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…

Graph data, especially large graph data, come up in many domains, such as social networks, the map of science, biological data, and even knitting! This presents a problem when we consider visualizing these structures. Layouts must be chosen carefully so that the structure of the graph is visible. Some graphs are large enough and connected enough…

Laboratory activities are a prevalent and essential part of chemistry learning because of their potential to help students develop problem solving abilities, visualize chemistry concepts learned in lecture, and gain practical skills. However, learning in the laboratory environment is not without its challenges. For example, cookbook-style…

This study applies human-centered design principles and involves end users in creating a usable knowledge graph. The aim was to explore the potential advantages of capturing and presenting networked knowledge in a domain for information discovery and decision-making purposes. The case taken for the research is the interdisciplinary Ph.D. program…

The purpose of the study was to explore the use of Visual Thinking Strategies as it applied to mathematics instruction for teachers in a small, urban elementary school containing grades 1-6 in a large Midwestern metropolis. This study was implemented to address the problem of low math scores in urban schools that have students with low…

Visual analysis is the primary method of analyzing data in single-subject methodology, which is the predominant research method used in the fields of applied behavior analysis and special education. Previous research on the reliability of visual analysis suggests that judges often disagree about what constitutes an intervention effect. Considering…

This thesis work is mainly focused on two problems related to improving accessibility of information graphics for visually impaired users. The first problem is automated analysis of information graphics for information extraction and the second problem is multi-modal representations for accessibility. Information graphics are graphical…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…