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

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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.

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Notes

  1. Previous research has shown that also higher education students tend to exclude realistic considerations when solving P-items, even though at some smaller rates (Inoue 2005; Verschaffel et al. 1997). So we expected to find similar findings with higher education students as with upper elementary school pupils in our previous studies.

  2. It must be noted that this warning was of a different nature than the one used in the study of Dewolf et al. (2014) and in other previous studies with P-items (Verschaffel et al. 2000). In those studies learners received a general alert that the test could involve some non-standard word problems that may require a different kind of response, whereas in the present experiment the warning aimed at convincing participants of the usefulness of the accompanying illustrations for solving the word problems.

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Acknowledgments

This research was funded by grant GOA 2012/010 “Number sense: analysis and improvement” from the Research Fund KU Leuven, Belgium. Frouke Hermens was supported by a postdoctoral research grant from the Research Fund Flanders (FWO).

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Correspondence to Tinne Dewolf.

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Dewolf, T., Van Dooren, W., Hermens, F. et al. Do students attend to representational illustrations of non-standard mathematical word problems, and, if so, how helpful are they?. Instr Sci 43, 147–171 (2015). https://doi.org/10.1007/s11251-014-9332-7

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  • DOI: https://doi.org/10.1007/s11251-014-9332-7

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