Just Answering . . . or Thinking? Contrasting Pupils' Solutions and Classifications of Missing-Value Word Problems

摘要

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3 for which proportionality is an appropriate model, 3 implying an invariant additive relationship, and 3 for which the result is constant) and to solve a parallel version of this set of problems. Half of the children first found the solution and then did the classification task (SC-condition), while for the others the order was the opposite (CS-condition). On the word problem test, children often overused proportional methods, but those in the CS-condition performed better than those in the SC-condition, suggesting a positive impact of the classification task. On the classification task, most pupils took into account the underlying mathematical models, but they did not always distinguish proportional from non-proportional problems. Students in the SC-condition performed worse than those in the CS-condition, suggesting that solving the word problems first negatively affects later classifications.