Do students attend to representational illustrations of non-standard mathematical word problems, and, if so, how helpful are they?

Abstract

During the last two decades various researchers confronted upper elementary and lower secondary school pupils with word problems that were problematic from a realistic modelling point of view (so-called P-items), and found that pupils in general did not use their everyday knowledge to solve such P-items. Several attempts were undertaken to encourage learners to use their everyday knowledge more when solving such problems, e.g., by presenting the P-items together with representational illustrations that represent the problematic situation described in the problem. These illustrations were expected to help learners to mentally imagine the situation and consequently solve the items more realistically. However, no effect of the illustrations was found. In this article we build further on the use of representational illustrations. We report two related experiments with higher education students that investigated whether and how illustrations that represent the problematic situation described in a P-item help to imagine the problem situation and thereby solve the problem more realistically. In Experiment 1 we measured students’ eye movements when solving P-items that were accompanied by representational illustrations, to analyse whether the illustrations are processed at all. In Experiment 2 we manipulated the presentation of the illustrations so students could not but look at them, before the word problem appeared. We found that students scarcely looked at the representational illustrations (Experiment 1) and when they did, there was no effect of the illustrations on the realistic nature of their solutions (Experiment 2). Possible explanations for these findings are discussed.