Exploring students' creative thinking in the use of representations in solving mathematical problems based on cognitive style

Aryo Andri Nugroho(1*), Nizaruddin Nizaruddin(2), Ida Dwijayanti(3), Anggi Tristianti(4)

(1) Department of Mathematics Education, Universitas PGRI Semarang
(2) Department of Mathematics Education, Universitas PGRI Semarang
(3) Department of Mathematics Education, Universitas PGRI Semarang
(4) Department of Mathematics Education, Universitas PGRI Semarang
(*) Corresponding Author


Creative thinking is the cognitive activities that process the received information to produce new representations. Therefore, it is necessary to develop creative thinking and represent a problem. This study aims to investigate the students' creative thinking processes based on representation in solving mathematical problems reviewed from cognitive style. Qualitative research was used as a procedure of the study. The data was collected through MFFT questionnaires, mathematics problem tests, and interviews. This research involved 31 eighth-grade students at one of junior high school in Kendal regency, Central Java. Those two subjects represented the reflective and impulsive cognitive styles that have been selected based on their mathematical abilities. The data was analyzed through iterative method. The results of the study showed that both subjects demonstrated a different performance in solving problem. In term of fluency, both subjects used visual representations in interpreting information. On the originality, the reflective subject used symbolic representations. while the impulsive one used symbolic and verbal representations in constructing the mathematical expressions. However, both of them have not yet created new ideas in solving problems. Moreover, on the flexibility, these both subjects used visual and symbolic representations that could solve the problems by utilizing the environment objects towards the interpret problems into mathematical expressions. However, the reflective subject made a mistake in elaborating the formula as well as the impulsive subject can do it. These results indicated that both subjects have used the representation of each indicator of creative thinking in solving problems.


Creative thinking process, representation, cognitive style, reflective, impulsive

Full Text:



Aggarwal, I., & Woolleyb, A. W. (2019). Team creativity, cognition, and cognitive style diversity. Management Science, 65(4), 1586–1599. https://doi.org/10.1287/mnsc.2017.3001

Anwar, R. B., & Rahmawati, D. (2017). Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem Based Polya’s Stages. International Education Studies, 10(10), 20. https://doi.org/10.5539/ies.v10n10p20

Ariefia, H. E., As’ari, A. R., & Susanto, H. (2016). Proses Berpikir Siswa Dalam Menyelesaikan Permasalahan Pada Materi Trigonometri. Jurnal Pembelajaran Matematika, 3(1), 1–6. http://journal.um.ac.id/index.php/pembelajaran-matematika/article/view/5565%0A

Arshad, M. N., Atan, N. A., Abu, M. S., Abdullah, A. H., & Mokhtar, M. (2017). Improving the reasoning skills of students to overcome learning difficulties in additional mathematics. J. Sci. Math. Lett. UPSI, 5, 28–35.

Azhil, I. M. (2017). Profil Pemecahan Masalah Matematika Siswa Ditinjau dari Gaya Kognitif Reflektif dan Impulsif. Jurnal Review Pembelajaran Matematika, 2(1), 60–68. https://doi.org/10.15642/jrpm.2017.2.1.60-68

Bartolini, M. G. (2014). Encyclopedia of Mathematics Education. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-94-007-4978-8

Birgili, B. (2015). Creative and Critical Thinking Skills in Problem-based Learning Environments. Journal of Gifted Education and Creativity, 2(2), 71–71. https://doi.org/10.18200/jgedc.2015214253

Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehen