Penalaran Matematis Siswa Madrasah Aliyah dalam Menyelesaikan Soal Integrasi Matematika dan Ilmu Faraidh

Abstract

This research focuses on exploring the mathematical reasoning abilities of Madrasah Aliyah students in solving problems that integrate mathematical concepts with the Islamic science of faraidh (inheritance law), specifically within the topic of fractions. The study employs a qualitative approach with a case study design and was conducted among 11th-grade students enrolled in the Religious Program at MA Raudlatul Ulum Putri. Data collection techniques included written tests, semi-structured interviews, and classroom observations, focusing on three selected students who represented high, moderate, and low levels of mathematical ability. The analysis centers on several key indicators of mathematical reasoning: identifying problems, formulating hypotheses, presenting logical arguments, and drawing conclusions. The results show that most students fall into the moderate reasoning category, while a smaller number are categorized as high or low. Students in the high category demonstrate a strong capacity to approach problems systematically and accurately, combining mathematical logic with a proper understanding of Sharia-based inheritance rules. In contrast, students in the low category struggle with interpreting problem contexts and executing fraction calculations correctly, which indicates gaps in both conceptual understanding and application skills. These findings underscore the importance of contextual and integrative learning, particularly the combination of mathematics with Islamic values, to enhance deeper comprehension. By embedding religious relevance into mathematical instruction—especially through real-life contexts such as inheritance laws—educators can support the development of more meaningful reasoning abilities. The study suggests that integrating mathematics and Islamic teachings can significantly benefit student learning outcomes and foster stronger conceptual foundations.