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Assessing conceptual knowledge through solving arithmetic word problems

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Abstract

We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to solve one isomorphic word problem allowing two solving strategies. Results from experiment 1 showed that semantic context promoted a one-sided perspective, constraining the strategies used. The second experiment questioned if the strategy choices by students reflected a lack of procedural knowledge or difficulty in conceptual knowledge. Students solved several problems with the explicit task of proposing two strategies. Results showed that students struggled to identify the conceptual structure of the problems: they changed their strategy depending on semantic contexts, and did not succeed in adopting two encodings for the same problem. This lack of flexibility does not reflect weak procedural knowledge but difficulties in conceptual knowledge. Once conceptual knowledge is characterized as the ability to get over dependence on semantic context, using word problems as assessment tools for conceptual development opens up educational perspectives.

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Notes

  1. F-Nb/S-Price problems is an abbreviation for Factor–Number-of-elements/Summands–Price problems. This type of abbreviation will be used for each problem.

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Acknowledgments

We thank all students and teachers for their participation. We are also grateful to the experimenter Vincent Tambourin and the pedagogical advisor Arbya Eichi.

Funding

This research was supported in part by a National Research Agency Grant ANR-06-APPR-015 and in part by a grant from France’s “Programme d’Investissements d’Avenir” (ANRU/DSDP/D14-2780).

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Authors and Affiliations

  1. University of Geneva, IDEA Lab, 40 Bd du Pont-d’Arve, 1205, Geneva, Switzerland

    Calliste Scheibling-Sève & Emmanuel Sander

  2. Foundation La main à la pâte, 43 rue de Rennes, 75006, Paris, France

    Elena Pasquinelli

  3. Institut Jean Nicod, ENS, 29 rue d’Ulm, 75005, Paris, France

    Elena Pasquinelli

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  1. Calliste Scheibling-Sève
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  2. Elena Pasquinelli
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Correspondence to Calliste Scheibling-Sève.

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Scheibling-Sève, C., Pasquinelli, E. & Sander, E. Assessing conceptual knowledge through solving arithmetic word problems. Educ Stud Math 103, 293–311 (2020). https://doi.org/10.1007/s10649-020-09938-3

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