Methods of teaching differential equations (DE) have long focused on rote analytic solution methods that align poorly with more industry-relevant numerical and computational methods. Engineering and mathematics educators agree that there is a need to shape DE curricula to reflect the mathematical practices of the disciplines whose students take…

In many control systems changes in the dynamics occur unexpectedly or are applied by a controller as needed. The time at which a controller implements changes is not necessarily known a priori. For example, many manufacturing systems and flight operations have complicated control systems, and changes in the control systems may be automatically…

This qualitative narrative study examined high achieving college Black STEM students who enrolled in precalculus, calculus I and II, differential equations, linear algebra, and applied linear algebra courses at Rhowlin Bonsu University (RBU). RBU is located in the Midwestern region of the United States. This investigation used a semi-structured…

The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship…

This dissertation will look at large scale collaboration through the lens of online communities to answer questions about what makes a collaboration persist. Results address how collaborations attract contributions, behaviors that could give rise to patterns seen in the data, and the properties of collaborations that drive those behaviors. It is…

The goal of this 3-article dissertation was to examine the differential effects of varying campus experiences on student "thriving," drawing from Schreiner's (2010) conceptual framework. The articles are quantitative studies, all of which conducted structural equation modeling to identify differential pathways to thriving for students of…

The developmental sequence of mathematics courses in most 2-year and 4-year colleges is designed to prepare students to succeed in college-level math courses. That is, students must complete this sequence in order to progress to courses such as statistics, college algebra, precalculus, calculus, and differential equations. Research on the…

Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics…

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…

Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…

Piecewise latent growth modeling (PLGM) is a class of longitudinal models using a structural equation modeling framework to describe stage-like, discontinuous change of individuals over time. PLGM breaks the overall time window into non-overlapped segments where separate functions can be fitted to represent differential growth patterns for each…

Research on the impacts of mindfulness trainings (MTs) on teachers' psychological health and wellbeing suggests that MTs may be especially well-suited to preparing teachers for the unique demands of the profession (Iancu et al., 2017; Klingbeil & Renshaw, 2018). However, few studies have investigated whether different teachers benefit in…

Increasing higher education enrollment and decreasing state and national funding has created a fiscal problem for higher education institutions in the United States. Differential tuition charged to a variety of subsets of students is increasingly used to close funding gaps. This research uses demand analysis and elasticities to determine…

The predictive utility of cognitive abilities on reading, writing, and mathematics achievement domains helps inform high-stakes decision making, such as learning disabilities. An examination of differences in specific groups may increase understanding of obtained scores on cognitive ability and academic achievement standardized tests. One…

School finance scholars have called for the alignment of accountability policies with state finance formulae to allocate resources toward student learning goals (Adams, 2008; Ryan, 2008; Superfine, 2009; Verstegen, 2002). With the presence of accountability policies that focus on improving students' academic achievement, state finance systems must…