The Differences in Students’ Cognitive Processes in Constructing Mathematical Conjecture

I Wayan Puja Astawa


Constructing mathematical conjectures involves individuals’ unique and complex cognitive processes in which have not yet fully understood. The cognitive processes refer to any of the mental functions assumed to be involved in the acquisition, storage, interpretation, manipulation, transformation, and the use of knowledge. Understanding of these cognitive processes may assist individuals in constructing mathematical conjectures. This study aimed to describe the differences in students’ cognitive processes in constructing mathematical conjecture which is based on their mathematical ability and gender through a qualitative exploratory research study. The research subjects consisted of six mathematics students of Universitas Pendidikan Ganesha, the representative of high, medium, and low mathematical ability and either genders, male and female, respectively. The data of cognitive processes were collected by task-based interviews and were analyzed qualitatively. The differences in students’ cognitive processes in constructing mathematical conjectures were grouped into five distinct stages, namely understanding the problem, exploring the problem, formulating the conjecture, justifying the conjecture, and proving the conjecture. The results show that there were several differences in the students’ cognitive processes in constructing mathematical conjectures in the previously mentioned stages.


cognitive process; mathematical conjecture; level of mathematical ability; gender

Full Text:



Ardila, A., Rosselli, M., Matute, E., Inozemtseva, O. (2011). Gender differences in cognitive development. Developmental Psychology. 47 (4), Jul 2011, 984990

Astawa, I W. P, Budayasa, I K., & Juniati, D. (2018). The Process of Student Cognition in Constructing Mathematical Conjecture. Journal on Mathematics Education, 9 (1), 15–26

Belnap, J. K and Parrot, A.L. (2013). Understanding Mathematical Conjecturing. In S. Brown, G. Karakok, K. H Roh, and M. Oehrtman (Eds). Proceeding of the 16th Annual Conferenceon Research in Undergraduate Mathematics Education. Feb 21-23, 2013. Denver: Colorado

Benbow, C.P., Lubinski, D., Shea, D. L., and Eftekhari-Sanjani, H. (2000). Sex Differences in Mathematical Reasoning Ability at Age 13: Their Status 20 Years Later. Pshycological Science, 11 (6), 474480

Blazhenkova, O and Kozhevnikov, M. (2009). The New Object-Spatial-Verbal Cognitive Style Model: Theory and Measurement. Appl. Cognit. Psychol. 23, 638–663

Canadas, M, C., Deulofeu, J., Figueiras, L., Reid, D. and Yevdokimov, O. (2007). The Conjecturing Process: Perspectives in Theory and Implication in Practice. Journal of Teaching and Learning, 5 (1), 5572

Geist, E. A & King, M. (2008). Different, Not Better: Gender Differences in Mathematics Learning and Achievement. Journal of Instructional Psychology, 35 (1), 43–52

Herlitz, A. and Rehnman, J. (2008). Sex Differences in Episodic Memory. Current Direction in Psychological Science, 17 (1), 5256

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). 2002. Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for thePsychology of Mathematics Education, 717729. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Lim, H. K., Buendia, G., Kim, O., Cordero, F., and 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

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

Miles, M. B. and Huberman, A. M. (1994). Qualitative Data Analysis 2nd an Exanded Source book. California: Sage Publication

Morseli, F. (2006). Use of Examples in Conjecturing and Proving: An Exploratory Study. In Novotna, J., Moraova, K., Kratka, M., and Stehlikova, N. (eds). Proceeding 30th Conference of the International Group for the Psychology of Mathematics Educations, Vol. 4. 185192. Prague: PME

Norton, A. (2000). Student Conjectures in Geometri. Paper presented at the 24th conference of the international group for the Psychology of Mathematics Education. Hirosima, Japan

Pedemonte, B. (2001). Some Cognitive Aspects of the Relationship between Argumentation and Proof in Mathematics”. In van den Heuvel-Panhuizen M. Preceeding of the 25th conference of the international group for the Psychology of Mathematics Education. Utrech, Netherland

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

Potur, A. A & Barkul, O. (2009). Gender and creative thinking in education: A theoretical and experimental overview. ITU A|Z, 6 (2), 4457

Scafidi, T dan Bui, K. (2010). Gender similarities in math performance from middleschool through high school. Journal of Instructional Psychology, 37 (3), 252–255

Turgut, M & Yilmaz, S. (2012). Relationship Among Preservice Primary Teachers’ Gender, Academic Success and Spatial Ability. International Journal of Instruction, 5 (2), 5  20

Unal, H., Elizabeth Jakubowski and Darryl Corey. (2009). Differences in learning geometry among high and low spatial ability pre-service mathematics teachers. International Journal of Mathematical Education in Science and Technology, 40 (8), 997–1012

Weinstein, L. and Laverghetta, A. (2010). Sex Differences in College Students’ Elementary Arithmatic Ability. College Student Journal, Sept 2010 44 (3), 700702

Yang, J. C dan Chen, S. Y. (2010). Effects of gender differences and spatial abilities within a digital pentominoes game. Computers & Education, 55 (3), 1220–1233


Article Metrics

Abstract view : 470 times
PDF file view : 212 times


  • There are currently no refbacks.

Copyright (c) 2020 JPI (Jurnal Pendidikan Indonesia)

Jurnal Pendidikan Indonesia (JPI) is published by:



Jl. Udayana, Kampus Tengah, Singaraja-Bali
Kode Pos 81116
Telp. 0362-22928

Jurnal Pendidikan Indonesia (JPI) is indexed by:

Akreditasi SINTA 2   Crossref JPI  Index Copernicus JPI JPI Undiksha OneSearch   Microsoft Academic JPI  JPI indexing by Asean Citaion Index 

Creative Commons License

Jurnal Pendidikan Indonesia is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.