Kriswandani Kriswandani(1), Dani Kusuma(2*)

(1) Universitas Kristen Satya Wacana
(2) Universitas Kristen Satya Wacana
(*) Corresponding Author


This study aims to describe and examine the refractive thinking process of students with intuitive cognitive styles in solving complex problems. This research is an exploratory, descriptive study with a qualitative approach. The prospective research subjects were SWCU and UMS Mathematics Education undergraduate students, totaling 239 students consisting of 155 SWCU students and 84 UMS students. The subjects of this study consisted of 2 students with intuitive cognitive styles. The research instruments include the main and supporting instruments, including complex problems, cognitive style questionnaires, and interview grids. This research results from the refractive thinking process of Mathematics Education students with an intuitive cognitive style in solving complex problems, including perplexity, investigation, construct, evaluation and decision. The stages of an investigation, construct, and evaluation is carried out repeatedly and not sequentially (randomly). The perplexity stage occurs not only at the beginning of the stage but also occurs at each stage of refractive thinking. In addition, students decide to make sewing scheduling guesses based on their intuition.


efractive thinking, mathematic education, complex problems

Full Text:



Badjeber, R. Mailili, W.H. (2018). Analisis Pengetahuan Prosedural Siswa Kelas SMP pada Materi Sistem Persamaan Dua Variabel ditinjau dari Gaya Kognitif. Jurnal Penelitian dan Pembelajaran Matematika, 11(2), 41-54

Barry, M. (2012). What skills will you need to succeed in the future? Phoenix Forward (online). Tempe, AZ, University of Phoenix

Bialik, M. & Fadel, C. (2015). Skills for the 21 st Century: What Should Students Learn? Center for Curriculum Redesign. Boston: Massachusetts

Creswell, J. W. (2012). Educational Research: Planning, Conducting, dan Evaluating Quantitative and Qualitative Research. Boston: Pearson Education.

Dewey, J. (1993). How we think: A restatement of the relation of reflective thinking to the educative process. Chicago: Henry Regnery

Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.

Downey, Greg. (2005). How to Guide and Facilitate Self Reflective Practice in Re-Entry Programs. Presented at CIEE Conference, Miami, FL. November 17, 2005

Ennis, R. H. (1996). Critical Thinking Dispositions: Their Nature and Assessability. Informal Logic, 18(2), 165–182.

Ennis, R. H. (1996). Critical Thinking. Upper Saddle River: Prentice-Hall.

Fisher, A. (2001). Critical Thinking: An introduction. Cambridge University Press

Funke, J. (2012). Complex Problem Solving. Encyclopedia of the sciences of learning. Publisher: Springer. DOI: 10.1007/978-1-4419-1428-6_685

Griffin, P., McGaw, B., & Care, E. (2012). Assessment and Teaching of 21st Century Skills. London: Springer

Gurol. A. (2011). Determining the reflective thinking skills of pre-service teachers in learning and teaching process. Education Science and Technology Part B: Social and Educational Studies, 3(3), 387-402

Jansen, A., & Spitzer, S. M. (2009). Prospective middle school mathematics teachers’ reflective thinking skills: Descriptions of their students’ thinking and interpretations of their teaching. Journal of Mathematics Teacher Education, 12(2), 133–151.

Kolb, D. (1984). Experiential learning. Englewood Cliffs, NJ: Prentice Hall.

Martin, L. P. (1998). THE COGNITIVE-STYLE INVENTORY. The Pfeiffer Library, 8. Dari

Medeni, T. D., & Medeni, I. T. (2012). Reflection and Refraction for Knowledge Management Systems. International Journal Of eBusiness And eGovernment Studies, 4(1), 55–64.

Muin, A. (2011). The Situations That Can Bring Reflective Thinking Process in Mathematics Learning. International Seminar and the Fourth National Conference on Mathematics Education 2011 “Building the Nation Character through Humanistic Mathematics Education”. Department of Mathematics Education, Yogyakarta State University, Yogyakarta, July 21-23 2011, 978–979

Pagano, M., & Roselle, L. (2009). Beyond reflection through an academic lens: Refraction and international experiential education. Frontiers: The Interdisciplinary Journal of Study Abroad, 18(II), 217–229. link: URL:

Prayitno, A. (2015). Proses Berpikir Refraktif Mahasiswa dalam Menyelesaikan Masalah Matematika. Disertasi. Universitas Negeri Malang

Ratuanik, M. (2018). Cognitive Process of Students in Solving Mathematical Problem Judging from Cognitive Style of Field Independent and Field Dependent in Junior High School. The International Conference on Mathematical Analysis, Its Applications and Learning. Dari

Rodger, C. R. (2002). Seeing Student Learning: Teacher Change and The Role of Reflection. Harvard Educational Review, 72(2), 230–253

Rosen, J. G. (2010). Problem-Solving and Reflective Thinking: John Dewey, Linda Flower, Richard Young. Journal of Teaching Writting, 69–78

Sezer, R. (2008). Integration of Critical Thinking Skills into Elementary School Teacher Education Courses in Mathematics. Education, 128(3), 349-362.

Skemp, R. R. (1988). Reflective Intelligence and Mathematics,. British Journal of Educational Psychology, 31, 45–55.

Suharna, H. (2018). Teori Berpikir Reflektif dalam Menyelesaikan Masalah Matematika. Yogyakarta: Deepublish

Thompson, A.R. & O’Loughlin, V.D. (2015). The Blooming Anatomy Tool (BAT): A Discipline-Specific Rubric for Utilizing Bloom’s Taxonomy in the Design and Evaluation of Assessments in the Anatomical Sciences. Research Reports. Anatomical Sciences Education, 8, 493-501

Wagner, T. (2010). Overcoming The Global Achievement Gap (online). Cambridge, Mass., Harvard University. Dari

Zhang, L. (2002). Thinking styles and modes of thinking: implications for education and research. The Journal of Psychology, 136, 245–261.

Zubaidah, S. (2016). Keterampilan Abad ke-21: Keterampilan yang diajarkan melalui Pembelajaran. Conference: Seminar Nasional Pendidikan dengan tema “Isu-isu Strategis Pembelajaran MIPA Abad 21” di Program Studi Pendidikan Biologi STKIP Persada Khatulistiwa Sintang Kalimantan Barat. Dari

Article Metrics

Abstract view : 243 times
PDF - 104 times



  • There are currently no refbacks.

Copyright (c) 2022 Jurnal Karya Pendidikan Matematika

Jurnal Karya Pendidikan Matematika | P-ISSN: 2339-2444 E-ISSN: 2549-8401


Creative Commons Licence

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Jurnal Karya Pendidikan Matematika | P-ISSN: 2339-2444 E-ISSN: 2549-8401