Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics

First Advisor

McKenzie A. Clements

Second Advisor

Nerida F. Ellerton


Thirty-two seventh-grade students attending a public middle school in a rural district in a midwestern state of the United States of America participated in a mixed-method intervention study aimed at enhancing student understandings of the algebraic concept of a variable, especially in relation to structure and modeling. Participating students were randomly allocated to two class groups, with one class initially being taught by Mr. X and the other by Mr. Y, who had both participated in professional development sessions led by two senior mathematics educators. Mr. X initially led one of the class groups in seven sessions on algebraic structures and Mr. Y led the other class group in seven sessions on modeling using algebra. Then, halfway through the intervention, the class groups swapped, with the teachers repeating the workshops with their new classes. Pre-teaching, mid-intervention, post-teaching, and retention assessment of learning occurred over a period of 24 weeks, with data gathered from pencil-and-paper tests and from 56 one-to-one interviews at various stages of the study. The theoretical bases for the study derived from the writings of two main scholars—first, the semiotic theory of Charles Sanders Peirce; and second, the theory of apperception put forward by Johann Friedrich Herbart. Six research questions were identified, and answered after all data had been collected and analyzed. Most of the participating students showed large gains in their understandings of algebraic structure and modeling, effect sizes of the intervention were large, and concept images of a variable were substantially modified.

KEYWORDS: Algebra education, Charles Sanders Peirce, Common core algebra, Concept image, Johann Friedrich Herbart, Modeling in middle-school mathematics


Imported from ProQuest Kanbir_ilstu_0092E_10787.pdf


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