Students’ Misconceptions About Exponents

This study analyzes student misconceptions about exponents, an essential element of the middle school mathematics curriculum. Content analysis, a qualitative research methodology, was used. The study group was 150 students attending a public middle school in Kayseri, Turkey. A specially designed, formulated eight-question exponents conceptual test was administered as a data collection tool. The exponents test was revised with expert opinions to identify students’ misconceptions regarding exponents. The final version of the exponents conceptual test includes eight questions. In the analysis, the students’ answers were individually classified as correct, incorrect, or blanks, and the specific misconceptions they held, along with examples of correct and incorrect responses (as misconceptions), were analyzed. Students exhibit several misconceptions regarding exponents, including an inability to calculate exponents, a misunderstanding of the condition of zero exponent, and a failure to distinguish between different exponent cases, such as −a b versus (−a) b . They also struggle to comprehend negative exponents, fail to recognize that even exponents yield positive values, and confuse the relationships between a b and b a . These challenges reflect broader conceptual misunderstandings related to the operational properties of exponents.