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…

In this article, the authors focus on hypothesis testing--that peculiarly statistical way of deciding things. Statistical methods for testing hypotheses were developed in the 1920s and 1930s by some of the most famous statisticians, in particular Ronald Fisher, Jerzy Neyman and Egon Pearson, who laid the foundations of almost all modern methods of…

When people speak of "the Law of Gravity" they are generally referring to what is more specifically known as "Newton's Law of Gravitation." This law states that the gravitational force (that is, the mutual attraction) between any two physical bodies is directly proportional to the product of their individual masses and inversely proportional to…

Invention is a natural part of the human condition. It does not exist outside everyday activities, and it certainly does not come like a bolt out of the blue. The prepared mind, as always, is favored for success. Setting the stage for invention is as important as carrying it out. Good corporate leaders know this--as does any astute technology…

The utility of an "ecologically rational" recognition-based decision rule in multichoice decision problems is analyzed, varying the type of judgment required (greater or lesser). The maximum size and range of a counterintuitive advantage associated with recognition-based judgment (the "less-is-more effect") is identified for a range of cue…

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

In this note, it is shown through an example that the assumption of the independence of Bernoulli trials in the geometric experiment may unexpectedly not be satisfied. The example can serve as a suitable and useful classroom activity for students in introductory probability courses.

The United States no longer has a workforce dependent on operating machinery and performing repetitive tasks. Educators are therefore challenged to change the way students learn and to provide a workforce that is innovative and that has the ability to design new jobs. To do this, students must learn to be problem solvers, to create products that…

Although word problems pose greater language demands, they also encourage more meaningful problem solving and mathematics understanding. With proper instructional support, a student-centered, investigative approach to contextualized problem solving benefits all students. This article presents a lesson built on an author-adapted version of the…