Computational learning theory studies the design and analysis of learning algorithms, and it is integral to the foundation of machine learning. In the modern era, classical computational learning theory is growingly unable to catch up with new practical demands. In particular, problems arise in the following aspects: i). "scalability":…

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…

In recent years, knowledge tracing (KT) within intelligent tutoring systems (ITSs) has seen rapid development. KT aims to assess a student's knowledge state based on past performance and predict the correctness of the next question. Traditional KT often treats questions with different difficulty levels of the same concept as identical…

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…

Automatic short answer grading (ASAG) is a challenging task that aims to predict a score for a given student response. Previous works on ASAG mainly use nonneural or neural methods. However, the former depends on handcrafted features and is limited by its inflexibility and high cost, and the latter ignores global word cooccurrence in a corpus and…

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

Technological advances have significantly affected education, leading to the creation of online learning platforms such as virtual learning environments and massive open online courses. While these platforms offer a variety of features, none of them incorporates a module that accurately predicts students' academic performance and commitment.…

In the era of the "reproducibility crisis" and the "P-value controversy" new ways of presentation and interpretation of the results of a meta-analysis are desirable. One suggestion that has been made for single studies almost six decades ago and taken up now and then is the P-value function. For a given outcome, this function…

Enzymes are nature's catalysts, mediating chemical processes in living systems. The study of enzyme function and mechanism includes defining the maximum catalytic rate and affinity for substrate/s (among other factors), referred to as enzyme kinetics. Enzyme kinetics is a staple of biochemistry curricula and other disciplines, from molecular 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…

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…

Interrupted time series (ITS) studies are frequently used to examine the impact of population-level interventions or exposures. Systematic reviews with meta-analyses including ITS designs may inform public health and policy decision-making. Re-analysis of ITS may be required for inclusion in meta-analysis. While publications of ITS rarely provide…

Research shows that though some students can easily find the correct solutions to the problem(s) at hand, the algorithms that these students create are not always ones that would, when implemented, produce the correct solution(s). Towards shedding light on this phenomenon, the present study explicates a mechanism--accounting for features of the…

In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically,…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…