Social and Behavioral Sciences, v. 31, p. 183-187, 2012.