# The effects of using drawings in developing young children’s mathematical word problem solving: A design experiment with third-grade Hungarian students

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## Abstract

The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students’ knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (*N* = 106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen’s *d* proved to be 0.20 and 0.62. There were significant changes also in experimental group students’ beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade 3 (around age 9–10).

## Keywords

Word problem Visual representation Design experiment Elementary school mathematics## Notes

### Acknowledgments

This research was supported by a grant from the Hungarian Scientific Research Fund (OTKA 63360) awarded to Csaba Csíkos and by the MTA-SZTE Research Group on the Development of Competencies. Thanks are due to Gabriella Pataky for her help in the use of the Clark Drawing Test. We would also like to thank Paul Andrews, Andrea Kárpáti, Julianna Szendrei, Malcolm Swan and Lieven Verschaffel for their constructive comments on an earlier draft of this paper. Parts of the present study have been presented at a conference (Csíkos, Szitányi & Kelemen, 2009). Also, part of the data have been published in Hungarian in Magyar Pedagógia (Csíkos, Szitányi & Kelemen, 2010).

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