The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the…

In recent years, there has been an increase in the number of course-based undergraduate research experience (CURE) courses. These courses provide research opportunities for many more students than are typically exposed to traditional independent research experiences, including women, historically underrepresented groups in science, and…

Following the frameworks for research and inquiry-based learning, this paper describes a series of activities that can be used in undergraduate management classrooms to expose students to management research. The focus of these activities on finding reputable article summaries allows instructors to introduce management research, explain how to…

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…

In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

Colloidal stability is one of the most important criteria in the application strategy of colloidal nanoparticles in the continuous phase. The branches include ecology, involving coagulation as a purification method; medicine as nanocarriers; biology as blood coagulation, etc. A chemist versed in these concepts is a high-performing chemist in…

The implementation of a laboratory exercise in an undergraduate chemistry course, where students perform a comparison of three different synthetic methods toward [Cu(Cl)(IPr)]-complexes (IPr = N,N'-bis(2,6-diisopropylphenyl)imidazol-2-ylidene), is described. The students are introduced to the continuous improvement of reactions in terms of green…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

This paper reflects on teaching sport in political geography undergraduate courses in the United States, through which I simultaneously aim to de-essentialize geopolitics and de-essentialize sport. I integrate sport examples in diverse courses on political geography and teach a dedicated "Geopolitics of Sport" course. By framing my…

We present a concrete situation where there is a difference between the theoretical security of a cipher and its limitations when implemented in practice. Specifically, when entering a PIN, smudges on the keypad substantially reduce its security. We show how the number of possible keys in the presence of the "smudge attack" can be…

Experiential learning in biomedical engineering curricula is a critical component to developing graduates who are equipped to contribute to technical design tasks in their careers. This paper presents the development and implementation of an undergraduate and graduate-level soft material robotics design course focused on applications in medical…

This article is an exploration of the potential of a more purposeful application of criticality in undergraduate classrooms. Conventional pedagogy, often lecture-based, does not prepare students well for life, a career, or service toward the common good. A more critical approach in the classroom stimulates critical thinking, critical…

Purpose: In the following theoretical article, the author generates a theory of Leadership Pedagogy and its connection to Creative Arts Education. Design/methodology/approach: The article analyzes Leadership Theory across three pillars: Socio-relational, Cognitive and Creative, and how these areas underscore thoughtful and caring pedagogy and…