Mathematical critical thinking skills play a crucial role in helping students analyze information, determine problem-solving strategies, and make logical decisions when solving mathematical problems. Efforts to develop these skills require instruction that encourages active student participation while also taking into account internal factors, such as self-efficacy. This study aims to (1) test the effectiveness of implementing Teams Games Tournament (TGT)-style cooperative learning supported by Baamboozle on mathematical critical thinking skills and (2) describe the characteristics of these skills based on levels of self-efficacy. The study employed a mixed-methods approach with a sequential explanatory design. A total of 64 seventh-grade students at SMP Negeri 13 Semarang participated in the quantitative phase using a pretest-posttest control group design, while six students were selected via purposive sampling for the qualitative phase. Data were collected using a mathematical critical thinking skills test, a self-efficacy questionnaire, and interviews. The instrument validation results showed that all test items and questionnaire items were valid , with reliability coefficients of 0.929 and 0.921, respectively, which fall into the very high category. Quantitative analysis included classical achievement tests, tests of the difference between two means, tests of the difference between two proportions, and normalized gain (N-Gain) analysis, while qualitative analysis used the Miles and Huberman model, which encompasses data reduction, data presentation, drawing conclusions, and triangulation of techniques. The research results show that (1) TGT-type cooperative learning supported by Baamboozle meets the criteria for effectiveness in improving mathematical critical thinking skills and (2) students with high self-efficacy demonstrate more optimal achievement of the indicators compared to students with moderate or low self-efficacy. These findings reinforce the notion that self-efficacy contributes to the development of mathematical critical thinking skills and should therefore be considered as an important aspect in the design of mathematics instruction.
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