Everyday Knowledge and Mathematical Modeling of School Word Problems

Abstract

Some years ago Greer (1993) and Vcrschaffel, De Corte and Lasure (1994) provided evidence that after several years of traditional mathematics instruction children have developed a tendency to reduce mathematical modeling to selecting the correct formal-arithmetic operation with the numbers given in the problem, without seriously taking into account their common-sense knowledge and realistic considerations about the problem context. This evidence was obtained by means of a series of especially designed word problems with problematic modeling assumptions from a realistic point of view, administered in the context of a mathematical lesson. After having summarized these two initial studies, we briefly review a series of replication studies executed in different countries showing the omnipresence of this tendency among pupils. Then two related but different lines of follow-up studies arc presented. While the first line of research investigated the effects of different forms of scaffolds added to the testing setting aimed at enhancing the mindfulness of students' approach when solving these problematic items, the second one looked at the effectiveness of attempts to increase the authenticity of the testing setting. After having discussed these empirical studies, the results are interpreted against the background of schooling in general, and the mathematics classroom in particular. The notion of 'the game of word problems' is introduced to refer to the 'hidden' rules and assumptions that need to be known and respected in order to make the game of word problems function efficiently. In this respect a study is reported which reveals that the strong tendency toward non-realistic mathematical modeling is found among (student-)teachers too. Afterwards two studies aimed at changing students' perceptions of word problem solving by taking a radical modeling perspective, are reported. The chapter ends with some theoretical, methodological and instructional implications of the work reviewed.