We introduce the "Whitehead complex", a one-complex associated to a finite regular cover of the rose and show that it is connected if and only if the fundamental group of the associated cover is generated by its intersection with the set of elements in proper free factors of the fundamental group of the rose. The Whitehead complex admits…

This thesis identifies and explains the gaps in prior and current applications of representational competence construct in chemistry. Representational competence (RC) describes a set of skills that chemistry researchers Kozma and Russell observed experts demonstrate when engaging with disciplinary representations (Kozma & Russell, 1997; Kozma…

Integrating agent-based models (ABMs) has been a popular approach for teaching emergent science concepts. However, students continue to find it difficult to explain the emergent process of natural selection. This study adopted an ontological framework--the Pattern, Agents, Interactions, Relations, and Causality (PAIR-C)--to guide the design of…

Twenty nine students who had previously taken an undergraduate thermal physics course were interviewed about their basic knowledge about statistical mechanics at the undergraduate level. Of these 29, fourteen were undergraduate students, and fifteen were graduate students at varying stages of their career. This project aimed to identify and…

Knowledge about the interior density distribution of a planetary body can constrain geophysical processes and reveal information about the origin and evolution of the body. Properties of this interior distribution can be inferred by analyzing gravity acceleration data sampled by orbiting satellites. Usually, the gravity data is complemented with…

Resonance is a fundamental chemistry concept first introduced to students in General Chemistry I, reintroduced in Organic Chemistry I, and then utilized throughout other higher-level chemistry courses. A molecule or ion can be said to exhibit resonance when it can be represented by two or more chemical structures (i.e., Lewis structures) that…

In recent years, modern technologies have enabled the collection of exponentially larger quantities of data in the biomedical domain and elsewhere. In particular, the advent of single-cell genomics has allowed for the collection of datasets containing hundreds of thousands of cells measured in tens of thousands of dimensions. This rapid expansion…

The purpose of this convergent parallel mixed methods study was to explore the use of personification stories as an instructional strategy by high school science teachers to inform the creation of a new model for personification storytelling to support science instruction. There are a limited number of models available to science instructors to…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

A significant body of scholarship in Physics Education Research (PER) has documented that students have intuitive knowledge resources that they use to make sense of the physical world. Similarly, for physicists, symmetry is fundamental to making sense of the universe. In this dissertation, I explore students' intuitive resources related to…

The post-pandemic classroom dealt with not only the mental health struggles of educators and students, but also the technological and virtual learning dependence in a time ridden with misinformation. At this time, it was important to not only consider the purpose and intent of science education as a learning experience, but also pedagogical…

This dissertation contains findings from two research projects. The first research area focused on assessing engineering students problem solving skills. Problem solving related to two material and energy balance topics--vapor liquid equilibrium and reacting systems with recycle - were examined first followed by a more holistic analysis across two…

The central focus of my dissertation concerns the issue of representation. The issue of representation is important for science education research for two reasons: (1) the use of external representation in science teaching and learning, particularly in chemistry education, is ubiquitous as microscopic entities are not directly visible, and (2) the…

The central focus of my dissertation concerns the issue of representation. The issue of representation is important for science education research for two reasons: (1) the use of external representation in science teaching and learning, particularly in chemistry education, is ubiquitous as microscopic entities are not directly visible, and (2) the…

Students come to their high school physics classroom with experiences and knowledge that can be used to help explain physics concepts, but those experiences may not fully align with the scientifically accepted science concept. When there is a misalignment between a student's prior knowledge and the scientifically accepted concept a misconception…