### PROCESS OF STUDENT COGNITION IN CONSTRUCTING MATHEMATICAL CONJECTURE

#### Abstract

This research aims to describe the process of student cognition in constructing mathematical conjecture. Many researchers have studied this process but without giving a detailed explanation of how students understand the information to construct a mathematical conjecture. The researchers focus their analysis on how to construct and prove the conjecture. This article discusses the process of student cognition in constructing mathematical conjecture from the very beginning of the process. The process is studied through qualitative research involving six students from the Mathematics Education Department in the Ganesha University of Education. The process of student cognition in constructing mathematical conjecture is grouped into five different stages. The stages consist of understanding the problem, exploring the problem, formulating conjecture, justifying conjecture, and proving conjecture. In addition, details of the process of the students’ cognition in each stage are also discussed.

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Alibert, L., & Thomas, M. (2002). Research on mathematical proof. In D. Tall (Ed.), Advance Mathematical Thinking (pp. 215?230). New York: Kluwer Academic Publishers.

Burtch, M. (2012). The evolution of conjecturing in a differential equations course. Retrieved from: http://zircon.mcli.dist.maricopa.edu/mlx/warehouse/01401-01500/01415/burtch_rpt.pdf.

Canadas, M.C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjecturing process: perspectives in theory and implication in practice. Journal of Teaching and Learning, 5(1), 55-72.

Fiallo, J., & Guitierrez, A. (2007). Analysis of conjectures and proofs produced when learning trigonometry. In D. Pitta-Pantazi and G. Philippou (Eds.), Proceeding of the 5th congress of the European society for research in mathematics education, (pp. 622?632). Cyprus: Larnaca

Gillis, J.M. (2005). An investigation of student conjectures in static and dynamic geometry environments. (Unpublished doctoral dissertation). Aburn, Alabama: Graduate Faculty of Auburn University.

Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for research in mathematics education, 31(4), 396-428.

Jiang, Z. (2002). Developing preservice teachers’ mathematical reasoning and proof abilities in the Geometer’s Sketchpad environment. In Mewborn, D.S., Sztajn, P., White, D.Y., Wiegel, H.G., Bryant, R.L., & Nooney, K. (Eds.), Proceedings of the 24th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education, (pp. 717?729). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Kemendikbud (2013). Modul Pelatihan Implementasi Kurikulum 2013 SMA Matematika. Jakarta: Badan Pengembangan Sumber Daya Manusia Pendidikan dan Kebudayaan dan Penjaminan Mutu Pendidikan.

Lim, H.K., Buendia, G., Kim, O., Cordero, F., & Kasmer, L. (2010). The role of prediction in the teaching and learning of mathematics. International Journal of Mathematical Education in Science and Technology, 41(5), 595-608.

Liu, S., & Ho, F. (2008). Conjecture activities for comprehending statistics terms through speculations on the functions of imaginary spectrometers. AMT, 64(3), 17-24.

Manizade, A.G., & Lundquist, B. (2009). Learning about proof by building conjectures. In S.L. Swars, D.W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education. (1566-1571). Atlanta, GA: Georgia State University.

Mazur, B. (1997). Conjecture. Synthese, 111, 197-210.

Miles, M.B., & Huberman, A.M. (1994). Qualitative data analysis: An expanded source book. 2nd ed. California: Sage Publication.

Morrow, M. (2004). Calculus students’ views of justification and proof in mathematics. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14(2), 104-126.

Morseli, F. (2006). Use of examples in conjecturing and proving: An exploratory study. In J. Novotna, K. Moraova, M. Kratka, & N. Stehlikova, (Eds.), Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Educations, (185?192). Prague: PME.

NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM Inc.

Nurhasanah, F., Kusumah, Y.S., & Sabandar, J. (2017). Concept of Triangle: Examples of Mathematical Abstraction in Two Different Contexts. International Journal on Emerging Mathematics Education, 1(1), 53-70.

Norton, A. (2000). Student conjectures in geometry. Paper presented at the 24th conference of the International Group for the Psychology of Mathematics Education, Hiroshima, Japan.

Pedemonte, B. (2001). Some Cognitive Aspects of the Relationship between Argumentation and Proof in Mathematics. In M. van den Heuvel-Panhuizen (Ed.). Proceeding of the 25th conference of the international group for the Psychology of Mathematics Education PME-25, vol. 4, (33-40). Utrech (Olanda)

Polya, G. (1945). How to solve it. Princeton, New Jersey: Princeton University Press.

Ponte, J.P., Ferreira, C., Brunheira, L., Oliveira, H., & Varandas, J. (1998). Investigating mathematical investigation. In P. Abrantes, J. Porfirio, & M. Baia (Eds.), Les interactions dans la classe de mathematiques: Proceedings of the CIEAEM 49. (3-14). Setubal: Ese de Setubal.

Yevdokimov, O. (2006). About a constructivist approach for stimulating students’ thinking to produce conjectures and their proving in active learning of geometry. Paper presented at the 4th Congress of the European Society for Research in Mathematics Education, (17–21). Sant Feliu de Guixols, Spain.

DOI: https://doi.org/10.22342/jme.9.1.4278.15-26

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