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

Abstract

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.

Keywords

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

Full Text:

PDF

References

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 comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001

Chiu, F. C., Hsu, C. C., Lin, Y. N., Liu, C. H., Chen, H. C., & Lin, C. H. (2019). Effects of Creative Thinking and Its Personality Determinants on Negative Emotion Regulation. Psychological Reports, 122(3), 916–943. https://doi.org/10.1177/0033294118775973

Coelho, A., & Cabrita, I. (2015). A Creative Approach to Isometries Integrating Geogebra and Italc with ‘Paper And Pencil’ Environments. Journal of the European Teacher Education Network, 10(0), 71–85.

Damayanti, H. T., & Sumardi, S. (2018). Mathematical Creative Thinking Ability of Junior High School Students in Solving Open-Ended Problem. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 36. https://doi.org/10.23917/jramathedu.v3i1.5869

Dwijayanti, I., Budayasa, I. K., & Siswono, T. Y. E. (2019). Students’ gestures in understanding algebraic concepts. Beta: Jurnal Tadris Matematika, 12(2), 133-143.. https://doi.org/10.20414/betajtm.v12i2.307

Erdogan, T., Akkaya, R., & Çelebi Akkaya, S. (2009). The effect of the Van Hiele model based instruction on the creative thinking levels of 6th grade primary school students. Educational Sciences: Theory and Practice, 9(1), 181–194.

Fauziah, E. W., Hobri, Yuliati, N., & Indrawanti, D. (2019). Student’s Creative Thinking Skills in Mathematical Problem Posing Based on Lesson Study for Learning Community. IOP Conference Series: Earth and Environmental Science, 243(1). https://doi.org/10.1088/1755-1315/243/1/012142

Firdausi, Y. N., & Asikin, M. (2018). Analisis Kemampuan Berpikir Kreatif Siswa Ditinjau dari Gaya Belajar pada Pembelajaran Model Eliciting Activities ( MEA ). PRISMA, Prosiding Seminar Nasional Matematika, 1, 239–247.

Firestone, P. (1997). The Effects of Verbal and Material Rewards and Punisher on The Performance of Impulsive and Reflective Children. Child Study Journal, 7(2), 71

Gregory, R.J. (2000). Psychological Testing: History, Principles and Application. Boston: Allyn and Bacon

Gube, M., & Lajoie, S. (2020). Adaptive expertise and creative thinking: A synthetic review and implications for practice. Thinking Skills and Creativity, 35(August 2019), 100630. https://doi.org/10.1016/j.tsc.2020.100630

Hasibuan, A. M., Saragih, S., & Amry, Z. (2019). Development of Learning Materials Based on Realistic Mathematics Education to Improve Problem Solving Ability and Student Learning Independence. International Electronic Journal of Mathematics Education, 14(2), 243–252. https://doi.org/10.29333/iejme/5729

Hendriana, H., & Fadhillah, F. M. (2019). the Students’ Mathematical Creative Thinking Ability of Junior High School Through Problem-Solving Approach. Infinity Journal, 8(1), 11. https://doi.org/10.22460/infinity.v8i1.p11-20

Huda, U., Musdi, E., & Nari, N. (2019). Analisis Kemampuan Representasi Matematis Siswa dalam Menyelesaikan Soal Pemecahan Masalah Matematika. JURNAL TA’DIB, 22(1), 19-25. http://dx.doi.org/10.31958/jt.v22i1.1226

Hutagaol, K. (2013). Pembelajaran Kontekstual Untuk Meningkatkan Kemampuan Representasi Matematis Siswa Sekolah Menengah Pertama. Infinity Journal, 2(1), 85. https://doi.org/10.22460/infinity.v2i1.27

Inuusah, M., Regine, K., Jonathan, M. K., Ebenezer, A., & Richard, M. (2019). Relationship between Creative Thinking and Students Academic Performance in English Language and Mathematics: The Moderating Role of Gender. Journal of Education, Society and Behavioural Science, 31(4), 1–10. https://doi.org/10.9734/jesbs/2019/v31i430159

Jankowska, D. M., Gajda, A., & Karwowski, M. (2019). How children’s creative visual imagination and creative thinking relate to their representation of space. International Journal of Science Education, 41(8), 1–22. https://doi.org/10.1080/09500693.2019.1594441

Kagan, J. (1965). Reflection-Impulsivity and Reading Ability in Primary Grade Children. Child Development, 36(3), 609. https://doi.org/10.2307/1126908

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press

Kim, K. H. (2006). Can we trust creativity tests? A review of the Torrance Tests of Creative Thinking (TTCT). Creativity Research Journal, 18(1), 3–14. https://doi.org/10.1207/s15326934crj1801_2

Kirton, M. J. (2003). Adaption-Innovation. in the Context of Diversity and Change. London, UK: Routledge

Masalimova, A. R., Mikhaylovsky, M. N., Grinenko, A. V., Smirnova, M. E., Andryushchenko, L. B., Kochkina, M. A., & Kochetkov, I. G. (2019). The interrelation between cognitive styles and copying strategies among student youth. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), 1–7. https://doi.org/10.29333/ejmste/103565

NCTM. (2000). Six Principles for School Mathematics. In National Council of Teachers of Mathematics (pp. 1–6). http://www.nctm.org/uploadedFiles/Math_Standards/ 12752_exec_pssm.pdf

Nugraha, D. A. (2017). Penerapan Pembelajaran Berbasis Masalah Berbantuan Program Geometer’S Sketchpad Untuk Meningkatkan Kemampuan Representasi Multipel Matematis Siswa. TEOREMA : Teori Dan Riset Matematika, 1(2), 1. https://doi.org/10.25157/teorema.v1i2.545

Nurdin, S., & Setiawan, W.A. (2016). Improving Students’ Cognitive Abilities And Creative Thinking Skills On Temperature And Heat Concepts Through An Exelearning-Assisted Problem Based Learning. International Journal of Scientific & Technology Research, 5, 59-63

Octaviani, D., Dwijanto, & Ahmadi, F. (2019). Mathematics Creative Thinking Skill Viewed from the Student Life Skill in SAVI Model Based ICT. Journal of Educational Research and Evaluation, 8(2), 108–115. https://doi.org/10.15294/jere.v8i2.34862

OECD. (2016). Assesing Scientific, Reading and Mathematical Literacy A Framework for PISA 2015. Paris: OECD Publishing

Panduwinata, B., Tuzzahra, R., Berlinda, K., & Widada, W. (2019). Analisis Kesulitan Representasi Matematika Siswa Kelas VII Sekolah Menengah Pertama Pada Materi Sistem Persamaan Linier Satu Variabel. 04(02), 202–210. https://doi.org/10.33449/jpmr.v4i2.9819

Permendikbud. Nomor 65. (2013). Tentang standar proses pendidikan dasar dan menengah. Jakarta: Kementrian Pendidikan dan Kebudayaan

Purwati, H., & Nugroho, A. A. (2015). Analisis Kemampuan Komunikasi Matematis Mahsiswa dalam Menyelesaikan Masalah pada Mata Kuliah Program Linier. Jurnal Ilmiah Pendidikan Matematika, 1(2), 39–104. https://doi.org/10.26877/jipmat.v1i2.1239

Putri, Dwijanto, & Sugiman. (2017). Analisis Kemampuan Komunikasi Matematis dan Rasa Percaya Diri Siswa SMKKelas X pada Pembelajaran Geometri Model Van Hiele Ditinjau dari Gaya Kognitif. Unnes Journal Of Mathematics Education, 6(1), 97–107. https://doi.org/10.15294/ujme.v6i1.1264

Rahmad, B. A., Ipung, Y., Abdur, R. A., Sisworo, & Dwi, R. (2016). Mathematical representation by students in building relational understanding on concepts of area and perimeter of rectangle. Educational Research and Reviews, 11(21), 2002–2008. https://doi.org/10.5897/err2016.2813

Rahmadian, N., Mulyono, & Isnarto. (2019). Kemampuan Representasi Matematis dalam Model Pembelajaran Somatic, Auditory, Visualization, Intellectually (SAVI). PRISMA, Prosiding Seminar Nasional Matematika, 2, 287–292. Retrieved from https://journal.unnes.ac.id/sju/index.php/prisma/article/view/28940

Robinson, J. R. (2006). WEBSTER’S DICTIONARY DEFINITIONS OF CREATIVITY. Journal of Workforce Education and Development, III(2), 34–47. http://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=1071&context=ojwed

Rozencwajg, P., & Corroyer, D. (2005). Cognitive processes in the reflective-impulsive cognitive style. Journal of Genetic Psychology, 166(4), 451–463. https://doi.org/10.3200/GNTP.166.4.451-466

Sagi, L., Arieli, S., Goldenberg, J., & Gooldschmidt, A. (2010). The interplay between externally imposed structure and personal cognitive style. Journal of Organizational Behaviour, 31(8), 1086–1110. https://doi.org/10.1002/job.664

Schoevers, E. M., Leseman, P. P. M., Slot, E. M., Bakker, A., Keijzer, R., & Kroesbergen, E. H. (2019). Promoting pupils’ creative thinking in primary school mathematics: A case study. Thinking Skills and Creativity, 31(October 2018), 323–334. https://doi.org/10.1016/j.tsc.2019.02.003

Setyana, I., Kusmayadi, T. A., & Pramudya, I. (2019). Problem-solving in creative thinking process mathematics student’s based on their cognitive style. Journal of Physics: Conference Series, 1321(2). https://doi.org/10.1088/1742-6596/1321/2/022123

Solso, R. L. (2000). The cognitive neuroscience of art: a preliminary MRI observation. Journal of Consciousness Studies, 7(8-9), 75-86

Utami, R. E., Nugroho, A. A., Dwijyanti, I., & Sukarno, A. (2018). Pengembangan E-Modul Berbasis Etnomatematika Untuk Meningkatkan Kemampuan Pemecahan Masalah. JNPM (Jurnal Nasional Pendidikan Matematika), 2(2), 268. https://doi.org/10.33603/jnpm.v2i2.1458

Wang, X., Duan, H., Kan, Y., Wang, B., Qi, S., & Hu, W. (2019). The creative thinking cognitive process influenced by acute stress in humans: an electroencephalography study. Stress, 22(4), 472–481. https://doi.org/10.1080/10253890.2019.1604665

Warli. (2013). Kreativitas Siswa SMP Yang Bergaya Kognitif Reflektif Atau Impulsif Dalam Memecahkan Masalah Geometri. Jurnal Pendidikan Dan Pembelajaran Universitas Negeri Malang, 20(2), 190–201.

DOI: 10.23917/jramathedu.v5i2.9983

Article Metrics

Abstract view(s): 1823 time(s)
PDF: 1136 time(s)

Refbacks

  • There are currently no refbacks.