INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 05, MAY 2020 ISSN 2277-8616 84 IJSTR©2020 www.ijstr.org How Do Students’ Mathematical Epistemological Beliefs Affect Their Critical Thinking Tendencies? Rahaju, Purwanto, I Nengah Parta, Swasono Rahardjo Abstract: The study aimed to investigate the tendency of students to think critically and explore the relationship between the students’ critical thinking with their mathematical epistemological beliefs. This descriptive qualitative study involved 32 students from the Department of Mathematics Education. The result showed that subjects who were non-critical thinkers exhibited carelessness in understanding, recognizing errors, and overviewing the tasks because they believed that mathematical tasks are always right and problem-solving with formulas and procedures results in correct solutions. On the other hand, critical-thinker students were more careful in comprehending the tasks, checking the errors, and doing an overview. The belief that mathematical tasks can contain errors and that conceptual understanding is highly crucial in mathematical problem-solving increased the tendency of the students to think critically. Besides, the students also had to highlight that numbers in mathematical problems have meaning and logical relationships. Index Terms: critical thinking tendecies, closed ended problem, ill-logical problems, mathematical epistemological beliefs. ——————————  —————————— 1 INTRODUCTION Critical thinking is a skill needed to face challenges in life. Critical thinking helps individuals test, connect, and evaluate all aspects of a situation or a problem [1] to carry out their duties and responsibilities [2],[3]. In the globalization era, critical thinking is used to filter information that is disseminated through various media [4],[5],[6]. However, research shows that the majority of students in Asia have poor critical thinking performance. Some studies even proved that Malaysian [7], Indonesian [8], and Middle Eastern [9] high school students were unable to achieve satisfactory scores in critical thinking. In addition, a great deal of mathematics teacher candidates cannot be categorized into critical thinkers [10] and had their low critical-thinking dispositions [11]. Rasiman [12] examined students’ critical thinking dispositions using closed-ended problems and identified three levels of critical thinkers. Types of problems, such as closed-ended problems, implicit open- ended problems, ill-logical problems, and incomplete information problems require different critical thinking tendencies [10]. This study aimed to explore students' critical thinking tendencies by using ill-logical mathematics problems and closed-ended problems. Futhermore, investigated mathematical beliefs that supported the tendencies. It is hoped that the results of this study can provide preliminary information about students’ mathematical epistemological beliefs that support the tendency of the students to think critically. 2 METHOD The subjects of this descriptive qualitative study consisted of 32 students from the Department of Mathematics Education of a private university in Malang who had learned and solved various triangle problems. Data of the study were gathered using two instruments, triangle problem-solving tasks (PSTt) and an interview guideline. PSTt contained ill-logical mathematics problems and closed-ended problem that were used to pinpoint the subjects’ critical thinking tendencies (Fig. 1 and Fig. 2). Data collection was conducted by asking the participants to solve PSTt 1. Two weeks later, the participants were re-invited to solve PSTt 2. An interview was conducted to explore the subjects’ thinking process when solving PSTt and elicit the reasons why they chose a specific way to solve the problems. The interview was carried out after the participants completed PSTt tasks. The subjects’ answers to PSTt problems were scored and the data were classified. After that, an interview guideline was developed. The subjects’ thinking process was analyzed to investigate their critical thinking tendencies and mathematical epistemological beliefs. 3 RESULTS The results of the analysis were categorized into two groups: critical thinker subjects (TCT subjects) and non-critical thinker subjects (NTCT subjects). The categorization of subjects was presented on Table 1 dan 2. ______________________________________ • Rahaju, student in Mathematics Education Departement, Universitas Negeri Malang, Indonesia. E-mail: rahaju.1503119@students.um.ac.id • Purwanto, Universitas Negeri Malang, Indonesia. E-mail: purwanto.fmipa@um.ac.id • I Nengah Parta, Universitas Negeri Malang, Indonesia. E-mail: nengah.parta.fmipa@um.ac.id • Swasono Rahardjo, Universitas Negeri Malang, Indonesia. E-mail: swasono.rahardjo.fmipa@um.ac.id