Reversible thinking in solving mathematics problems in terms of cognitive style

Background: Reversible thinking, the ability to think bidirectionally, is a crucial component of mathematical problem-solving. Differences in cognitive styles, particularly field-dependent and field-independent characteristics, play a significant role in students' reversible thinking, necessitating a deeper exploration of these relationships.Aim: This study aims to describe students' reversible thinking processes in solving mathematical problems based on their cognitive styles, focusing on field-dependent and field-independent traits.Method: A qualitative descriptive approach was applied to 32 eighth-grade students from a junior high school in Malang City, Indonesia. Data were collected using the Group Embedded Figures Test (GEFT), a reversible thinking test, and semi-structured interviews. Students were categorized into field-dependent and field-independent groups using GEFT before undertaking a reversible thinking test. Semi-structured interviews were conducted to gain deeper insights into their problem-solving approaches.Results: The findings indicate that students with field-independent cognitive styles exhibit better performance in the aspects of negation and reciprocity. They carefully apply problem-solving strategies, consistently reverting to initial values after achieving correct solutions. Conversely, students with field-dependent cognitive styles are more prone to errors, particularly in changing operation signs and applying the concept of reciprocal equivalence.Conclusion: This study highlights significant differences in reversible thinking between students with field-dependent and field-independent cognitive styles. The results suggest the need for tailored teaching methods to enhance reversible thinking based on cognitive styles. Further research is recommended to explore barriers and additional factors influencing reversible thinking.