The effectiveness of problem solving as a learning tool is often diminished because students typically use only an algorithmic approach to get to the answer. We discuss a way of encouraging students to reflect on the solution to their problem by requiring them--after they have arrived at their solution--to draw solution maps. A solution map…

Improving students' problem-solving skills is a major goal for most science educators. While a large body of research on problem solving exists, assessment of meaningful problem solving is very difficult, particularly for courses with large numbers of students in which one-on-one interactions are not feasible. We have used a suite of software…

Using fictional stories with adults in group and individual counseling sessions facilitates exploration of difficult topics in a safe and nonthreatening way. These stories deepen awareness and increase problem solving skills. This article describes how fictional stories can be used by counselors with adult clients. It also illustrates strategies…

A historical discussion of the theories which deal with the formation of real images in mirrors and lenses is presented in this paper. Speculations on mirrors appeared as early as Plato. Euclid's, Hero's and Ptolemy's approaches to visual rays are described. The theory on burning mirrors starts with Diocles and later was continued by the Arabs. Al…

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Cochise College, Cochise County, and the Cochise Community Foundation partnered to create the Cochise County Quality of Life Index--the first to be developed in Arizona. The project brought together stakeholders to address shared problems in new ways, based on non-traditional partnerships. The college's Center for Economic Research provided…

This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

After evaluating a proposal by Jon Star (2005) that mathematics educators reconceptualize the construct of procedural knowledge, we offer an alternative reconceptualization based on an extension and amalgamation of his and other conceptualizations of procedural knowledge and conceptual knowledge. We then propose some implications for research…

Accurate and effective decision-making is one of the most essential skills necessary for organizational success. The problem-solving process provides a systematic means of effectively recognizing, analyzing, and solving a dilemma. The key element in this process is critical analysis of the situation, which can be executed by a taking a Socratic…

A major motorcycle vendor, based in the U.S. Midwest, is the world's largest custom V-Twin motorcycle manufacturer and domestically the second largest motorcycle manufacturer behind Harley-Davidson. This project describes the process used used by a K-State undergraduate distance learning student to design and develop the initial version of a…

Families and teachers spend countless hours supporting preschoolers and primary age children in the development of mental tools like focus, memory, and other problem-solving skills that help children think better, pay attention, and remember what they have experienced. Children use these tools to succeed in reading, writing, math, science, and…

Today's students will require knowledge and skills that differ from those typically provided by schools. Comparisons of learning and assessments in informal, everyday settings (e.g., homes, businesses) with those that occur in typical school settings provide ample evidence that new assessment strategies are needed. Those comparisons reveal many…

Although not all teachers can invite scientists into classrooms on a regular basis, they can invite them into their students' worlds through literature. Here the author shares how she used the nonfiction selection, "Science to the Rescue" (Markle 1994), as an opportunity for students to investigate socially significant problems and empower them to…

The authors discuss the challenges that might be faced if gifted education moves toward an RtI (Response to Intervention) approach. The challenges they share can be used as discussion points for planning and reflection. In spite of the remaining challenges, the authors conclude that RtI is certainly changing the face of education and that gifted…

President Barack Obama's call for innovation to improve the nation's schools strikes a chord with many in policy circles, who are already discussing how the federal government can play a role not only in supporting the expansion of what works, but also in creating solutions to unsolved problems. But some experts are pointing out that significant…