Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students' algorithmatizing activity. In both…

Nomographs (or nomograms, or alignment charts) are graphical representations of mathematical relationships (extending to empirical relationships of data) which are used by simply applying a straightedge across the plot through points on scales representing independent variables, which then crosses the corresponding datum point for the dependent…

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is…

In mathematic courses, construction of some concepts by the students in a meaningful way may be complicated. In such circumstances, to embody the concepts application of the required technologies may reinforce learning process. Onset of learning process over daily life events of the student's environment may lure their attention and may…

The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in…

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

This paper provides surface area and volume formulas for surfaces of revolution in R[superscript n]. In addition the authors illustrate how to obtain the formulas for volume and surface areas of revolution about the x- or y-axis in two different ways: a "heuristic" argument and a rigorous calculation using "cylindrical" coordinates. In the last…

This note considers a family of piece-wise linear functions that can be used in the classroom to illustrate various concepts involved in iteration theory such as periodicity. These functions require minimal background on the part of the student. (Contains 2 figures.)

This paper, the second of a two part article, expands on an idea that appeared in literature in the 1950s to show that by restricting the domain to those complex numbers that map onto real numbers, representations of functions other than the ones in the real plane are obtained. In other words, the well-known curves in the real plane only depict…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example…

The Mobius strip, torus, and Klein bottle are used to graphically and analytically illustrate the differences between orientable and non-orientable surfaces. An exercise/laboratory project using the non-orientable Boy surface is included. (Contains 11 figures.)

The paper describes the use of a spreadsheet in a mathematics teacher education course. It shows how the tool can serve as a link between seemingly disconnected mathematical concepts. The didactical triad of using a spreadsheet as an agent, consumer, and amplifier of mathematical activities allows for an extended investigation of simple yet…