Towards understanding the error analysis thinking of prospective mathematics teachers

High school teachers often encounter incorrect solutions from students, especially when teaching combinatorics. This study investigates the ability of prospective mathematics teachers to assess the correctness of solutions to combinatorial problems and to falsify incorrect ones. 39 second-year prospective teachers participated in the experiment, analysing both correct and incorrect solutions to combinatorial tasks. They were asked not only to judge the correctness but also to identify the cause of procedural or conceptual errors. The results indicate that for incorrect solutions, 44.16% of the error identifications were accurate, and only 36.36% of cases could be successfully falsified. Furthermore, when evaluating correct solutions, 57.1% of the correct solutions were mistakenly judged as incorrect. Overall, 31 out of the 39 participants were unable to accurately determine the correctness of the solutions, despite their advanced mathematical background. These findings highlight the need to foster error-detection skills and thorough reasoning in teacher training programs.