This paper tells the story of what happened when students in the authors' sophomore-level introduction-to-proof classes were given a theorem to prove with no expectation about what proof method to use. The paper discusses the nine different student-produced proofs of the statement: If "n" is an integer such that "n" is greater than or equal to 3,…

Science is the study of nature's rules. The most basic of these are the laws of physics, most of which are expressed in equation form. Physics equations show how concepts connect to one another. But does a study of these equations enhance student understanding? Not always, for too often in an introductory course students are tempted (or even…

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students' flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent…

In an age of uncertainty, one of the aims of higher education is to establish lifelong learning abilities in students. However, different authors remain divided on the question of what constitutes "lifelong learning ability". This article proposes the hypothesis that the cultivation of lifelong learning abilities in higher education needs to be…

Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred to as abstract algebra. Current pedagogy conceals from the student many of the great ideas generated by significant problems in the history of the discipline. In…

The aim of this article is to establish some interesting inequalities involving arithmetic functions.

The standard approach to the general rules for differentiation is to first derive the power, product, and quotient rules and then derive the chain rule. In this short article we give an approach to these rules which uses the chain rule as the main tool in deriving the power, product, and quotient rules in a manner which is more student-friendly…

Youths in residential care have likely experienced trauma as they have had atypical and disruptive events occur in their lives that has contributed to their out-of-home placement. For people who have been traumatized, the regulation of emotions is an important feature of their recovery. This article presents a model that traces phases from…

Who, rather than what, decides what giftedness is? The academic world traditionally focuses on theoretical descriptors whereas society as a whole is more interested in practical function. This partly divided focus is becoming increasingly critical and problematic as economies are becoming global and the political objective is to create a knowledge…

The full promise of class room learning is dependent on its ability to incorporate 21st century skills in its instructional design, delivery and implementation. In this increasingly competitive global economy, it is not enough for students to acquire subject-level mastery alone. Skills like creative thinking, problem-solving, communication and…

This article describes the use of a progressive paper in a capstone course to develop students' writing skills. A progressive paper is one that students write one section at a time: as they add each new section, they go back and revise the previous parts based on actionable feedback from the instructor. In this course, the progressive paper takes…

The Borough of Manhattan Community College (BMCC) in New York City is fourth among all community colleges in awarding degrees to minority students and in awarding degrees to African Americans. The BMCC student body is approximately 37 percent Hispanic, 33 percent black, 15 percent white, and 15 percent Asian. In addition, a significant proportion…

This essay uses the experience of one community engagement program at the American University of Beirut (AUB), a prominent private university in Lebanon, to reflect on the value and challenges of civic engagement in a non-Western context. It describes the Lebanese sectarian political system, provides an overview of the AUB Neighborhood Initiative,…

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common…

Secondary school principals face no shortage of issues and challenges when it comes to ensuring that their teachers and students are ready for the Common Core State Standards. With so many issues competing for scarce time and resources, it is understandable that for many school leaders, the needs of high-ability and high-potential students are not…