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…

Over the last few years, different sociomaterial research orientations have emerged. In this article, we argue that most of these orientations are relying on a relational mode of thinking, that is, a way of conceiving of educational practices in terms of the relations between the different actors present in these particular practices. In doing so,…

Currently, modelling of knowledge and skills in a MOOC and the associated instructional and pedagogical engineering process is a major challenge in order to support designers and facilitate learning. This article explains how visuo-cognitive metaphors of the "metro map" and "travel" make possible the design of connections…

This paper describes the student-driven Senior Seminar Program at Hamilton College, giving a brief history, a list of past and current seminars, and illustrative details about one of the seminars.

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

This paper presents the introduction of problem-based learning (PBL) in a power electronics course at the University of Oviedo, Gijon, Spain, by means of two practical projects: the design and construction of a switching-mode power supply (SMPS) prototype and the static study of a dc-dc converter topology. The goal of this innovation was for…

Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Good quality scientific teaching depends on the ability of researchers to translate laboratory experiments into high school and undergraduate classes, bridging the advanced and basic science with common knowledge. A fast-growing field in biomedical sciences is oxidative stress, which has been associated to several diseases, including cancer and…

The process of protein biogenesis culminates in its correct targeting to specific subcellular locations where it serves a function. Contemporary molecular and cell biology investigations often involve the exogenous expression of epitope- or fluorescent protein-tagged recombinant molecules as well as subsequent analysis of protein-protein…

Teaching mathematics with games and puzzles goes back in history. Presents an example with the set theory game called Subset Takeaway in which two players can play. Creates a geometric representation of Subset Takeaway starting with a triangle and going to a three-dimensional simplex. Illustrates the winning strategy in the game and features a…

Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…