Children's Reactions to Verbal Arithmetical Problems with Missing, Surplus or Contradictory Data.
Ewa Puchalska, Zbigniew Semadeni · for the learning of mathematics · 1987
l.L The aim of the paper A typical verbal arithmetical problem satisfies the following conditions: there is exactly one number providing the answer to the problem and this number can be computed by using the information supplied in the problem; moreover, no numerical data are superfluous (there maybe superfluous non-numerical information, e g colours or names). In this paper we consider problems that do not satisfy some of the above conditions, in particular, problems having either mi5sing data, or surplus data, or contradictory data. In what follows, problems of these three types will be called MSCD problems (for Missing, Surplus or Contradictory Data Problems) [I] A verbal problem may be considered either in a logic.omathematical setup or in an applied-mathematics setup In the former·, solvers can use only the infOrmation given in the text of the problem; in the latter, they may (or are even supposed to) find some data themselves For instance, suppose that a problem concerns Mary buying some items in a grocery. In the logico-mathematical setup, both Mary and the shop are typically unknown and there is no way of learning more about the situation, whereas in the appliedmathematics setup, Mary may be a girl from the solvers' class shopping in the nearby grocery and the solvers may go there and check prices, weights, etc Both setups should be the subject of regular teaching (because both kinds of reasoning are very impmtant). However they should not be confused (by teachers or educators) and the children should understand which setup is meant when they are given a task In this paper we restrict om attention to logico-mathematical setups only 1he aim of the present paper is an explmatmy investigation of how children react to MSCD problems. The topic has received little attention, particularly in the case of classroom instruction .. Our intent is to challenge some conclusions that may be drawn from previously-known results Problems with missing data, problems with surplus data, and problems with contradictory data, are logically different from each other Still, they have some common features. First, in order to explain such a problem successfully, the pupil has to read the text meaningfully and critically and not to jump into computations before analysing the arithmetical relations involved This feature is so significant that it justifies the joint investigation of children's reactions to problems of all three types