Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…

Generating creative ideas in a brainstorm session `is a crucial part of innovation. However, for actual implementation, the most creative ideas must be selected from a pool of ideas. To date, idea selection has remained relatively unexplored and validated instruments to measure idea selection performance are not systematically employed. This study…

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…

The article reports three experiments designed to explore heuristics used in comparing the lengths of completed Euclidean Traveling Salesman Problem (E-TSP) tours. The experiments used paired comparisons in which participants judged which of two completed tours of the same point set was shorter. The first experiment manipulated two factors, the…

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

Dealing with problem-solving has been a growing challenge in teaching engineering and over the career of these professionals. To increase the ability to understand a problem and consequently improve the quality of the solutions, an exercise was proposed to students of an MBA program, and they have experienced some challenges on interpreting…

Members of a third-grade class were involved in a heated discussion. They were using a fixed number of links to create fences for toy cows. The children could change the shape of the field produced by the links, but they could not add any links or take any away. Understanding the relationship between perimeter and area is a difficult concept for…

Most teachers try to avoid having students experience uncertainty in their schoolwork. But if we want to prepare students to tackle complex problems (and the uncertainty that accompanies such problems), we must give them learning experiences that involve feeling unsure and sometimes even confused. Beghetto presents five strategies that help…

Flotation is usually taught in Indian schools after students have been introduced to the concepts of mass, density, pressure, volume and buoyancy. This paper describes an attempt to teach the principle of flotation to a class of sixth graders--who had not yet been taught these concepts--so they could understand (and perhaps, arrive at) Archimedes'…

This article focuses on developing musical creativity through reflective and collaborative practices in elementary music. Studies on reflective practices reveal that students of any age are able to reflect knowingly. Researchers who have examined thinking, creativity, and musical understanding have discussed the importance of teaching practices…

Problems for students with a high mathematical potential can be far more complex and challenging than problems normally used in regular classrooms. The problems we developed for mathematically gifted students offer the possibility of acquiring and using heuristics (so called patterns of actions) which are useful in problem solving processes.…

The application of factor analysis to the "Force Concept Inventory" (FCI) has proven to be problematic. Some studies have suggested that factor analysis of test results serves as a helpful tool in assessing the recognition of Newtonian concepts by students. Other work has produced at best ambiguous results. For the FCI administered as a…

We present a preliminary theory of innovation in social work science. The focus of the piece is two case studies from our work that illustrate the social nature of innovations in the science of social work. This inductive theory focuses on a concept we refer to as transformative innovation, wherein two sets of individuals who possess different…

We discuss strategies for the general solution of single-step 1D constant acceleration problems. In a slightly restricted form, these problems have five variables (?"x," "v[subscript 0]," "v," "a" and "t") and two independent equations, so three variables must be given to solve for the other two,…