Task variables in compare word problems
Treść / Zawartość
The paper is a report on the solutions of one-step additive and multiplicative compare problems, which were part of a larger test written in 2007 by 70 thousand 10-year-olds at the beginning of grade IV. A sample of 788 responses was analysed in detail and various types of students' difficulties were identified (the difficulty depended not only on the structure of the problem but also on many other factors).Tasks in which additive problems alternated multiplicative ones caused serious troubles; in particular, many students (some 10%) correctly solved the first problem and then erroneously used the same operation to the next one, not reading the text attentively, or (also some 10%) used the result of the first task as if it were the given number in the next one ("chain effect"). Thus, the impact of the order of tasks was considerable.Many solvers searched for key words and could not cope with problems which were formulated in inconsistent language or required inverting the relation (particularly in the case of multiplicative problems). Many students wrote an incorrect operation and a correct answer.The paper begins with a comprehensive discussion of task variables (context variables, structure variables and format variables) related to possible types of one-step additive and multiplicative compare problems, relevant to children's difficulties. In particular, it is shown why a problem of the type Joe has 8 marbles. Tom has 5 marbles more than Joe. How many marbles does Tom have?, which is regarded as an arithmetical one-step problem, is actually a multi-step problem if the number of mental operations is considered.