Problem-Based Learning within UbD Framework to Enhance Mathematical Conceptual Understanding of Circle Equation - Khikmatus Shahrin Maghfiroh; Indhiadma Parnata; Alifiani Alifiani (Universitas Sembilanbelas November Kolaka, 2026)
This study aims to explore and describe the implementation of PBL within the Understanding by Design (UbD) framework to enhance students' mathematical conceptual understanding of the circle equation. This research employed a mixed-methods approach with a sequential explanatory design. The subjects were 30 eleventh-grade students at SMAN 4 Malang. Quantitative data were collected through pre-test and post-test, while qualitative data were gathered through questionnaires, observations, interviews, and documentation. The results showed a significant improvement in students' conceptual understanding, with the mean score increasing from 6.06 (pre-test) to 8.21 (post-test). The paired sample t-test revealed a statistically significant difference with a large effect size (Cohen's d = 1.131). Questionnaire results indicated that students responded positively to the implementation, particularly appreciating the clarity of learning objectives, the alignment between assessments and instruction, the use of contextual problems, and the support of visual media and collaborative activities. This study contributes a validated instructional design that mathematics teachers can adopt to improve the quality of mathematics instruction at the senior high school level.