Students' critical thinking ability on application questions systems of linear equations through learning models project based learning - Rahmawati, Nurina Kurniasari; Kusuma, Arie Purwa; Sari, Wiwin Rita; Ramadoni, Ramadoni (Universitas Islam Raden Intan Lampung, INDONESIA, 2025)
Purpose: This study investigates the impact of application-based problems in systems of linear equations through the Project-Based Learning (PjBL) model on students’ critical thinking abilities. Critical thinking is a vital 21st-century skill, yet Indonesian students often demonstrate low proficiency in this area, particularly in mathematical contexts such as linear algebra. Method: A mixed-methods design was employed, combining qualitative and quantitative approaches. The participants were 28 students from STKIP Kusuma Negara, selected using purposive sampling. Data were collected through pre-tests and post-tests involving application problems, including chemical reaction equations and polynomial interpolation. Additionally, six students were selected for in-depth qualitative analysis based on their initial critical thinking levels. The data were analyzed using descriptive methods and N-gain calculations. Findings: Findings showed a significant improvement in students’ critical thinking skills after the intervention. The post-test average score increased to 81.93 with an N-gain score of 0.61, categorized as moderate. High-achieving students met all critical thinking indicators, while those with moderate or low abilities showed partial improvement. The use of structured learning worksheets (LKM) and real-world mathematical tasks within the PjBL framework effectively facilitated students’ ability to interpret, analyze, evaluate, and draw conclusions. Significance: This study demonstrates the potential of the PjBL model in fostering critical thinking, especially when combined with contextualized algebra problems. These findings offer practical implications for mathematics instruction, particularly in preparing future educators to promote analytical and reflective learning practices.