Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

As students with autism spectrum disorder (ASD) participate in the general education setting at greater rates, they are expected to meet rigorous grade-level academic standards. Students with ASD typically struggle with problem solving, higher-ordered thinking, and mathematical reasoning. When students enter middle school, mathematics becomes more…

The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing…

Previous research has individually assessed parallel analysis and minimum average partial for factor retention in exploratory factor analysis using ordinal variables. The current study is a comprehensive simulation study including the manipulation of eight conditions (type of correlation matrix, sample size, number of variables per factor, number…

In this dissertation, I explore ways to support secondary school students' meaningful understanding of quadratic functions. Specifically, I investigate how students co-developed representational fluency (RF) and functional thinking (FT), when they gained meaningful understanding of quadratic functions. I also characterize students' co-emergence of…

Evidence-based instructional strategies in mathematics provide critical support related to academic achievement for students with disabilities. Data from national achievement assessments suggest that students with disabilities' academic growth in mathematics stagnates at the secondary level. Given that the majority of previously researched…

This dissertation is composed of a study of estimation methods in classical and test theories and the elaboration and application of a cluster-robust variance estimator. Variance estimators derived from generalized estimating equations are known to be robust to most covariance structures and are therefore well suited for psychometric analysis of…

Many secondary students in the United States are struggling to find success in math creating a preparation gap in the U.S. STEM workforce. Based on national and international assessments, little improvement has been made over the past several decades in U.S. secondary students' knowledge and skills in higher-order math tasks like translating and…

The ways teachers understand mathematics that is useful for teaching, known as mathematical knowledge for teaching (MKT), has been a center of attention for the research and policy communities. A teacher's MKT has been shown to be a significant factor in predicting student outcomes and positively related to the quality of mathematics instructional…

Conductive ink from a printer allows for the fabrication of conductive material with tight tolerances without the cost and time of chemical etching. This paper explores the use of AGIC printable conductive ink on a paper substrate as design tool for antennas as well as classroom use in antenna education. The antenna designs satisfy the…

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…

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

The purpose of this study was to establish the reliability and validity of the construct map for students' conception of equivalence with special emphasis on investigating the impact of structure of equation on students' conception of equivalence. The study examined the role of structure of equations in identifying students' conception of…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

End-Of-Chapter (EOC) problems have been part of many physics education studies. Typically, only problems "localized" as relevant to a single chapter were used. This work examines how well this type of problem represents all EOC problems and whether EOC problems found in leading textbooks have changed over the past several decades. To…