Middle School Students and Generative AI Solving Exponent Problems: A Comparative Analysis of Written Solutions and Solution Reliability

Abstract This study compares the independent written solutions produced by 22 students aged 12–13 for 10 exponent problems with the first responses generated by ChatGPT, Claude, Gemini, and Grok for the same problems. Using a comparative case study design, the data were analyzed inductively in line with Braun and Clarke’s (2006) six-phase thematic analysis approach. The solutions were examined in terms of problem representation and mathematization, strategy selection, mathematical execution, reasoning, justification, error patterns, and solution reliability. The findings showed that students’ solutions were generally brief and symbolic, with intermediate relationships and justifications remaining implicit in many cases. Generative AI outputs made givens, intermediate steps, and justifications more explicit and more clearly sequenced. Student errors were concentrated primarily in procedural execution, exponent rules, decimal decomposition, and relationships between negative exponents and signs. Generative AI errors occurred particularly in tasks requiring interpretation of visual structures and mathematization of context. In some student and AI solutions, a process error co-occurred with a correct final answer, indicating that answer correctness alone does not establish solution reliability. Under the tasks, model versions, and first-response protocol examined in this study, no coded mathematical error was identified in the ChatGPT outputs. Errors were observed in specific visual and contextual tasks in the outputs of Claude, Gemini, and Grok. The findings indicate that generative AI solutions should be treated not as ready-made correct answers in mathematics education, but as digital mathematical products that require critical validation in terms of representation, strategy, execution, justification, and checking.