Date of Award


Document Type


Degree Name

Doctor of Education (EdD)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Steven Greenstein

Committee Member

Monica Taylor

Committee Member

Teo Paoletti


CCSSM (2010) describes quantitative reasoning as expertise that mathematics educators should seek to develop in their students. Researchers must then understand how to develop covariational reasoning. The problem is that researchers draw from students’ dialogue as the data for understanding quantitative relationships. As a result, the researcher can only conceive the students’ reasoning. The objective of using the self-study research methodology is to examine and improve existing teaching practices. To improve my practice, I reflected upon the implementation of my algebra curriculum through a hermeneutics cycle of my personal history and living educational theory. The critical friend provoked through dialogues and narratives the reconceptualization of my smooth covariational reasoning from a “transformational perspective” to a “solving algebraic equations” perspective. This study showed that by creating images in motion, graphs, or algebraic representation, I recognized the importance of students’ cognitive development in the conceptual embodied and proceptual symbolic worlds. The results presented the transformation of my teaching practices by building new algebraic connections. By using these findings, researchers can gain additional understanding as to how they can transform their teaching practices.

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