Teachers' critical thinking skills are essential for fostering the development of the same skills in their students. To demonstrate how teachers' ability to examine solutions critically can be developed and supported, we analyse a classroom activity performed by a group of pre-service secondary school mathematics teachers (N = 37) who were asked: (1) to solve a geometrical problem; and (2) to reflect upon different strategies that lead to contradictory solutions. The data demonstrate difficulties in students' ability to analyse possible mistakes and cope with mental dissonance when faced with contradiction.