Recent studies show that English learning students are a growing population within the United States school system. Language barriers have been shown to negatively influence reading scores as well as math scores, and math scores are a predictor of future academic success in many subject areas. This qualitative action research study demonstrates…

The purpose of this study was to create an educative guidebook for teachers based on the principles of Cognitively Guided Instruction (CGI), a constructivist approach to teaching mathematics through contextual word problems. The guidebook is designed to be used as a First- Grade mathematics supplemental curriculum resource with complete, daily…

Research has shown that computational thinking and kindergarten mathematics instruction can be integrated; however, evidence of how specific mathematical knowledge relates to computational thinking remains scarce. Additionally, we do not know if and how children's mathematical knowledge co-occurs with computational thinking and how these…

Math achievement is an important predictor of progression to later science, technology, engineering, and math (STEM) education and careers. However, attitudinal factors also play a role, and interventions attempting to improve math attitudes may be important for increasing the number of STEM-aspiring students. To design effective interventions, it…

Many students enter into higher education institutions to pursue degrees in STEM fields with varying levels of academic preparedness, and many students will never finish a college degree. To address academic underpreparedness, many institutions have developed remedial coursework to increase student persistence and graduation rates with varying…

Although everybody learns at their own pace, the traditional, standardized education system remains prevalent. Unfortunately, this traditional system does not meet all learner needs and results in low academic achievement as demonstrated by state and national standardized tests (Netcoh, 2017; Pennsylvania Department of Education, 2019c; Schwahn…

The purpose of this qualitative interpretive study was to understand the ways teachers were influenced in their curricular and instructional decision-making processes in a freshman level mathematics class. Understanding what influences teachers' decision-making processes, and how (the ways) these processes were influenced, may lead to improved…

One of the most predominant measures of a community's appeal is the high school graduation rate. National "best places to live" ratings utilize educational statistics to rank the quality of life in a community (Morse & Brooks, 2020). Additionally, an individual's future prospects depend on a high school credential (HSC) as the…

This theoretical, methodological, and empirical networking study investigated the potential of inferentialism to contribute to the study of meaning and collective argumentation in mathematics. I carefully attended to my worldview and explicated my philosophical process for identifying inferentialism as my theory of choice. I then drew on Prediger…

For students to be successful in future mathematics classes, mathematics teachers must be able to help students decipher content in Algebra I, the foundation of higher mathematics. Research on vocabulary in the math classroom shows there are multiple ways to represent vocabulary and reading comprehension. The research question, which focused on…

In this work, we delve into geometric analysis, particularly examining the interplay between lower bounds on Ricci curvature and specific functionals. Our exploration begins with an investigation into the implications of Yamabe invariants for asymptotically Poincare-Einstein manifolds and their conformal boundaries under conditions of…

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…

Measurement invariance is crucial for making valid comparisons across different groups (Kline, 2016; Vandenberg, 2002). To address the challenges associated with invariance testing such as large sample size requirements, the complexity of the model, etc., applied researchers have incorporated parcels. Parcels have been shown to alleviate skewness,…

This research advocates for content integration and literacy-based practices in the world of reading and mathematics education, as well as the connection to outside sources that can either positively or negatively impact learning. More importantly, this research explored the connection to literacy and mathematics instruction as it pertains to…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…