EFEKTIVITAS MODEL PROBLEM-BASED LEARNING (PBL) TERHADAP PENINGKATAN BERPIKIR KRITIS DAN KEMAMPUAN KOMUNIKASI MATEMATIKA PADA SISWA SMK

The low level of critical thinking and mathematical communication skills at the vocational high school level requires the application of innovative learning models. This study aims to test the effectiveness of the Problem-Based Learning (PBL) model in improving the Critical Thinking Skills (CTS) and Mathematical Communication Skills (MCS) of vocational high school students in arithmetic sequences and series. This study uses a mixed methods approach with a sequential explanatory design. The research sample consisted of 25 tenth-grade TJKT students at SMK Muhammadiyah 6 Donomulyo, selected through purposive sampling. The research instruments included descriptive tests (pre-test and post-test) to measure quantitative abilities, as well as observation sheets and interview guides for qualitative analysis.
Critical thinking skills were measured through the following indicators: interpretation, analysis, evaluation, and inference. Meanwhile, mathematical communication skills focused on: expression of mathematical ideas, use of symbolic/notational representations (a, b, Un, and Sn), and written procedure justification. Quantitative analysis results showed a significant increase in both variables. The average BK score increased from 59.48 to 79.96 (p < 0.001) with an N-gain value of 0.47 (moderate category). The average KKM score also increased significantly from 66.36 to 79.96 (p < 0.05). Qualitative findings confirm that the PBL syntax encourages students to conduct in-depth analysis and evaluation. Group discussions and presentations in PBL have been proven to facilitate scaffolding that improves the accuracy of formal notation and mathematical representation. This study concludes that PBL is effective as a solution for developing the strategic competencies of vocational high school students in mathematics