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…

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…

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.

Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately…

Emerging scholarship has brought critical attention to the increasing influence of digital platform architectures on learning across disciplines and contexts. Allied with such scholarship, this study examines how the logics of social media platforms create the conditions for new formations of literacy to emerge at the intersection of digital…

The design and initial implementation of a project-based directed study course in mathematical research and communication is described. The intention of the course is to expose students to the foundation of mathematical research through inquiry-based learning. Students are asked to approach an exercise in topology as though it is an open problem.…

This paper presents the ways that reflective questions were used to develop pre-service mathematics teachers' understanding of metric and topological spaces. In particular, the purpose of developing PSTs' understanding of metric and topological spaces is that understanding these mathematical concepts leads to PSTs' understandings on how to teach…

This article presents a research apparatus for investigating and making sense of stories that emerge from feedback that mathematicians provide on students' proofs. Using the commognitive framework, the notion of "didactical discourse on proof" is developed as a lens for conceptualizing mathematicians' practice of feedback provision. The…

This paper aims at defining and exploring design principles in a distance technological setting for an educational activity for mathematics undergraduate students, devoted to the construction of basic concepts in general topology, the promotion of problem-solving processes, the development of metacognitive aspects, and, in general, the development…

Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive…

Example use in undergraduate mathematics has been extensively studied. However, little is known about undergraduates' example use in the context of introductory point-set topology. We present a case study of one undergraduate and describe her example use when constructing proofs in the context of introductory topology. We describe her use of a…