Educational Studies in Mathematics

, Volume 94, Issue 2, pp 117–137 | Cite as

Explicating mathematical concept and mathematicalconception as theoretical constructs for mathematics education research

  • Martin A. SimonEmail author


Mathematical understanding continues to be one of the major goals of mathematics education. However, what is meant by “mathematical understanding” is underspecified. How can we operationalize the idea of mathematical understanding in research? In this article, I propose particular specifications of the terms mathematical concept and mathematical conception so that they may serve as useful constructs for mathematics education research. I discuss the theoretical basis of the constructs, and I examine the usefulness of these constructs in research and instruction, challenges involved in their use, and ideas derived from our experience using them in research projects. Finally, I provide several examples of articulated mathematical concepts.


Mathematical concept Mathematical conception Mathematical understanding Mathematics learning Instructional goals 



This work is supported by the National Science Foundation under Grant No. DRL-1020154. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Teaching & LearningNew York UniversityNew YorkUSA

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