Most executives have not heard of human performance technology (HPT), but a recent Google search showed 25 times more Google hits for "lean six sigma" than for "human performance technology." This article describes five factors that make HPT a hard sell: (1) HPT is not part of standard business jargon, (2) organizational executives associate…

"Why is it," writes noted assessment expert W. James Popham, "that today's educators seem almost compelled to replicate their predecessors' blunders?" Looking back over a career of more than fifty years in education, Popham identifies six key "unlearned lessons" in education and reflects on their impact on schools, teachers, and students. In an…

Although most computer users will never need to write a computer program, many students enjoy the challenge of creating one. Computer programming enhances students' problem solving by forcing students to break a problem into its component pieces and reassemble it in a generic format that can be understood by a nonsentient entity. It promotes…

English teachers are by nature rather imaginative, a trait that is not taught in a methods class or listed as a disposition in standards for teacher preparation. Whether as part of a learning activity or a "what if" question posed in a literature discussion, imagination and creativity are integral parts of classrooms and their inclusion is as…

We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [second derivative of]x + x + epsilonx[superscript 2] = Fcoswt and the [second derivative of]x + x + epsilonx[superscript 3] = Fcoswt and report the results of a systematic numerical investigation on the global stability of…

A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…

In the last two decades, playgrounds have gotten safer, more streamlined--and progressively worse. Today's playgrounds are distinctly less fun, and distinctly worse for kids. But there's a new vision for tomorrow's playgrounds--letting children design their ideal playgrounds, which parents and community leaders look through when selecting the…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

A number of schools have recently introduced new courses dealing with various aspects of iteration theory or at least have found ways of including topics such as chaos and fractals in existing courses. In this note, we will consider a family of functions whose members are especially well suited to illustrate many of the concepts involved in these…

Distinguishing between problems that have solutions and dilemmas that need to be managed, the authors identify three overarching questions from the School ABC case that center around data and perceptions. Because the ability to talk openly and honestly about difficult issues is critical to the health of a school, the authors consider the obstacles…

The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…

One of those features that set human societies apart from animal societies is the use of language. Language is a vital part of every human culture and is a powerful social tool that we master at an early age. A second feature of humans is our ability to solve complex problems. For centuries philosophers have questioned whether these two abilities…

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

Early in their introductory college linear algebra class, the author's students learn to use a matrix to represent and solve systems of linear equations. Indeed, this simple idea is perhaps the foundational idea of the course. Nevertheless, the author was delighted to find that the study of linear systems can lead to surprisingly deep mathematics.…

Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…