Consider a circular segment (the smaller portion of a circle cut off by one of its chords) with chord length c and height h (the greatest distance from a point on the arc of the circle to the chord). Is there a simple formula involving c and h that can be used to closely approximate the area of this circular segment? Ancient Chinese and Egyptian…

In this article we propose building sets of problems rooted in the same concept, a process that allows students to develop understanding and take on increasingly complex problems. By beginning with "foundation stories" and using strategies similar to those for literary constructs, we have dramatically increased our students' mathematical…

An exercise on structure elucidation for advanced undergraduate students is described. To determine the structure of an unknown product, students are required to use spectra together with an organic chemistry mechanism. This exercise exemplifies the procedure commonly used in research, thus helping students develop problem-solving skills. In…

It is well known that the discoverer of radio waves, Heinrich Hertz, was the first man to apply Maxwell's electrodynamic theory to a problem in radio wave propagation. In this paper, we scrutinize his near-field lines of force using computers and his theory. In one of his four figures, a feature was found which was not to be obtained by…

The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y(the unknown) is a function f of other physical quantities A[subscript 1], ..., A[subscript n] (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition…

Most differences that people see across identity groups are not essential. They're not hard coded into people's genes. They originate in communities and in cultures and are reinforced by daily practice. People act the ways they do because they're conforming to the people around them. In this article, the author introduces a new way of thinking…

The classic experiment presented in this problem-solving test was designed to identify the template molecules of translation by analyzing the synthesis of phage proteins in "Escherichia coli" cells infected with bacteriophage T4. The work described in this test led to one of the most seminal discoveries of early molecular biology: it dealt a…

These notes and questions have been prepared to promote discussion of the ideas set out in the Clarifying paper, "Living and learning in EcCoWell cities" to be found on the PASCAL International Exchanges (PIE) website. This Discussion Paper sets ten questions for discussion. We are hoping to encourage discussions of these issues around the world.

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

"Leadership for Recreation, Parks and Leisure Services" presents new perspectives on the importance of leadership in the profession. Integrating theory with practice, the book provides foundational perspectives in the study of leadership at all levels--direct service, supervisory, managerial and community/civic--in recreation, parks and…

The most recent figures place the number of juvenile arrests in the United States at 2.11 million. (OJJDP, 2009). In some states, children as young as 10 years old are incarcerated for violent offenses. Crowded juvenile facilities are often unable to meet the needs of these large numbers of youth. The cost to treat offenders within long-term…

The Mathematics Performance Expectations (MPE) define the content and level of achievement students must reach to be academically prepared for success in entry-level, credit-bearing mathematics courses in college or career training. They were developed through a process that involved faculty from Virginia's two- and four-year colleges and…

Marketing faculty use cases, simulations, and client-sponsored projects to achieve learning objectives in the marketing capstone class. This class typically aims to integrate and apply previously learned material and to transition students into their careers. Drawing on the professional school, creative problem solving and constructivist learning…

This assessment is used in a class titled Ethical Leadership as part of a graduate level principal preparation program. The assessment has been approved by NCATE as meeting all of the stipulated ELCC standards for which it is designed (ELCC 5.1, 5.1. & 5.3). The assignment has two sections. In the first section candidates are asked to…

Technology is a means that makes work or tasks easy, efficient, and operative. A more encompassing definition refers to it "as the tools created by human knowledge of how to combine resources to produce desired products, to solve problems, fulfill needs, or satisfy wants" (Koehler and Mishra. 2008:5). It can either be contrivances of tradition or…