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…

Misleading data visualizations have become a significant issue in our information-rich world due to their negative impact on informed decision-making. Consequently, it is crucial to understand the factors that make viewers vulnerable to misleading data visualizations and to explore effective instructional supports that can help viewers combat the…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

This work was developed to present constructive steps of multiple integrals using the open-source software Geogebra. The main focus was directed towards creating three-dimensional graphs of integrals through Riemann sums in two variables. Some practical examples are developed to demonstrate the reliability of the presented results, which are…

Curriculum-based measurement (CBM) represents a critical strategy for data-based decisionmaking within educational settings. Visual analysis is frequently used to analyze CBM data; thus, CBM vendors often automatically generate graphs based on student data to facilitate analysis. Differences in graph formatting are apparent across CBM vendors, and…

This case study investigated the development of prospective mathematics teachers' technological pedagogical content knowledge (TPACK) in graphical data displays with (VM) within the context of a microteaching lesson study (MLS). This research investigated how five participants integrated technology and implemented a lesson plan aimed to teach…

Recent research has indicated that the manner in which single-case data are typically displayed for visual analysis may influence rater decisions regarding the effect of an intervention. Subsequently, researchers have encouraged adherence to a standard assembly for linear graphs in order to control these effects. Others, however, have encouraged…

Network meta-analysis (NMA) is an established method for assessing the comparative efficacy and safety of competing interventions. It is often the case that we deal with interventions that consist of multiple, possibly interacting, components. Examples of interventions' components include characteristics of the intervention, mode (face-to-face,…

Visual inspection of single-subject data is the primary method for behavior analysts to interpret the effect of an independent variable on a dependent variable; however, there is no consensus on the most suitable method for teaching graph construction for single-subject designs. We systematically replicated and extended Tyner and Fienup (2015)…

Technological Pedagogical Content Knowledge (TPACK) is a theoretical framework used to assess information teaching. However, its application and popularity in practice is limited due to usability and accuracy issues. This study presents a quantitative model called TPACK-Venn, which is based on the graphical calculation of a Venn diagram determined…

This study focuses on a case study that highlights the mathematical discourse developed by two pairs of students when dealing with a specific transition task, i.e., an activity leading to the construction of a graph of a function based on the exploration of another representation of the same function. Such a task was designed to work on the…

Idiograms are graphical representations in which chromosomes appear ordered by their relative size, homology groups, and the presence of cytogenetic landmarks such as centromeres, secondary constrictions, and banding patterns. They have become crucial elements in cytogenetic research. Here, we describe a simple protocol for spreadsheet software to…

Despite the increased number of quantitative effect sizes developed for single-case experimental designs (SCEDs), visual analysis remains the gold standard for evaluating methodological rigor of SCEDs and determining whether a functional relation between the treatment and the outcome exists. The physical length and range of values plotted on x and…

Despite the increased number of quantitative effect sizes developed for single-case experimental designs (SCEDs), visual analysis remains the gold standard for evaluating methodological rigor of SCEDs and determining whether a functional relation between the treatment and the outcome exists. The physical length and range of values plotted on x and…

Visual representations of data are widely used for communication and understanding, particularly in science, technology, engineering, and mathematics (STEM). However, despite their importance, many people have difficulty understanding data-based visualizations. This work presents a series of three studies that examine how understanding time-based…