Volume 6 Issue 1 (2017)

Problem Posing of High School Mathematics Student’s Based on Their Cognitive Style

pp. 7-23  |  Published Online: March 2017  |  DOI: 10.22521/edupij.2017.61.1

Abdul Rahman, Ansari Saleh Ahmar

Abstract

Mathematical problem posing plays an important role in mathematics curriculum, since it encompasses the core of mathematics activities, among other things, with students’ activities to construct their own problems as the preliminary step to actual problem solving steps. This study aims at revealing the profile of students’ mathematical problem posing based on their cognitive styles in order to know and understand the learning of mathematics students. As a result of this study, students who have the cognitive style ‘field independent’ (FI) are able to propose a solvable mathematical problem and load new data, and also pose problems categorized as high-quality mathematical problems. Students who have the cognitive style of ‘field dependent’ (FD) are generally limited to solvable mathematical problems that do not contain new data, and mathematical problems of a moderate level. In this study, it is seen how student’s work mathematical problem posing using their cognitive style, resulting in a breakthrough in the process of learning to use students’ cognitive styles so as to increase the quality of learning outcomes.

Keywords: cognitive style, field dependent, field independent, problem posing, mathematical statement

References

Bullock, A., Stallybrass, O., Trombley, S., & Eadie, B. (1977). The Fontana dictionary of modern thought. Cambridge Univ Press.

Cooney, T. J. (1985). A beginning teacher’s view of problem solving. Journal for Research in Mathematics Education, 324–336.

Dillon, J. T. (1982). Problem finding and solving. The Journal of Creative Behavior, 16(2), 97–111.

Duncker, K., & Lees, L. S. (1945). On problem-solving. Psychological Monographs, 58(5), i, 113.

English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.

Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78–84.

Hamzah. (2003). Meningkatkan kemampuan memecahkan masalah matematika siswa sekolah lanjutan tingkat pertama negeri di Bandung melalui pendekatan pengajuan masalah (Unpublished Doctoral Dissertation). Bandung: Program Pascasarjana Universitas Pendidikan Indonesia.

Hashimoto, Y. (1997). The methods of fostering creativity through mathematical problem solving. ZDM, 29(3), 86–87.

Kilpatrick, J. (1969). Problem solving in mathematics. Review of Educational Research, 39(4), 523–534.

Mayer, R. E., Larkin, J. H., & Kadane, J. B. (1984). A cognitive analysis of mathematical problem-solving ability. Erlbaum.

McGivney, J. M., & DeFranco, T. C. (1995). Geometry proof writing: A problem-solving approach a la Polya. The Mathematics Teacher, 88(7), 552–555.

Messick, S. (1984). The nature of cognitive styles: Problems and promise in educational practice. Educational Psychologist, 19(2), 59–74.

Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23(1), 9–50.

Polya, G. (2014). How to solve it: A new aspect of mathematical method. Princeton University Press.

Rahman, A. (2006). Deskripsi pengajuan masalah matematika berdasarkan gaya kognitif siswa Kelas XII IA 1 SMA Negeri 11 Makassar. Surabaya, Indonesia.

Ratumanan, T. G. (2003). Pengaruh Model Pembelajaran dan Gaya Kognitif terhadap Hasil Belajar Matematika Siswa SLTP Negeri 1 dan SLTP Negeri 4 Ambon. Disertasi. Surabaya: Program Pascasarjana Unesa.

Romagnano, L. (1994). Wrestling with change: The dilemmas of teaching real mathematics. BOOK, Heinemann Educational Books.

Romberg, T. A., & Carpenter, T. P. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry. In T. A Romberg & T. P Carpenter (Eds.), Handbook of Research on Teaching (pp. 850–873).

Santrock, J. W. (2007). Psikologi Pendidikan (2nd ed.). Jakarta, Indonesia: Prenada Media Group.

Sigel, I. E., & Coop, R. H. (1974). Cognitive style and classroom practice. Psychological Concepts in the Classroom. New York: Harper & Row.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

Silver, E. A., & Cai, J. (1996). An Analysis of Arithmetic Problem Posing by Middle School Students. Journal for Research in Mathematics Education, 27(5), 521-539.

Siswono, T. Y. E. (2008). Model Pembelajaran Matematika Berbasis Pengajuan Masalah dan Pemecahan Masalah untuk Meningkatkan Kemampuan Berpikir Kreatif. Doctoral Dissertation. Surabaya: Unesa University Press.

Soedjadi, R. (1996). Diagnosis Kesulitan Siswa Sekolah Dasar dalam Belajar Matematika. In Proceedings of Hasil Deseminasi Penelitian PMIPA LPTK Tahun Anggaran 1995/1996 Bidang Kependidikan.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. Technology in Mathematics Education, 518–525.

Vernon, P. E. (1973). Multivariate approaches to the study of cognitive styles. Multivariate Analysis and Psychological Theory, pp. 125–148.

Waber, D. (1989). The biological boundaries of cognitive styles: A neuropsychological analysis.

Wilis Dahar, R. (1996). Teori-teori belajar. Jakarta: Erlangga.

Witkin, H. A., Moore, C. A., Goodenough, D. R., & Cox, P. W. (1975). Field‐dependent and field‐independent cognitive styles and their educational implications. ETS Research Bulletin Series, 1975(2), 1–64.

Zelniker, T. (1989). Cognitive style and dimensions of information processing. Cognitive Style and Cognitive Development, 172–191.

Announcement

EDUPIJ is indexed in ERIC now.

We are delighted to announce that Educational Process: International Journal has been included in ERIC - Education Resources Information Center (Coverage: Volume 8, 2019 & forward).

-----------------------------------------

EDUPIJ is included in The Philosopher’s Index (Coverage: Volume 5, 2016 & forward).

The Philosopher’s Index is the premiere bibliographic database covering worldwide research in all subject areas of philosophy.

Thank you so much to the editorial board members, authors and reviewers for their contribution to Educational Process: International Journal.