Tomsk State Pedagogical University Bulletin
RU EN






Today: 29.03.2023
Home Issues 2020 Year Issue №6 METHOD OF REFLEXIVE LEARNING TO SOLVE MATHEMATICAL PROBLEMS
  • Home
  • Current Issue
  • Bulletin Archive
    • 2023 Year
      • Issue №1
      • Issue №2
    • 2022 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2021 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2020 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2019 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
    • 2018 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
    • 2017 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2016 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2015 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2014 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2013 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2012 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2011 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2010 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2009 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2008 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
    • 2007 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
    • 2006 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2005 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 2004 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 2003 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
    • 2002 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
    • 2001 Year
      • Issue №1
      • Issue №2
      • Issue №3
    • 2000 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
    • 1999 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 1998 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 1997 Year
      • Issue №1
      • Issue №2
      • Issue №3
  • Rating
  • Search
  • News
  • Editorial Board
  • Information for Authors
  • Review Procedure
  • Information for Readers
  • Editor’s Publisher Ethics
  • Contacts
  • Manuscript submission
  • Received articles
  • Accepted articles
  • Subscribe
  • Service Entrance
vestnik.tspu.edu.ru
praxema.tspu.edu.ru
ling.tspu.edu.ru
npo.tspu.edu.ru
edujournal.tspu.edu.ru

TSPU Bulletin is a peer-reviewed open-access scientific journal.

E-LIBRARY (РИНЦ)
Ulrich's Periodicals Directory
Google Scholar
European reference index for the humanities and the social sciences (erih plus)
DOAJ (Directory of Open Access Journals)
Search by Author
- Not selected -
  • - Not selected -
Яндекс.Метрика

METHOD OF REFLEXIVE LEARNING TO SOLVE MATHEMATICAL PROBLEMS

Kislyakova Mariya Andreyevna

DOI: 10.23951/1609-624X-2020-6-92-98

Information About Author:

Kislyakova M. A., Senior Lecturer, Pacific State University (ul. Tikhookeanskaya, 136, Khabarovsk, Russian Federation, 680035). E-mail: rabota2486@yandex.ru

Introduction. The method of teaching mathematics has a long history, which reflects all the success of teachers in creating a system of mathematical education both in Russia and in the world. Despite the fact that this system has been functioning for a long time and has produced outstanding results, mathematical subjects are currently the most difficult subjects for students both at school and at University. This leads to the fact that there are extreme points of view calling for the exclusion of the subject «Mathematics» from school and University courses due to its difficulty and low student performance. The solution to this problem in the modern world can be the use of psychologically-oriented learning concepts, one of which is the theory of reflexive learning. This article presents one of the aspects of applying this theory to the practice of mathematical education, namely reflexive learning to solve mathematical problems. The purpose of the article is to develop a methodology for teaching a «generalized algorithm» for solving mathematical problems based on stimulating reflexive mechanisms of activity. Materials and methods. The research material is the work of domestic and foreign authors devoted to the problems of teaching methods for solving problems and the psychology of reflexive learning. Their ideas allowed us to apply the theory of reflexive learning to teaching students to consciously regulate their own mathematical activities. Reflexive skills are the basis of the ability to intellectual self-regulation, and, consequently, a condition for productive intellectual mathematical activity. Results and discussion. The authors see the possibility of stimulating students’ cognitive activity based on reflection of their thought processes as one of the ways to solve psychological and methodological difficulties in learning to solve mathematical problems. The method of teaching problem solving involves teaching students to consciously perform four main stages. Formation of skills to analyze the problem, the solution to this problem, proper design of the idea of solving the problem and verifying the implemented solution is based on the mental experience of the student with the use of reflective learning strategies. Conclusion. As a result of reflexive learning to solve mathematical problems, students will develop a «generalized ability» to solve mathematical problems.

Keywords: reflexive learning, self-regulation training, reflexive strategies, mathematical problems, methods of teaching mathematics

References:

1. Kislyakova M. A. Refleksivnoye obucheniye matematike: uroven’ nauchnoy prorabotki, vnedreniye v praktiku obrazovaniya [Reflexive teaching of mathematics: the level of scientific study, implementation in the practice of education]. Materialy konferentsii «Aktual’nye problemy metodiki obucheniya informatike i matematike v sovremennoy shkole». Pod redaktsiyey L. L. Borisovoy, D. I. Pavlova [Proceedings of the conference «Actual problems of methods of teaching computer science and mathematics in a modern school». Edited by L. L. Borisova, D. I. Pavlov]. Moscow, MPSU Publ., 2019. Pp. 314–322 (in Russian).

2. Lipatnikova I. G. Refleksivnyy podkhod k obucheniyu matematike uchashchikhsya nachal’noy i osnovnoy shkoly v kontekste razvivayushchego obucheniya. Diss. dokt. ped. nauk [Reflexive approach to teaching mathematics to primary and primary school students in the context of developmental learning. Diss. doct. ped. sci.]. Ekaterinburg, 2005. 395 p. (in Russian).

3. Kislyakova M. A. Refleksivnoe obuchenie matematike: uroven’ nauchnoy prorabotki, vnedrenie v praktiku obrazovaniya [Reflexive teaching of mathematics: the level of scientific study, implementation in the practice of education]. Materialy konferentsii «Aktual’nye problemy metodiki obucheniya informatike i matematike v sovremennoy shkole». Pod redaktsiyey L. L. Borisovoy, D. I. Pavlova [Materials of the conference «Actual problems of methods of teaching computer science and mathematics in a modern school». Edited by L. L. Borisova, D. I. Pavlov]. Moscow, MPSU Publ., 2019. Pp. 314–322 (in Russian).

4. Kholodnaya M. A. Psihologiya intellekta: Paradoksy issledovaniya [Psychology of intelligence: Paradoxes of research]. Saint Petersburg, Piter Publ., 2002. 272 р. (in Russian).

5. Gel’fman E. G. Psikhodidaktika shkol’nogo uchebnika. Intellektual’noye vospitaniye uchashchikhsya [Psychodidactics of a school textbook. Intellectual education of students]. Saint Petersburg, Piter Publ., 2006. 384 р. (in Russian).

6. Kolyagin,Yu. M. Zadachi v obuchenii matematike. Chast’ 1 [Problems in teaching mathematics. Part 1]. Moscow, Prosveshcheniye Publ., 1977. 112 p. (in Russian).

7. Kislyakova M. A. O nekotoroy klassifikatsii matematicheskikh zadach [Some classification of mathematical problems]. Metodika prepodavaniya matematicheskikh i estestvenno-nauchnykh distsiplin: sovremennye problemy i tendentsii razvitiya: materialy Mezhregional’noy nauchno-praktichskoy konferentsii [Methods of teaching mathematical and natural science disciplines: modern problems and trends of development]. Omsk, OmSTU Publ., 2019. Pp. 45–48 (in Russian).

8. Kislyakova M. A. Etap aktualizatsii v obuchenii resheniyu zadach s parametrami [The stage of actualization in learning to solve problems with parameters]. Nauchno-metodicheskiy elektronnyy zhurnal «Kontsept» – Periodical scientific and methodological electronic journal «Koncept», 2017, vol. 15, pp. 80–82 (in Russian).

9. Fridman L. M., Turetskiy E. N. Kak nauchit’sya reshat’ zadachi? [How to learn to solve problems?]. Moscow, Prosveshcheniye Publ., 1984. 175 p. (in Russian).

10. Finkel’shteyn V. M. Chto delat’, kogda reshit’ zadachu ne udaetsya? [What to do when the problem cannot be solved?]. Moscow, ILEKSA Publ., 2008. 74 p. (in Russian).

11. Karpov A. V., Skityayeva I. M. Psikhologiya metakognitivnykh protsessov lichnosti [The psychology of metacognitive processes of the personality]. Moscow, Psychology Institute RAS Publ., 2005. 352 p. (in Russian).

12. Konopkin O. A. Obshchaya sposobnost’ k samoregulyatsii kak faktor sub”ektnogo razvitiya [General ability to self-regulation as a factor of subjective development]. Voprosy psikhologii – Voprosy Psychologii, 2004, no. 2, pp. 128–135 (in Russian).

13. Prokhorov A. O., Chernov A. V. Refleksivnaya regulyatsiya psikhicheskikh sostoyaniy v uchebnoy deyatel’nosti studentov [Reflexive regulation of mental states in students’ educational activities]. Obrazovaniye i samorazvitiye, 2013, no. 4 (38), pp. 11–16 (in Russian).

14. Kislyakova M. A. Obuchenie uchashchikhsya sposobam samoregulyatsii pri reshenii matematicheskikh zadach [Teaching students methods of self-regulation in solving mathematical tasks]. Elektronnye biblioteki – Russian Digital Libraries Journal, 2019, vol. 22, no. 6, pp. 609–618 (in Russian).

15. Kislyakova M. A. Pedagogicheskaya podderzhka preodoleniya poznavatel’nykh zatrudneniy u studentov gumanitarnykh spetsial’nostey pri izuchenii matematiki [Pedagogical support for overcoming cognitive difficulties in students of humanitarian specialties in the study of mathematics]. Materialy Mezhdunarodnoy zaochnoy nauchno-prakticheskoy konferentsii (23 noyabrya 2011 g.) [Proceedings of the International virtual scientific and practical conference (November 23, 2011)]. Novosibirsk, Sibirskaya assotsiatsiya konsul’tantov Publ., 2011. 136 p. Pp. 28–36 (in Russian).

kislyakova_m._a._92_98_6_212_2020.pdf ( 450.02 kB ) kislyakova_m._a._92_98_6_212_2020.zip ( 435.22 kB )

Issue: 6, 2020

Series of issue: Issue 6

Rubric: GENERAL AND INCLUSIVE EDUCATION

Pages: 92 — 98

Downloads: 328

For citation:


© 2023 Tomsk State Pedagogical University Bulletin

Development and support: Network Project Laboratory TSPU