This research uses a design-based approach aimed at exploring the critical thinking skills of university students through an advanced linear algebra project. The subjects involved are 32 students enrolled in the Advanced Linear Algebra course during the odd semester of the 2023/2024 academic year. To support the research, the instruments used include a critical thinking skills instrument, Hypothetical Learning Trajectory, Local Instruction Theory, Learning Activity Observation Based on Video, and a Google Drive-Based Portfolio. The data analysis technique involves several stages, starting with data condensation (transcription, coding, categorization, and theme identification), data presentation (process analysis, matrix, iterative processes, and conclusion drawing and verification), and data validity checking (triangulation and generalizability of research results). Based on the research findings, students' critical thinking skills are determined by reviewing five components: interpretation, analysis, evaluation, argumentation, and self-regulation. The harmonization and synchronization across various activities are still in the moderately developed category, indicating the need for dynamic and interactive activities to support proficiency fulfillment.
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