A structural categorization of verbal problems with missing, surplus or contradictory data

Verbal arithmetical problems with missing, or surplus, or contradictory data (called shortly MSCD problems) are considered as a possible means of teaching mathematics in the primary school. The problems are considered here in the logico-mathematical setup, that is, the solvers are told that they can use only the data and the information given in the problem formulation. The paper consists of three parts. The first part is concerned with a categorization of MSCD problems while the two other parts are reports on two independent, exploratory studies. In one of them, subjects were interviewed individually and given the same set of MSCD problems. In the second, MSCD problems were used during regular classroom lessons and various observations were gathered.