An exploration of students beliefs and self-confidence in constructing mathematical proofs
DOI:
https://doi.org/10.30606/absis.v9i1.4230Keywords:
mathematical proof, belief, self-confidence, deductive process, abductive process, pembuktian matematis, keyakinan, kepercayaan diri, proses deduktif, proses abduktifAbstract
The ability to construct mathematical proofs is one of the essential competencies in mathematics learning at the university level. Understanding the process of constructing mathematical proofs cannot be achieved solely through cognitive aspects, but also requires attention to students’ affective aspects. This study aims to examine affective aspects in the form of students’ beliefs and self-confidence in constructing mathematical proofs. The study employed a qualitative approach with a case study design. The research subjects were 42 second-semester students at a public university in Indonesia who had completed a Number Theory course. Data were collected through a written test consisting of mathematical proof problems and semi-structured interviews. For in-depth analysis, three students were purposively selected to represent variations in the mathematical proof construction process. Data analysis was conducted using a descriptive qualitative method by examining students’ beliefs and self-confidence during the process of constructing mathematical proofs. The results show that students’ beliefs can be classified into three categories based on each proof construction process they performed. In addition, students’ self-confidence is also grouped into three categories, ranging from confidence associated with reaching answers quickly despite being incorrect, to confidence demonstrated through the ability to explain and defend the proof construction process in a coherent and convincing manner. These findings emphasize the important role of affective aspects, in addition to cognitive aspects, in understanding students’ behavior in constructing mathematical proofs.
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