A tale of four cities: reflections of master's students in mathematics on a visual word problem

A group of master’s students in mathematics was asked to reflect on a visual word problem. No one of the students identified the correct solution and defended instead an incorrect one. The results are explained by the difficulty of the problem itself (reflecting into the students’ overall difficulty in imagining its solution) as well as by the students’ tendency to overgeneralize. Interestingly, some of the students reach a contradictory statement (which they do not dismiss or acknowledge as such) as a consequence of the effort to accommodate their own mathematical reasoning with what they perceive to be a normative characterization of the problem coming from the lecturer. I conclude by discussing psycho-pedagogical considerations on imagination and intuition with related issues of university curriculum reform.