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Constructing a system of covariational relationships: two contrasting cases

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Abstract

Although there is much research exploring students’ covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute across different objects, each covary with respect to a third quantity and in relation to each other. We first describe relevant theoretical constructs, including reasoning covariationally to construct relationships between quantities and reasoning covariationally to compare quantities. We then present a conceptual analysis entailing three interrelated activities we conjectured could support students in reasoning covariationally to conceive of a system of covariational relationships and represent the system graphically. We provide results from two teaching experiments with four middle school students engaging in tasks designed with our conceptual analysis in mind. We highlight two different ways students reasoned covariationally compatible with our conceptual analysis. We discuss the implications of our results and provide areas for future research.

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Notes

  1. We note that this construct is distinct from but related to a system of equations. We discuss some similarities and differences in greater detail in Sect. 4.

  2. All demographic information is from parental surveys.

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Funding

This material is based upon work supported by the Spencer Foundation under Grant No. 201900012.

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Authors and Affiliations

  1. School of Education, University of Delaware, Willard Hall, Newark, DE, 19716, USA

    Teo Paoletti & Allison L. Gantt

  2. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Madhavi Vishnubhotla

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  1. Teo Paoletti
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Correspondence to Teo Paoletti.

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Paoletti, T., Gantt, A. & Vishnubhotla, M. Constructing a system of covariational relationships: two contrasting cases. Educ Stud Math 110, 413–433 (2022). https://doi.org/10.1007/s10649-021-10134-0

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