In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

Gaining expertise in leadership requires time, commitment, an adequate knowledge base, and a working plan for learning and growth. Without a plan for learning, only tacit or "how-to" expertise is developed. Leaders often know how to solve the problems facing them, but they fail to analyze and act on the underlying causes. This results in…

This paper illustrates the role of a "Thinking-about-Derivatives" task in identifying learners' derivative conceptions and for promoting their critical thinking about derivatives of absolute value functions. The task included three parts: "Define" the derivative of a function f(x) at x = x[subscript 0], "Solve-if-Possible" the derivative of f(x) =…

This article takes a critical look at administrative decision making in schools and the extent to which complex decisions conform to normative models and common expectations of rationality. An alternative framework for administrative decision making is presented that is informed, but not driven, by theories of rationality. The framework assumes…

In the spring of 2003, University of California President Richard Atkinson forwarded to the U.C. Academic Senate a proposed revision of the existing regulation bearing on how university teachers should treat contentious and disputed issues, both political and academic, in their classrooms. The existing regulation on this matter, APM-010, had been…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

Critical thinking has long been a goal of social studies education, and its importance has been reiterated in documents delineating standards for the social studies. Yet, teaching critical thinking is problematic because there are competing definitions and practices and many barriers to its implementation (Wright 1995; Onosko 1989). In this…

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

A simple circuit problem treating an inductor, resistor and battery in series has uncovered a basic misconception of first-year students. The misconception is not about circuits or electrical properties but concerns rather the meaning and interpretation of the rate of change (instantaneous slope or derivative) of physical quantities. Resolving the…

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

The purpose of action learning is to learn through devising solutions and strategies in response to problems and implementing them through deliberative action. To understand the relation between action and learning, learners and facilitators need sufficient understanding of both concepts, but they are handicapped by lack of adequate theory and…

Current theories of learning emphasize the importance of learner-centered, active, authentic, environments for meaningful knowledge construction. From this perspective, computerized case-based learning systems afford practice fields for learners to build domain knowledge and problem-solving skills and to support contextualized transfer of…

Client projects are an opportunity for universities to create long-lasting, mutually beneficial relationships with businesses through an academic consultancy service. This article discusses the rationale and logistics of two models for conducting such projects. One model, used at Clemson University, is a formal academic consultancy service in…

Several approaches to response to intervention (RTI) described in the literature could be blended into an RTI model that would be effective in the schools. An effective RTI model should employ three fundamental variables: (a) systematic data collection to identify students in need, (b) effective implementation of interventions for adequate…