Graduation Year

2025

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Curriculum, Instruction, and Learning

Major Professor

Sarah van Ingen Lauer, Ph.D.

Committee Member

Catherine Beneteau, Ph.D.

Committee Member

Robert Dedrick, Ph.D.

Committee Member

Eugenia Vomvoridi, Ph.D.

Keywords

college, high quality mathematics instruction, instructors, mathematics, undergraduate mathematics education

Abstract

Many undergraduate students struggle to learn college level mathematics. This may be because they have not developed their mathematical processes. Mathematical processes are the habits of mind of successful mathematicians and are how one learns and subsequently applies mathematics content. Five categories of mathematical processes are problem solving, reasoning and proof, communication, connections, and representation.

Students need opportunities to develop their mathematical processes. This is the foundation of high quality mathematics instruction. Many instructors, however, lack practical knowledge on how to enact a pedagogy that provides students with opportunities to engage in mathematical processes.

The purpose of this study was to develop an instrument that provides undergraduate mathematics instructors with the practical knowledge of how to enact a pedagogy that provides students with opportunities to engage in mathematical processes. This was accomplished by conducting steps to develop and initially validate the Increasing Mathematical Processes: Opportunities for Vital Engagement (IMPrOVE) instrument. The vision of high quality mathematics instruction shaped the framework of how to teach mathematics for understanding and, thus, guided the development of the instrument items. The instrument development and initial validation was organized into three phases—initial development in Phase One, an expert panel and cognitive interviews in Phase Two, and a pretest in Phase Three.

Across all three phases, the findings provided validity evidence based on test content, response processes, and relations to other variables. The findings supported the claim that the instrument could be used to measure and improve instructors’ attention to mathematical processes. Implications for mathematics teachers include using the instrument as a professional development tool to develop equitable and high quality mathematics instruction.

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