Cognitive Construction Through Problem Posing: The Transformation of Mathematical Problem-Solving Skills Among High School Students

Abstrak

Mathematical problem-solving ability is a fundamental competency in mathematics education; however, Indonesian students' achievement remains critically low, as evidenced by PISA 2022 rankings (70th out of 80 countries) and TIMSS 2019 results. This study examined the effectiveness of the problem posing learning model compared to direct instruction on eighth-grade students' mathematical problem-solving ability in circle geometry. A quasi-experimental design with a posttest-only control group was employed, as full randomization was not feasible in a formal school setting. The sample consisted of 56 students selected via purposive sampling from a Madrasah Tsanawiyah in Muna Regency, Southeast Sulawesi: 30 in the experimental class and 26 in the control class. Data were collected using validated essay-based tests aligned with Polya's problem-solving indicators (Cronbach's Alpha = 0.786). Data analysis employed the Kolmogorov–Smirnov normality test, Levene's homogeneity test, and independent sample t-test. The novelty of this study lies in testing problem posing within an Islamic school context in an Indonesian archipelagic region, specifically for circle geometry topics. Results showed the experimental class mean (58.25) was significantly higher than the control class (48.63), with a significance value of 0.002 < 0.05 and Cohen's d = 0.87 (large effect). These findings confirm that problem posing effectively fosters cognitive construction through pre-solution, within-solution, and post-solution posing stages, with important implications for mathematics teaching strategies in remote Indonesian regions.

Kata kunci

• circle geometry
• mathematical problem solving
• problem posing learning model
• quasi-experiment