The Impact of Illustrations and Warnings on Solving Mathematical Word Problems Realistically

Abstract

The present research investigated whether an illustration and/or a warning could help students to (a) build a situational model of the problem situation and (b) solve problematic word problems (P-items) that require realistic thinking more realistically. In 2 similar studies conducted in Turkey and Belgium, the authors presented 10- to 11-year-old children with several P-items. These problems were accompanied with an illustration that depicted the problem situation and/or a warning that alerted that some items may be nonstandard. Contrary to the authors’ expectation, findings from both studies showed that neither the illustration nor the warning, or even the combination of both manipulations, had a positive impact on the number of realistic reactions.

Keywords:

• mathematics education
• problem solving
• elementary school
• reasoning
• critical thinking

Acknowledgments

Emre Ev Cimen is now affiliated with Eskişir Osmangazi University in Turkey.

The authors thank Tugce Tosun for the illustrations that were used in this research. They also thank Kamil Beki, Yaşar Şişman, Hüsamettin Oztütüncü, Annemie Van Der Smissen, and Liesbeth Velghe for their help in the collection and analysis of the data.

This study was funded by the GOA grant 2012/010 “Number sense: Analysis and improvement” from the Research Fund KU Leuven, Belgium.

Notes

Elia and Philippou's (2004) categorization is based on, but somewhat different from, the categorization of Carney and Levin (2002), who distinguished five types of pictures in relation to text processing: decorational, representational, organizational, interpretational, and transformational pictures. Elia and Philippou (2004) adopted the first three categories, linked them to mathematical problem solving, and added the category informational pictures instead of the categories interpretational and transformational pictures in Carney and Levin's (2002) categorization.

In the original study of Verschaffel et al. (1994), the items S10 and P10 were accompanied with a drawing of, respectively, a cylindrical and a cone-shaped flask. Since the problem text did not say anything about the shape of the flask, these pictures were—in terms of Elia and Philippou's (2004) classification—informational. With a view to stick to the design of Verschaffel et al.'s (1994) original study, in the present studies we removed these informational pictures and rephrased the original text slightly so that it contained the essential information about the shape of the flask.

Whether the increase in extraneous cognitive load will actually lead to a decrease in performance will depend on the total load (the sum of extraneous, intrinsic, and germane load) on working memory (Sweller, 2005).