In this paper a brief survey is initially undertaken about the usual focuses of studies in the field of mathematical problem solving. It is claimed that more has to be considered in this task. By conceiving that human being produces 'models' or 'metaphors' in the resolution of mathematical verbal problems imbedded in real contexts, it is, firstly, pointed out the need for understanding the meaning of 'mental model' as a cognitive structure where meanings related to the 'parts' of a 'whole' are structurally interconnected and, secondly, the cognitive complexity involved in the resolution of a problematic situation which can be idealised within a combinatorial 'mental model' or combinatorial 'metaphor', is explored. Some ways of solutions are exhibited showing the problem 'pitfalls' as well as some aspects of the problem solver's culture and subjectivity as three elements which seem to interfere in the production of a successful 'mental model'. Suggestions for other studies are presented.
analogy; idealisation; perceptual field; observacional field; combination; arrangement