Developing Children’s Concepts in Mathematics and Natural Sciences in Elementary School: From Initial Representations to Scientific Concepts

458

Abstract

The article provides psychological and pedagogical background for a technique aimed at transforming children’s initial representations in mathematics and natural sciences into scientific concepts in elementary school. The methodological basis underlying this technique is largely shaped by L.S.Vygotsky’s ideas of holistic and unified development of concepts in the process of learning. We emphasize the key ideas of designing tools for working with students’ initial representations and transforming them into mathematical and natural scientific concepts: identification and joint discussion of children’s naive representations, reflective assessment of different views on the explored subject concept, coordination of opinions and assessments. We analyze the main approaches and practices of working with the students’ initial representations developed in foreign and Russian psychological and pedagogical research. It is worth noting that there is no universally recognized technique for transforming students’ initial representations into scientific concepts in elementary school; nonetheless, there is a number of effective methods in pedagogical practice that we outline in the paper. Finally, we stress the importance of training teachers to work with children’s initial representations in the course of developing their scientific concepts within the learned subject.

General Information

Keywords: development, initial representations, mistakes in mathematics and natural sciences, naive theories, scientific concepts, educational tasks, dialogue and polylogue, reflection, joint activity

Journal rubric: Educational Psychology

Article type: scientific article

DOI: https://doi.org/10.17759/pse.2021260602

Funding. The study was carried out within the framework of the state task of the Ministry of Education of the Russian Federation No.073-00041-21-05 dated 07/14/2021 “Formation of the psychological component in the methodological training of future teachers necessary for analyzing the causes of student mistakes in order to develop their subject conceptual thinking in the process of solving educational tasks.”

Received: 01.10.2021

Accepted:

For citation: Isaev E.I., Margolis A.A., Safronova M.A. Developing Children’s Concepts in Mathematics and Natural Sciences in Elementary School: From Initial Representations to Scientific Concepts. Psikhologicheskaya nauka i obrazovanie = Psychological Science and Education, 2021. Vol. 26, no. 6, pp. 25–45. DOI: 10.17759/pse.2021260602. (In Russ., аbstr. in Engl.)

References

  1. Berlyand I.E.Uchebnaya deyatel’nost’ v shkole razvivayushchego obucheniya i shkole dialoga kul’tur [Educational activity at the school of developmental education and the school of dialogue of cultures].Diskurs = Discourse, 1997, no.3—4, pp.117—142.(In Russ.).
  2. Vygotskij L.S.Sobranie sochinenij: V 6-ti t.T.2.Problemy obshchej psihologii [Problems of general psychology].Moscow: Pedagogika, 1982.504 p.(In Russ.).
  3. Davydov V.V.Teoriya razvivayushchego obucheniya [Theory of developing learning].Moscow: Intor, 1996.544 p.(In Russ.).
  4. Kurganov S.YU.Kapriznaya individual’nost’ ponyatiya [Capricious individuality of the concept].Narodnoe obrazovanie= Public education, 2001, no.9, pp. 71—78.(In Russ.).
  5. Margolis A.A.Zona blizhajshego razvitiya (ZBR) i organizaciya uchebnoj deyatel’nosti uchashchihsya [The zone of proximal development (ZBR) and the organization of educational activities of students].Psihologicheskaya nauka i obrazovanie = Psychological science and education, 2020.Vol.25, no.4, pp.6—27.DOI:10.17759/pse.2020250402 (In Russ.).
  6. Perre-Klermon A.-N.Rol’ social’nyh vzaimodejstvij v razvitii intellekta detej [The role of social interactions in the development of children’s intelligence].Moscow: Pedagogika, 1991.248 p.(In Russ.).
  7. Piazhe Zh.Rech’ i myshlenie.Moskva; Leningrad: Gosudarstvennoe uchebno-pedagogicheskoe izdatel’stvo, 1932.412 p.(In Russ.).
  8. Rubcov V.V.Social’no-geneticheskaya psihologiya razvivayushchego obrazovaniya: deyatel’nostnyj podhod [Socio-genetic psychology of developing education: an activity approach] [Elektronnyi resurs].Moscow: Moscow State University of Psychology and Education, 2008.416 p.URL: http://psychlib.ru/inc/absid.php?absid=73234 (Accessed 08.12.2021).(In Russ.).
  9. Sovmestnaya uchebnaya deyatel’nost’ i razvitie detej: Kollektivnaya monografiya [Joint educational activity and development of children.Collective monograph] [Elektronnyi resurs].Rubcov V.V., Ulanovskaya I.M.(eds.).Moscow: Moscow State University of Psychology and Education, 2021.352 p.URL: https://psyjournals.ru/clcd_2021/index.shtml (Accessed 08.12.2021).(In Russ.).
  10. Pentin A.Yu.et al.Sostoyanie estestvennonauchnogo obrazovaniya v rossiiskoi shkole po rezul’tatam mezhdunarodnykh issledovanii TIMSS i PISA.Voprosy obrazovaniya = Educational studies Moscow, 2018, no. 1, pp.79—109.DOI:10.17323/1814-9545-2018-1- 79-109 (In Russ.).
  11. Cukerman G.A.Ot umeniya sotrudnichat’ k umeniyu uchit’ sebya [From the ability to cooperate to the ability to teach yourself] [Elektronnyi resurs].Psihologicheskaya nauka i obrazovanie = Psychological science and education, 1996, no.2, pp.27—42.URL: https://psyjournals.ru/psyedu/1996/n2/Tsukerman.shtml (Accessed 08.12.2021).(In Russ.).
  12. Cukerman G.A.Pedagogicheskie illyuzii, iskazhayushchie uchebnuyu deyatel’nost’ [Pedagogical illusions distorting educational activity].Costoyanie i perspektivy razvivayushchego obucheniya : Materialy konferentsii (Abakan, 1988) [The current state and prospects of developing learning: Conference materials (Abakan, 1988)].Krasnoyarsk: Krasnoyarsk University Publishing, 1990, pp.17—22.(In Russ.).
  13. Cukerman G.A.Sovmestnoe uchebnoe dejstvie: reshennye i nereshennye voprosy [Joint educational action: resolved and unresolved issues].Psihologicheskaya nauka i obrazovanie = Psychological science and education, 2020.Vol.25, no.4, pp.51—59.DOI:10.17759/pse.2020250405 (In Russ.).
  14. Carey S.Conceptual Change in Childhood.Cambridge, MA: Bradford Books, 1985.226 p.
  15. Vosniadou S.et al.Designing learning environments to promote conceptual change in science.Learning and Instruction, 2001.Vol.11, no.4—5, pp.381—419.DOI:10.1016/S0959-4752(00)00038-4
  16. Lee C.B., Tan S.C., Chai C.S.Knowledge building and reframed conceptual change: A cross fertilization [Elektronnyi resurs].2007 Knowledge Building Summer Institute (Toronto, Canada, 7—10 August 2007: Conference Papers.Toronto, 2077.17 p.URL: http:// hdl.handle.net/10497/9661 (Accessed 08.12.2021).
  17. Lipman M.Philosophy in the Classroom.Philadelphia: Temple University Press, 1980.248 p.
  18. McGuire P.Using online error analysis items to support preservice teachers’ pedagogical content knowledge in mathematics [Elektronnyi resurs].Contemporary Issues in Technology and Teacher Education, 2013.Vol.13, no.3, pp.207—218.URL: https://www.learntechlib.org/p/40389/ (Accessed 08.12.2021).
  19. Resnick L.B.et al.Next Generation Research in Dialogic Learning.In Hall G.E., Quinn L.F., Gollnick D.M.(eds.).Wiley Handbook of Teaching and Learning.Medford, MA: John Wiley & Sons, 2018, pp.323—338.
  20. Pine K., Messer D., St.John K.Children’s Misconceptions in Primary Science: A Survey of teachers’ views.Research in Science & Technological Education, 2001.Vol.19, no.1, pp.79—96.DOI:10.1080/02635140120046240
  21. Schwarz B.B., Groot R.Argumentation in a changing world.International Journal of Computer-Supported Collaborative Learning, 2007.Vol.2, no. 2—3, pp. 297— 313.DOI:10.1007/S11412-007-9020-6
  22. Bigozzi L.et al.The Influence of Teaching Approach on Students’ Conceptual Learning in Physics.Frontiers in Psychology, 2018.Vol.9.14 p.DOI:10.3389/ fpsyg.2018.02474
  23. The Monitoring of School Mathematics: Background Papers.Volume 2: Implications from Psychology; Outcomes of Instruction [Elektronnyi resurs].Romberg T.A., Stewart D.M.(eds.).Wisconsin Center for Education Research, School of Education, University of Wisconsin-Madison.Madison, 1987.292 p.URL: https:// files.eric.ed.gov/fulltext/ED289709.pdf (Accessed 08.12.2021).
  24. Vosniadou S.Capturing and modeling the process of сonceptual change.Learning and Instruction, 1994.Vol.4, no.1, pp.45—69.DOI:10.1016/0959- 4752(94)90018-3
  25. Vosniadou S.Reframing the Classical Approach to Conceptual Change: Preconceptions, Misconceptions and Synthetic Models.In Fraser B., Tobin K., McRobbie C.(eds.).Second International Handbook of Science Education. London; New York: Springer, 2012.Vol.24, pp.119—130.DOI:10.1007/978-1-4020-9041-7_10
  26. Vosniadou S.The Development of Students’ Understanding of Science.Frontiers in Education, 2019.Vol.4, no.1.6 p.DOI:10.3389/feduc.2019.00032
  27. Vosniadou S.The Framework Theory Approach to the Problem of Conceptual Change.In Vosniadou S., Vamvakoussi X., Skopeliti I.(eds.).International Handbookof Research on Conceptual Change. New York: Routledge, 2008, pp.3—34.DOI:10.4324/9780203874813-7
  28. Vosniadou S., Brewer W.F.Technical Report No. 467: The Concept Of The Earth’s Shape: A Study Of Conceptual Change in Childhood [Elektronnyi resurs].Center for the Study of Reading Technical Report.Champaing: University of Illinois at Urbana-Champaign, 1989.72 p.URL: https:// www.ideals.illinois.edu/bitstream/handle/2142/17996/ ctrstreadtechrepv01989i00467_opt.pdf (Accessed 08.12.2021).
  29. Vosniadou S., Stathopoulou C.Conceptual Change in Physics and Physics-Related Epistemological Beliefs: A Relationship under Scrutiny [Elektronnyi resurs].In Vosniadou S., Baltas A., Vamvakoussi X.(eds.).Reframing the conceptual change approach in learning and instruction.Amsterdam: Elsevier, 2007, pp.145—163.URL: https://psycnet.apa.org/ record/2007-04764-012 (Accessed 08.12.2021).

Information About the Authors

Evegeniy I. Isaev, Doctor of Psychology, professor, Professor, Chair of Pedagogical Psychology named after Professor V.A. Guruzhapov, Moscow State University of Psychology & Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-4652-5780, e-mail: eiisaev@yandex.ru

Arkadiy A. Margolis, PhD in Psychology, Rector, Professor, Chair of Pedagogical Psychology, Moscow State University of Psychology & Education, Moscow, Russia, ORCID: https://orcid.org/0000-0001-9832-0122, e-mail: margolisaa@mgppu.ru

Maria A. Safronova, PhD in Psychology, Dean of the Faculty of Psychology of Education, Research fellow of the laboratory of Theoretical and experimental issues in cultural-historical psychology, Moscow State University of Psychology and Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-3597-6375, e-mail: mariasaf@gmail.com

Metrics

Views

Total: 1074
Previous month: 25
Current month: 19

Downloads

Total: 458
Previous month: 14
Current month: 6