The purpose of this study was to examine the psychometric properties of the Precalculus Concept Assessment (PCA), a 25-item multiple-choice instrument designed to assess student reasoning abilities and understanding of foundational calculus concepts (Carlson et al., 2010). When this study was conducted, the extant research on the PCA and the PCA…

Functions are one of the most important topics in secondary school mathematics, especially for students who wish to take higher-level mathematics courses beginning with calculus. The prerequisites for Advanced Placement Calculus state that a thorough understanding of functions is needed for those who wish to succeed in the course and pass the AP…

This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet…

Historians of mathematics considered the nineteenth century to be the Golden Age of mathematics. During this time period many areas of mathematics, such as algebra and geometry, were being placed on rigorous foundations. Another area of mathematics which experienced fundamental change was analysis. The drive for rigor in calculus began in 1797…

A primary gateway to a career in engineering is the attainment of the bachelor of science degree in engineering. In contrast, a common barrier to becoming an engineer is failure to attain the degree. Those variables that are related to college graduation are often in place prior to college admission. The purpose of this study was to examine the…