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To add or to multiply in open problems? Unraveling children’s relational preference using a mixed-method approach

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Abstract

Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children’s preference for additive or multiplicative relations has been shown to contribute to those errors. The present research, using a mixed-method approach, investigated the nature of upper primary school children’s relational preference by empirically examining characteristics of intuitions that had been postulated previously. After administering a pre-test, selected children who preferred additive or multiplicative relations further participated in one of two studies using open problems for which both types of relations were appropriate: either a reaction time study (n = 110) in which children’s acceptance behavior and reaction times were measured or a semi-structured individual interview study (n = 18) in which their answers, verbalizations, and conviction scores were collected. Results of both studies revealed that relational preference was perseverant and exerted a coercive effect on children’s reasoning: Children mostly considered only the preferential type of relation as an appropriate answer in open problems and rejected alternative answers. Furthermore, relational preference appeared as immediate, self-evident, and certain: Children rejected the non-preferential answer more quickly than an irrelevant distractor of comparable size, experienced difficulties in justifying why they gave their preferential answer, and were very convinced of this preferential answer. While this characterization held for both relational preferences, it was especially prominent for the multiplicative one. These results not only have implications for research on and educational practice in multiplicative and additive reasoning but also for the measurement of relational preference.

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Notes

  1. At the end of the pre-test and the interview, some items containing non-integer ratios were also included, but these are not considered in the present paper. We focus on the items that are similar to these administered in study 1.

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Acknowledgments

We would like to thank Linde Zutterman and Laura Saitta for assisting in data collection.

Funding

This research was partially supported by the C16/16/001 grant “Early development and stimulation of core mathematical competencies” by the Research Council of the KU Leuven and by a postdoctoral fellowship (PDM/19/065) of the KU Leuven.

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  1. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, box 3773, B-3000, Leuven, Belgium

    Tine Degrande, Lieven Verschaffel & Wim Van Dooren

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  1. Tine Degrande
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  2. Lieven Verschaffel
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Correspondence to Tine Degrande.

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Degrande, T., Verschaffel, L. & Van Dooren, W. To add or to multiply in open problems? Unraveling children’s relational preference using a mixed-method approach. Educ Stud Math 104, 405–430 (2020). https://doi.org/10.1007/s10649-020-09966-z

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