Title: Get the picture? Are representational illustrations effective in helping pupils to solve mathematical word problems realistically?
Authors: Dewolf, Tinne; S0168955
Issue Date: 24-Oct-2014
Abstract: In this doctoral dissertation we started from the well-documented tendency of elementary school pupils to ignore everyday life knowledge when solving mathematical word problems that are problematic in the sense that considerations of everyday life should be taken into account to come to an appropriate reaction (named P-items in Verschaffel et al., 1994). Our aim was to investigate the effect of adding illustrations that represent the problem situation (representational illustrations) next to the P-items in the mathematics class in order to increase the number of pupilsÂ’ realistic reactions (RRs) to these items.In Study 1a, 1b, and 2, elementary school pupils (10 to 12 years old) received a paper-and-pencil test containing P-items together with such representational illustrations. All three studies showed that the illustrations were ineffective in increasing the number of RRs towards the P-items. Because of the absence of a positive effect in studies 1a, 1b and 2, two new studies, 3a and 3b, were set up, in which it was investigated whether the illustrations perhaps were ineffective because they were not looked at. First, an eye movement study was conducted with higher education students, which showed that the illustrations were hardly looked at. Second, also when experimentally forcing students to look at the illustration for five seconds before seeing the corresponding word problem no effect of the illustrations was found. Following these findings of Study 3a and 3b, a fourth study was set up in which two visual aids were added to the illustrations: 1) making the realistic modelling complexity more apparent in the illustration, and 2) highlighting this extra element in the illustration. However, no effect of the visual aids in the representational illustrations was found. Next, we did an interview study (Study 5) to investigate why there was no effect of the representational illustrations in all previous studies. In the interview 11 to 12 year old pupils had to solve a word problem together with a representational illustration from Study 4, and then were asked about looking or not looking at the illustration, about the helpfulness of the illustration, and to evaluate an illustration-based fictional realistic response. It was found that pupils reportedly did not look at the illustration because they were concentrating on the problem itself, and that most pupils thought the illustration was unhelpful. Concerning the illustration-based fictional response, only few pupils made a reference to the illustration. Few pupils thought that the illustration and word problem were not connected. In a last study, Study 6, which was more general in terms of aims and scope, the occurrence, function and nature of illustrations next to word problems was investigated in four mathematics textbooks in three different grades (2nd, 4th and 6th grade). The analysis showed that most problems are accompanied with illustrations, half of them being essential for finding the solution to the problem.Based on the findings of the studies, we concluded that illustrations are ineffective for increasing the number of RRs to P-items. We proposed several plausible factors. Following the when perspective (i.e., when the impact of the illustration in the process of mathematical modelling could have occurred), 1) pupils may simply not look at the illustrations, 2) may look but without building a mental model including the realistic modelling complexity, or 3) may look and activate the relevant real-world knowledge, but finally still opt for a non-realistic reaction (NR). Following the why perspective (i.e., why did the illustration not have the expected impact in the various phases of the solution process) some task-related factors such as the illustrations itself, the word problems itself, and the combination of the illustrations and word problems may have played a role, but also some subject-related factors such as pupilsÂ’ beliefs concerning realistic word problem solving in the mathematics class, and their (negative) beliefs about the helpfulness of illustrations next to word problems. At the end of this dissertation we discuss some theoretical and methodological considerations and provide some suggestions for future research and educational practice.
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Instructional Psychology and Technology

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