This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

Humans excel at detecting patterns in information, abstracting rules, and making inferences. Underlying these skills is relational reasoning: the cognitive ability to identify and map abstract, generalizable relations between pieces of information. Though this powerful ability supports higher-order cognition, it can also be a processing bottleneck…

With math scores stagnating in the United States and achievement gaps widening between demographic groups, improving student outcomes is imperative. Previous studies have shown that using visual representations to teach math concepts has been shown to be an effective component of equitable elementary math teaching. This action research study…

Visual notetaking has gained prominence in education due to its benefits in capturing information effectively. However, there is limited research on the neural and cognitive mechanisms involved in this way of taking notes. Therefore, to fill this research gap, this within-subject experimental study aimed to use an electroencephalogram (EEG) to…

This study investigated how emotion could enhance the effectiveness of a digital training game in improving the cognitive skill of shifting. Participants were randomly assigned to either an emotionally-positive visual design of the game, featuring warm colors, round shapes, and high-intensity character expressions, or an emotionally-neutral…

This study examines the visual design processes and strategies used by graphic design experts and non-design college students when applying visual design principles to compose an infographic. The focus is on the visual design stage, often reported as challenging for adult and young students (e.g., Fragou & Papadopoulou, 2020; O'Mahony et al.,…

In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

Sparse information exists on how elementary teachers might use reflective journaling as a tool for professional development (PD) to enhance their teaching methods. The problem is that even though elementary teachers have access to a variety of PD opportunities, these opportunities are often insufficient for meeting individual teachers' needs to…

Personalized learning, which has the potential to raise student achievement, requires understanding the competencies of students. Visualizations can help provide this understanding. Jeon et al. (2021) presented a latent space model that creates interaction maps visualizing response patterns from item response data. My dissertation proposes…

Language is a unique skill used by humans to communicate thoughts and feelings. For most individuals, language is understood through different sensory modalities--for instance, hearing auditory words relies on audition, while perceiving visual speech via lipreading and reading written text both utilize the visual system. Although these different…

Higher learning institutions teaching gross anatomy are implementing 3D technology, such as the Anatomage Table, to supplement cadaveric dissection. However, the literature is scant about the effects of introducing 3D technologies on students' learning outcomes in the study of gross anatomy. The purpose of this quantitative study was to determine…

The completion of developmental community college (DCC) courses is a crucial step in community college education to reach the national goal of increasing college success. DCC students are a unique population who require specific strategies such as vocabulary retention (VR) to achieve academic success. Prior research on vocabulary has been limited…

This study examined video and screenshot microlesson formats as a technology professional development for enhancing educators' technology skills. As educators face increasing demands for technology proficiency in the twenty-first century classroom, this study was conducted to help address a need for further investigation into whether screenshot or…

The COVID-19 pandemic has increased the issues of teacher attrition. According to the U.S. Bureau of Labor and Statistics, from January to November 2021, there was a 40% increase in the quit levels of teachers within the state and local education agencies (John, 2022). While prior research has examined early-career teachers leaving the profession,…

Unified Modeling Language (UML) Class Diagramming is the commonly accepted mechanism used to describe relationships between software components. In addition, it is an essential educational tool that is used to convey the structure of software and the patterns of software design to students. Unfortunately, UML is a visual-only mechanism and…