### The Differences in Students’ Cognitive Processes in Constructing Mathematical Conjecture

#### Abstract

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.

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DOI: http://dx.doi.org/10.23887/jpi-undiksha.v9i1.20846

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