Analysis of Misconceptions and Errors Regarding Exponential and Radical Expressions Through the Theory of Reducing Abstraction

Investigating the reasons for misconceptions and errors is essential and important for making improvements in mathematics teaching. The idea of reducing abstraction, utilized as the framework for this research, can essentially be based on students' tendency to work with a lower abstraction level than the concepts they encounter in the course or what experts (mathematicians, teachers, etc.) expect from them. Since the process of reducing abstraction often occurs unconsciously, it can lead to misconceptions and errors. Exponential and radical expressions, which students first encounter in secondary school, are significant topics in mathematics, offering ease of representation and various calculations in many fields of basic sciences and engineering. Research on exponential and radical expressions, perceived by secondary and high school students as a collection of unnecessary formulas unrelated to daily life and difficult to understand, has revealed various misconceptions and errors. In this study, through the theory of reducing abstraction, the possible reasons for the misconceptions and errors revealed by research will be interpreted from an alternative viewpoint. Thus, a new perspective on student approaches regarding these subjects will be provided to teachers and mathematics educators.