To explain human performance on the "Traveling Salesperson" problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors…

The majority of teacher candidates are eager to enter the field of teaching for their junior participation to try out methods, such the as Problem Solving Approach, that they have been learning throughout their classes at college. Teacher educators often place an emphasis on the use of Problem Solving Approach because it is natural to children.…

This study explored the performance of 75 seventh-grade students with and without disabilities, educated in inclusive mathematics classes, on open-ended, problem-solving mathematics assessments. In the study, approximately half of the students used a graphing calculator on the first assessment and not on the second assessment (n = 35; 46.7%),…

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. A common approach to problems involving deformable or rotating systems that has been discussed in the literature is to employ the work-kinetic energy theorem…

Differentiation and integration played large roles within classic developmental theories but have been relegated to obscurity within contemporary theories. However, they may have a useful role to play in modern theories as well, if conceptualized as guiding principles for analyzing change rather than as real-time mechanisms. In the present study,…

The design and empirical validation of a computer-based learning environment for acquiring long division skills, called the long division machine (LDM), are described. The construction of the LDM is primarily based on the didactic method of progressive schematisation. It offers the student a game-like environment for solving division problems by…

Although most online learning environments are predominately text based, researchers have argued that representational support for the conceptual structure of a problem would address problems of coherence and convergence that have been shown to be associated with threaded discussions and more effectively support collaborative knowledge…

Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…

The goal of the current study was to examine whether explaining to another person improves learning and transfer. In the study, 4- and 5-year-olds (N=54) solved multiple classification problems, received accuracy feedback, and were prompted to explain the correct solutions to their moms, to explain the correct solutions to themselves, or to repeat…

The purpose of this article is to demonstrate how counselors can use de Bono's Six Thinking Hats problem-solving technique in their work with couples. Part 1 of the article focuses on an introduction to the technique, including a theoretical rationale and supporting research. Following a detailed description of the process of using the model as a…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

In this article, a systematic approach is given for solving a magic star puzzle that usually is accomplished by trial and error or "brute force." A connection is made to the symmetries of a cube, thus the name Magic Hexahedron.

We answer a geometric question that was raised by the carpenter in charge of erecting helical stairs in a 10-story hospital. The explanation involves the equations of lines, planes, and helices in three-dimensional space. A brief version of the question is this: If A and B are points on a cylinder and the line segment AB is projected radially onto…

The authors describe a Modeling Instruction program that places an emphasis on the construction and application of conceptual models of physical phenomena as a central aspect of learning and doing science. (Contains 1 table.)

Superintendents are faced with conflicts every day. The conflicts arise around issues of personnel, community roles, funding, politics, and work/life balance. Good leadership involves an understanding of how to deal with conflict, whom to involve in the conflict resolution, how to set up structures and processes that ensure conflict doesn't…