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New approaches for two-variable inequality graphs utilizing the Cartesian Connection and the APOS theory

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Abstract

This study utilizes the Cartesian Connection and the action, process, object, and schema (APOS) theory to investigate how preservice mathematics teachers constructed and justified graphs of two-variable inequalities. The analysis shows that most teachers were not equipped with the skills and knowledge that were prerequisites for action, process, and object conceptions of two-variable inequality graphs. Many teachers used informal rules, rather than mathematical ideas such as the Cartesian Connection, to construct and/or justify inequality graphs. They also perceived inequality graphs as shapes rather than as representations based on the meaning of inequalities. I present a genetic decomposition for inequality graphs, through the concepts of variable and of parameter, as well as tasks associated with the genetic decomposition. I call for more studies on inequalities, including those relating to the implementation of the suggested genetic decomposition and tasks.

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Funding

This work was partially supported by a grant from the Spencer Foundation (Grant No. 201400165). The opinions expressed in the paper are those of the author and not those of the Foundation.

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  1. Department of Mathematics, University of West Georgia, Carrollton, GA, 30118, USA

    Kyunghee Moon

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  1. Kyunghee Moon
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Correspondence to Kyunghee Moon.

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Moon, K. New approaches for two-variable inequality graphs utilizing the Cartesian Connection and the APOS theory. Educ Stud Math 104, 351–367 (2020). https://doi.org/10.1007/s10649-020-09956-1

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