Main Article Content

Abstract

The purpose of this study was to investigate the critical role of equilibration in organizing and building students' cognitive structure in the practice of learning mathematics. This qualitative research was designed using a phenomenological study approach. Participants in this study were 30 high school students of XI level. The main research instrument was the interview guide format and the document of cognitive test questions with the circle equation material. Research data obtained were tested for the validity of the data by triangulation. Method triangulation was done by comparing student work data and interview data. Theory triangulation is done by comparing the descriptions of the data obtained with the relevant theoretical sources. The results showed that in the context of knowledge construction (cognitive structure), there is a strong relationship between the process of assimilation and accommodation with equilibration. The role of balance in forming cognitive structures is to guide students to organize previous knowledge (schemas) and new knowledge and create thinking structures to become more complex by considering the socio-cultural dimension (environment) in mathematics learning. Further studies suggest that when selecting topics for equilibration-based activities, teachers should provide an effective learning environment to support the formation of cognitive structures to become more prosperous and complex.

Keywords

Cognitive Conflict Cognitive Structure Equilibration Piaget’s theory

Article Details

Author Biographies

Imam Kusmaryono, Universitas Islam Sultan Agung

Mathematics Education Department

Mohamad Aminudin, Universitas Islam Sultan Agung

Department of Mathematics Education

Kartinah Kartinah, Universitas PGRI Semarang

Department of Mathematics Education

References

  1. Aloqaili, A. S. (2012). The relationship between reading comprehension and critical thinking: A theoretical study. Journal of King Saud University - Languages and Translation, 24(1), 35-41. https://doi.org/10.1016/j.jksult.2011.01.001

  2. Amineh, R. J., & Asl, H. D. (2015). Review of constructivism and social constructivism. Journal of Social Sciences, Literature and Languages, 1(1), 9-16.

  3. Bormanaki, H. B., & Khoshhal, Y. (2017). The role of equilibration in Piaget's theory of cognitive development and Its implication for receptive skills: A theoretical study. Journal of Language Teaching & Research, 8(5), 996–1005.

  4. Chang, J. Y., Wang, E. T., & Chao, R.-M. (2009). Using constructivism and scaffolding theories to explore learning style and effect in blog system environment. MIS REVIEW: An International Journal, 15(1), 29-61. https://doi.org/10.6131/MISR.200909_15(1).0002

  5. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.

  6. Dorko, A. (2019). Generalization, assimilation, and accommodation. The Mathematics Educator, 28(2), 33-51.

  7. Evtyugina, A., Zhuminova, A., Grishina, E., Kondyurina, I., & Sturikova, M. (2020). Cognitive-conceptual model for developing foreign language communicative competence in non-linguistic university students. International Journal of Cognitive Research in Science, Engineering and Education, 8(S), 69-77. https://doi.org/10.23947/2334-8496-2020-8-SI-69-77

  8. Garner, B. K. (2007). Getting to" got it!": Helping struggling students learn how to learn. Alexandria, Virginia: ASCD.

  9. Grokholskyi, V. L., Kaida, N. I., Albul, S. V., Ryzhkov, E. V., & Trehub, S. Y. (2020). Cognitive and metacognitive aspects of the development of lifelong learning competencies in law students. International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE), 8(2), 1-14. https://doi.org/10.5937/IJCRSEE2002001G

  10. Joubish, M. F., & Khurram, M. A. (2011). Cognitive development in Jean Piaget’s work and its implications for teachers. World Applied Sciences Journal, 12(8), 1260-1265.

  11. Khan, S. N. (2014). Qualitative research method-phenomenology. Asian Social Science, 10(21), 298-310. https://doi.org/10.5539/ass.v10n21p298

  12. Kholiq, A. (2020). How is Piaget's theory used to test the cognitive readiness of early childhood in school? Indonesian Journal of Early Childhood Education Studies, 9(1), 24-28. https://doi.org/10.15294/IJECES.V9I1.37675

  13. Kibalchenko, I., & Eksakusto, T. (2020). Cognitive and style predictors of the students’ psychological well-being. International Journal of Cognitive Research in Science, Engineering and Education, 8(1), 1-13. https://doi.org/10.5937/IJCRSEE2001001K

  14. Kusmaryono, I., Jupriyanto, J., & Kusumaningsih, W. (2021). Construction of students' mathematical knowledge in the zone of proximal development and zone of potential construction. European Journal of Educational Research, 10(1), 341-351. https://doi.org/10.12973/eu-jer.10.1.341

  15. Lee, G., & Kwon, J. (2001). What do we know about students' cognitive conflict in science classroom: A theoretical model of cognitive conflict process. In Proceeding of the Annual Meeting of the Association for the Education of Teachers in Science. Retrieved from https://files.eric.ed.gov/fulltext/ED472903.pdf

  16. Liu, C. H., & Matthews, R. (2005). Vygotsky's philosophy: Constructivism and Its criticisms examined. International education journal, 6(3), 386-399.

  17. Maharani, I. P., & Subanji, S. (2018). Scaffolding Based on Cognitive Conflict in Correcting the Students' Algebra Errors. International Electronic Journal of Mathematics Education, 13(2), 67-74. https://doi.org/10.12973/iejme/2697

  18. Miles, M. B., & Huberman, M. A. (2016). Analisis Data Kualitatif: Buku Sumber Tentang Metode-Metode Baru (11th ed.). Jakarta: Universitas Indonesia (UI-Press).

  19. Navaneedhan, C. G., & Kamalanabhan, T. J. (2017). What Is meant by cognitive structures? How does it influence teaching –learning of psychology? [Cognitive structure, Metaphorical thinking, Mental Representations, Intellectual framework and Teaching/Learning process]. IRA International Journal of Education and Multidisciplinary Studies, 7(2), 89-98. https://doi.org/10.21013/jems.v7.n2.p5

  20. Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of Research in Science Teaching, 2(3), 176-186. https://doi.org/10.1002/tea.3660020306

  21. Rutherford, G. D. (2011). A model of assimilation and accommodation in the cognitive & cultural realms. Dynamical Psychology.

  22. Simatwa, E., M. W. (2010). Piaget’s theory of intellectual development and its implication for instructional management at pre-secondary school level. Educational Research and Reviews, 5(7), 366-371.

  23. Steffe, L. P. (2002). The constructivist teaching experiment: Illustrations and implications. In E. V. Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177-194). Kluwer Academic Publishers.

  24. Vygotsky, L. S. (1987). Thinking and Speech. In R. W. Rieber & A. S. Carton (Eds.), The collected works of L.S. Vygotsky (pp. 37-285). Plenum Press. Retrieved from: https://www.marxists.org/archive/vygotsky/collected-works.htm

  25. Wang, P. (2011). Constructivism and learner autonomy in foreign language teaching and learning: To what extent does theory inform practice. Theory and Practice in Language Studies, 1(3), 273-277. https://doi.org/10.4304/tpls.1.3.273-277

  26. Zhiqing, Z. (2015). Assimilation, accommodation, and equilibration: A schema-based perspective on translation as process and as product. International Forum of Teaching & Studies, 11(1/2), 84-89.