The effects of 11th grade students' trigonometric problem solving on critical thinking skills in the process of teaching mathematics with problem-based instruction

This study aims to determine the progression of critical thinking skills in problem-based learning models in mathematics education. The study group consisted of 12 (twelve) 11th-grade students studying at Şirvan Anatolian High School in the Şirvan district of Siirt province during the 2021-2022 academic year. The instructional process of the study was designed using problem-based lerning method. The implementation process took place within nine weeks, from October 20, 2021, to December 28, 2021.A total of seven problem scenarios were used as data collection tools, three of which were implemented as pilot studies. These scenarios, which have trigonometric connections, were selected from students' real-life situations and gradually designed to be less structured for use in problem-based learning processes. Data were collected through interviews and observations. The questions used in the interviews during the implementation process were specifically based on Paul and Elder's (2002) "Questions That Define the Universal Structures of Thinking." The data collected in the study were analyzed using the phenomenology technique. The analysis involved categorizing the data into eight fundamental structures: Problem, Goal, Information, Assumption, Inference, Concepts, Implications and Consequences, and Point of View. These structures were identified by Paul and Elder (2002) as being present in all stages of reasoning. By categorizing the data into these structures, the researcher were able to gain insights into the students' critical thinking abilities and the development of their skills throughout the study. The research findings showed that students exhibited certain behavioral changes conducive to critical thinking and improvement in critical thinking skills. During the study, despite the scenarios becoming progressively less structured, the duration of the activity implementation decreased. This change was accompanied by a shift in students' thinking processes, as their invalid assumptions and reasoning were gradually replaced by the application of critical thinking skills. This indicates that the implementation of the problem-based instructional approach had a positive impact on the development of students' critical thinking abilities.In conclusion, this study revealed that an instructional process implemented based on problem-based learning methods enhances students' critical thinking skills. Keywords: Critical thinking, critical thinking skills, ill- structured problem, mathematics education, problem-based teaching