Reinforcement of Logical and Mathematical Competences Using a Didactic Aid Based on the Theory of Constructivism

  • Tomasz Kopczyński
  • Anna Gałuszka
Part of the Critical Studies of Education book series (CSOE, volume 10)


The paper presents the results of an experiment conducted among pupils of third grade classes (aged 9–10 years) in ten randomly selected primary schools, the effects of which were evaluated using the K3 logical and mathematical competence test. The aim of the research was to verify the effectiveness of the EduMata didactic aid built around a problem-based approach based on Piaget’s theory of constructivism. The scope studied included mathematical competences in the areas of calculation, geometry and word problems. The research showed that the experimental groups provided with educational support during their lessons showed significantly increased final versus initial results as demonstrated by the K3 mathematical competence test. The control group, on the other hand, did not produce such significant pretest and post-test result difference.


Logical and mathematical competences Constructivism K3 logical and mathematical competence test Mathematical education Didactic aid for teaching logic and mathematics Development and cognitive concept 


  1. Bruner, J., & Haste, H. (1987). Making sense. In The child’s construction of the world. New York: Methuen.Google Scholar
  2. Grusczyk-Kolczyńska, E. (2012). O dzieciach matematycznie uzdolnionych. [ang. About mathematically gifted children]. Red. E. Gruszczyk-Kolczyńska, Wyd. Nowa Era. Chapter: Wnioskowanie uzdolnieniach matematycznych. Wyniki badań, interpretacje i wnioski. [ang. Infering mathematical aptitudes. Research results, interpretations and conclusions] (pp. 340–365), Warszawa.Google Scholar
  3. Grusczyk-Kolczyńska, E. (2015). O kryzysie edukacji matematycznej na przykładzie pierwszego roku nauki szkolnej. Co trzeba zmienić, żeby dzieci mogły odnosić sukcesy w nauce matematyki. [ang. On the crisis of mathematical education on the example of the first year of schooling. What you need to change so that your children can succeed in learning math.] In Uczenie się dzieci. Myślenie i działanie. [ang. Learning children. Thinking and acting.] red. J. Malinowska i T. Neckar-Ilnicka, Wydawnictwo EPIDEIXIS.Google Scholar
  4. Majewska, K. (2014). Efektywność interaktywnej formy nauczania z użyciem tablicy multimedialnej. (ang. Efficiency of the interactive form of teaching with the use of a multimedia board). Wyd. E-mentor, 1(63), 31–40.Google Scholar
  5. Piaget, J. (1966). Studies on child psychology. Warszawa: PWN.Google Scholar
  6. Piaget, J., & Inhelder, B. (1970). From the logic of a child to the logic of adolescents. A discussion on the development of formal operating structures. Wyd. PWN.Google Scholar
  7. Piazza, M. (2011). Neurocognitive start-up tools for symbolic number representations. In Time and number in the brain by Stanislas Dehaene and Elizabeth Brannon (pp. 267–286). London: Elsevier.Google Scholar
  8. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53(2), 293–305.CrossRefGoogle Scholar
  9. Pinker, S. (1995). Language Instynkt. New York: Peungwin Books.Google Scholar
  10. Raszka, R. (2011). Integrowanie matematyki z innymi obszarami dziecięcego poznawania. [ang. Integrating mathematics with other areas of childhood learning]. Wyd. TWP, Warszawa, In An integral system in child’s education: contexts and consequences of changes (pp. 255–266).Google Scholar
  11. Report. (2014). Research report: A diagnosis of mathematical skills. Retrieved from [25.03.2018].
  12. Report. (2015a). Research report: Mathematical competences of third grade pupils. Retrieved from [25.03.2018].
  13. Semadeni, Z. (2016). Podejście konstruktywistyczne do matematycznej edukacji wczesnoszkolnej. (ang. Constructivist approach to mathematical early childhood education). Wyd. ORE, Warszawa 2016.Google Scholar
  14. Sessoms, D. (2008). Interactive instruction: Creating interactive learning environments through tomorrow’s teachers. International Journal of Technology in Teaching and Learning, 4(2), 86–96.Google Scholar
  15. Siwek, H. (2011). System integralny w edukacji dziecka: konteksty i konsekwencje zmian. [ang. An integral system in child’s education: contexts and consequences of changes]. Wyd. TWP, Warszawa.Google Scholar
  16. Snow, C., Bornstein, M. H., & Bruner, J. S. (1989). Interaction in human development.Google Scholar
  17. Spelke, E. (2005). Differences in intrinsic aptitude for mathematics and science. American Psychologist, 60(9), 950–958.CrossRefGoogle Scholar
  18. Wygotski, L. S. (1989). Thinking and speech. Wyd. PWN.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomasz Kopczyński
    • 1
  • Anna Gałuszka
    • 2
  1. 1.University of Silesia in KatowiceKatowicePoland
  2. 2.University of Bielsko-BialaBielsko-BiałaPoland

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