Effectiveness Of CTL- And Problem-Based Learning Worksheets In Enhancing Mathematical Problem-Solving Ability Among Students Of Smk Negeri 1 Sei Suka On Systems Of Linear Equations

Abstract

This study evaluated the methodological coherence of Contextual Teaching and Learning and Problem-Based Learning worksheets designed to improve mathematical problem-solving ability in systems of linear equations. A non-equivalent control-group case-study design was modelled using 72 synthetic student records, with 36 records in an Office Management and Business Services condition and 36 in an Accounting and Institutional Finance condition. The six-unit worksheets incorporated vocational mathematical modelling scaffolding, progressive fading, model validation, and transfer/problem-posing activities. Five open-ended items were scored using four Polya indicators. Analysis of covariance adjusted posttest performance for pretest scores, while raw change, normalized gain, and robustness checks supported the main analysis. The adjusted posttest difference was 10.410 points (95% CI [5.947, 14.872]), F(1,69)=21.656, p<.001, partial eta-squared=.239, with adjusted d=1.097. Simulated reliability, content-validity, and fidelity evidence was also coherent. Because all key data were simulated and only one class/program was modelled per condition, the results did not establish causal effectiveness in real students