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Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties

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A Correction to this article was published on 10 November 2020

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Abstract

We present a study that explores Kindergarten and first-grade students’ understandings and representations of arithmetic properties. The 16 students participated in a classroom teaching experiment designed to explore children’s algebraic understandings, including their understandings and symbolic representations of three arithmetic properties: additive identity, additive inverse, and commutativity. We characterized students’ understandings in terms of Skemp’s framework of instrumental (rules without reason) and relational (knowing what to do and why) understandings. Following Vergnaud, we analyzed the types of additive relationships (transformation, comparison, or combination) and representations used by students. Our findings show that students’ understandings developed in sophistication over time. We observed the least sophisticated understandings for the commutative property, particularly among Kindergarten students who exhibited instrumental understandings even after instruction.

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Acknowledgements

This work has been developed within the project with reference EDU2016-75771-P, financed by the State Research Agency (SRA) from Spain, and European Regional Development Fund (ERDF) and the grant “Jose Castillejo” funded by the Spanish Ministry of Economy and Competitiveness. This research study was supported in part by the National Science Foundation under Grant No. DRL-1415509. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. University of Granada, Campus de Cartuja s/n, 18071, Granada, Spain

    Rafael Ramirez Uclés

  2. Department of Education, Tufts University, 12 Upper Campus Rd., Paige Hall, Medford, MA, 02155, USA

    Bárbara M. Brizuela

  3. TERC, Inc. I Because Math and Science Build Futures, 2067 Massachusetts Avenue, Cambridge, MA, 02140, USA

    Maria Blanton

  4. Project LEAP https://www.leap.terc.edu

    Maria Blanton

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  1. Rafael Ramirez Uclés
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  2. Bárbara M. Brizuela
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Correspondence to Rafael Ramirez Uclés.

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The original online version of this article was revised: typo in author name Rafael Ramírez Uclés has been corrected.

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Ramirez Uclés, R., Brizuela, B.M. & Blanton, M. Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties. Early Childhood Educ J 50, 345–356 (2022). https://doi.org/10.1007/s10643-020-01123-8

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