<![CDATA[This research aims: (1) to determine whether problem-based learning models improve mathematical problem-solving abilities and self-efficacy; (2) to explore the interaction between students' initial mathematical abilities and the learning model. The study employed a quasi-experimental quantitative design, with ANOVA used for inferential data analysis. Fifty eighth-grade students from SMP Negeri 3 Aek Kuo in the academic year 2022/2023 were examined. The null hypothesis (H0) was accepted, and the alternative hypothesis (Ha) was rejected since the significant F-test value was 0.178 > 0.05, and the T-test value was 0.692 > 0.05, indicating no significant difference in the average scores between experimental classes I and II. PBL students demonstrated better performance in answering mathematical problems compared to those in the direct learning group. Experimental class 1 achieved a mastery level of 84%, while experimental class 2 achieved a mastery level of 64%. PBL learners exhibited higher self-efficacy compared to those learning through direct instruction. Hypothesis testing indicated that students in experimental class 1 had stronger confidence in mathematical problem-solving compared to students in experimental class 2. The problem-based learning (PBL) methodology did not have a significant impact on students' mathematical problem-solving abilities. Hypothesis testing using interaction analysis yielded a significance value of 0.730 > 0.05. Both PBL and students' basic mathematical abilities influenced self-efficacy. Interaction analysis indicated a significance value of 0.000 < 0.05.Keywords: Problem based learning, early math skills, math solving, self efficacy]]>
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