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Mathematical critical reasoning abilities among vocational secondary students are still insufficiently developed, specifically regarding the comprehension of circle central and inscribed angles. This research is designed to examine the impact of applying the Problem-Based Learning (PBL) framework combined with Artificial Intelligence (AI) upon these competencies. A quasi-experimental design utilizing a Nonequivalent Control Group Design was adopted, engaging 69 eleventh-grade accounting students at SMK Negeri 1 Pematangsiantar, comprising an experimental cohort (35 students) and a control cohort (34 students). The experimental cohort underwent PBL-oriented instruction utilizing AI as a supportive aid throughout the inquiry and evaluation stages, whereas the control cohort was exposed to traditional teaching methods. Data gathering was conducted via essay-based tests (pretest and posttest), observation instruments, and documentation, and processed through Shapiro–Wilk testing, Levene's test, along with an independent-samples t-test. The experimental cohort attained a superior average posttest score (78.79) compared to the control cohort (62.33), yielding a margin of 16.46 points. Hypothesis evaluation generated a t-value of 7.161 alongside a p-value below 0.001, signifying the rejection of the null hypothesis (H₀) and the acceptance of the alternative hypothesis (Hₐ). Consequently, PBL integrated with AI demonstrates a substantial effect on learners' mathematical critical reasoning capabilities when mastering circle central and inscribed angles.
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Putri et al. (2026) studied this question.
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