Societal structures and memory organization models share network-like features, offering insights into how information spreads and shapes collective memories. In this study, we manipulated the structure of lab-created community networks during a computer-mediated recall task using the Deese-Roediger-McDermott paradigm to test the spreading…

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 an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and…

Belonging is a complex relational concept. It has been shown to be processual, emergent, and dynamic. And yet this relationality, and complexity, sits in tension with increasingly voluble calls to measure, manage and maintain students' sense of belonging to an ostensibly fixed space of higher education. This article reports on research that…

In this article, we advocate for and propose a novel concept map driven knowledge tracing (CMKT) model, which utilizes educational concept map for learner modeling. This article particularly addresses the issue of learner data sparseness caused by the unwillingness to practice and irregular learning behaviors on the learner side. CMKT considers…

Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students' reasoning in topology is…

Visual representations, such as diagrams, are known to be valuable tools in problem solving and proof construction. However, previous studies have shown that simply having access to a diagram is not sufficient to improve students' performance on mathematical tasks. Rather, students must actively extract information about the problem scenario from…

The paper focuses on the sociological adaptation and development of the mental mapping method within the study of national identity. 'Mental map' is defined as a spatial image or model formed over time in the individual or collective consciousness, while the method of mental mapping is interpreted as a graphic representation of a certain area by…

Coming from a social perspective, we introduce a classroom organizational frame, where students' proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the…

Graph Signal Processing (GSP) plays a crucial role in addressing the growing need for information processing across networks, especially in tasks like supervised classification. However, the success of GSP in such tasks hinges on accurately identifying the underlying relational structures, which are often not readily available and must be inferred…

In high school, unit discs were all circular. Squares and diamonds were added to the list of shapes in a Real Analysis course and although more bizarre shapes appeared in graduate school, the list of possible shapes didn't appear endless. In this note, we'll show that unit discs can have almost any shape imaginable.

This contribution takes up and discusses topology as a relational approach to better understand and empirically trace policy mobilities in federal education systems. While topology echoes other relational approaches in its simultaneous focus on ongoing change and the "making" of stabilized forms (e.g., policy scales), it also brings…

This article presents topological genealogy (TG) as a methodology to research transnational digital governance, and particularly how digital infrastructures are implicated in enacting such forms of governance. Inspired by the field of social topology, TG is centrally interested in investigating the conjoined production of digital infrastructures…

As critical posthumanist and (new) materialist scholarship become more established in educational research, a reconsideration of methodological approaches suited to a radical relational onto-epistemology is required. A popular figuration adopted by researchers to help think and do such research is the Deleuze-Guattarian "rhizome." Coming…