Oehrtman, Michael C.


Novak, Jodie D.

Committee Member

Powers, Robert A.

Committee Member

Leth, Steven C.


Educational Mathematics


University of Northern Colorado

Type of Resources


Place of Publication

Greeley (Colo.)


University of Northern Colorado

Date Created





253 pages

Digital Origin

Born digital


Teacher education focuses on impacting teachers’ practice in ways aligned with current reform efforts. One particular emphasis in mathematics education is ensuring teachers, and subsequently students, are able to reason quantitatively. The purpose of this study was to document mathematics teachers’ models of quantitative reasoning as they participated in a Model-Eliciting Activity (MEA) grounded in their classroom practice. This MEA was designed and implemented in a master's course of 21 in-service mathematics teachers. The MEA asked teachers to construct and revise a quantitative reasoning task, along with supporting documents, intended for their middle and high school students. This MEA served as a method that simultaneously documented and developed teachers' models as they received feedback from the instructor, each other, undergraduate students, and in some cases teachers’ own students. The documents produced by the teachers, along with observations and interview data, were analyzed using a models and modeling perspective to determine how teachers' models of quantitative reasoning developed through the MEA. Findings from this study detail how teachers’ models of quantitative reasoning were not fully communicated in terms of defining quantitative reasoning in settings not connected to their classroom. As teachers went through the course and the MEA iterations, they began grappling with quantities and quantitative relationships as aspects of quantitative reasoning. Teachers’ attention to these aspects better positioned these teachers to reason covariationally about the mathematical content in their documents, thus promoting deep conceptual understanding of functions and more advanced mathematical topics. The development of these teachers’ models, along with the MEA itself, extends prior work regarding how teacher MEAs can document teachers' models within teacher education efforts. This study also identifies generalizable methods for understanding and promoting the productive development of mathematics teacher thinking about quantitative reasoning through this teacher MEA.

Degree type


Degree Name




Local Identifiers


Rights Statement

Copyright is held by author.