EXPLORING REVERSIBLE THINKING THROUGH THE LENS OF MATHEMATICAL DISPOSITION IN SECONDARY EDUCATION

Source abstract

As students are increasingly expected to face real-world problems requiring complex analysis, higher-order thinking skills such as reversible thinking have become indispensable. The importance of integrating numeracy with cognitive and affective student traits is rising, given the ongoing challenge to elevate the performance and confidence of learners in facing mathematical tasks. This study explores the relationship between students' mathematical disposition and their reversible thinking abilities in solving numeracy-based problems. Reversible thinking, including forward thinking and reverse thinking, is essential in mathematical problem-solving. The research employed a qualitative descriptive design with a case study approach, involving six tenth-grade students at States High Schools in Nganjuk City, East Java, Indonesia, categorized into high, medium, and low mathematical disposition groups. Data were collected using mathematical disposition questionnaires, numeracy-based tests, and semi-structured interviews. Findings reveal that students with high mathematical disposition exhibited strong reversible thinking, effectively solving problems through bidirectional reasoning. Those with moderate disposition showed partial application, especially in forward thinking but struggled with verification. Students with low disposition demonstrated limited understanding, lacked strategic planning, and failed to perform reflective checks. These results affirm the crucial role of mathematical disposition in fostering cognitive flexibility and problem-solving capabilities. This study underscores the need for instructional strategies that integrate affective and cognitive domains. Educators are encouraged to promote positive attitudes toward mathematics through problem-based learning, reflective activities, and encouragement of mathematical habits of mind. Enhancing mathematical disposition is pivotal in developing students' ability to engage with complex problems through reversible thinking.