Abstract
This article examines the application of problem-based learning (PBL) as a pedagogical strategy for developing problem-solving skills in mathematics among students of technical colleges. The relevance of the study stems from the persistent gap between students' procedural mastery of mathematical algorithms and their ability to apply mathematical reasoning to non-standard, practice-oriented tasks encountered in vocational training. The study was conducted with first- and second-year students of Bulokboshi District Technical College No. 1 across two academic groups, one taught through conventional explanation-and-practice methods and the other through structured problem-based learning sessions built around open-ended, profession-related mathematical problems. Diagnostic testing, structured observation, and comparative analysis of academic performance were used to evaluate changes in students' analytical reasoning, solution-strategy flexibility, and independent decision-making. The results demonstrate that students taught through problem-based learning showed measurably higher gains in problem-solving competence, deeper conceptual understanding, and greater willingness to attempt unfamiliar problem types compared to the control group. The article concludes with practical recommendations for technical college mathematics teachers on designing and sequencing problem-based tasks within limited instructional time.
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