Abstract
This study examines how a large language model (LLM) can support lower secondary mathematics education, not by measuring performance, but by analysing how complete and didactically useful its solution processes are. The focus is on whether the model explicitly verifies results, which is an important but often neglected phase of mathematical problem solving. Two exploratory experiments were conducted with Gemini 2.5 Pro using 24 lower secondary mathematics tasks presented in Czech. In Experiment 1, the model solved all tasks in a baseline condition and then again using a structured prompt inspired by Pólya’s four phases of problem solving. In Experiment 2, the model was asked to simulate solution attempts of three contrasting student profiles. The results show that verification is a fragile step. In the baseline condition, the model often produced correct answers but did not check them. When guided by the structured prompt, verification appeared in every task. In student simulation, the model produced plausible mistakes and omissions in routine tasks, but often became unrealistically advanced in non-routine and construction problems, reducing profile fidelity. Overall, LLM outputs can support a priori didactic analysis, but they require careful interpretation, especially when used to simulate student thinking in demanding tasks.
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