Analyzing Role of Abstract Thinking: Teaching Solvable and Nilpotent Groups in Algebra

Abstract

This study explored the role of abstract thinking in teaching solvable and nilpotent groups in abstract algebra. We used an ethnographic approach, preparing a set of questionnaires and working with three university-level abstract algebra teachers to gather detailed insights. The main research objective was to explore the role of abstract thinking in understanding and teaching the concepts of solvable and nilpotent groups in algebra, and the research question was how abstract reasoning influences students’ conceptual clarity, problem-solving ability, and mathematical maturity in group theory. We used open-ended questionnaires to facilitate in-depth discussions about their pedagogical approaches, and we observed the classroom teaching of abstract algebra for finding challenges and successes in conveying concepts in solvable and nilpotent groups. The study maintained rigorous ethical considerations throughout data collection and analysis, ensuring participant confidentiality and informed consent. Findings highlighted the critical role of abstract thinking in enhancing comprehension and promoting a supportive learning environment, ultimately empowering students to navigate advanced algebraic structures confidently and creatively.