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…

This paper offers a methodological framework to research data practices in education critically. Data practices are understood in the generic sense of the word here, i.e., as the actions, performances, and the resulting consequences, of introducing data-producing technologies in everyday educational situations. The paper first distinguishes…

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…

Technology-mediated interactions and datafication are increasingly central in contemporary social dynamics and institutions, including teaching and learning processes. In order to fully understand the complex entanglements of human and non-human actants that emerge in postdigital education, it is essential to imagine new methodological approaches…

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.…

In this work, a bibliometric analysis of the investigations of the last 54 years focused on the teaching of topology and its applications in the learning of other areas of knowledge was carried out. The articles that appear in the SCOPUS database were taken into account under the search criteria of the words topology and teaching, connected with…

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…

Online networks, as digital images reflecting every aspects of real world especially under the current context of information technology, have become the most massive and opulent data source these days, where vast amount of information keeps being produced and transmitted. Their rapid expansion in scale and data volume draws wide attention and…

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…

Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data's domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological…

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…

Captured under the umbrella term Open Education, a wide range of educational initiatives has been popping up in the educational landscape. This study aims to offer empirical ground for understanding how Open Education introduces new forms of education. It does so by focusing on one initiative, namely the Interactive Open Online Courses included in…