We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

This article discusses two examples of geometric problem solving suitable for middle and high school students. Both problems are related to students' everyday life experience and allow them to discover deep connections between mathematical properties and nature. With the help of dynamic mathematics software, students have the opportunity to…

Nearly 50 years ago, Henry Bent published his groundbreaking article in this "Journal" introducing the "global" formulation of thermodynamics. In the following years, the global formulation was elaborated by Bent and by one of the present authors. The global formulation of the first law focuses on conservation of energy and the recognition that…

The term "restriction endonuclease mapping" covers a number of related techniques used to identify specific restriction enzyme recognition sites on small DNA molecules. A method for restriction endonuclease mapping of a 1,000-basepair (bp)-long DNA molecule is described in the fictitious experiment of this test. The most important fact needed to…

Playing mathematical games enables middle school students to engage their minds while discovering and using meaningful strategies. Blokus[R] is one such game. While playing, students exercise spatial awareness, analyze attributes of two-dimensional shapes, compare patterns, and use logic--all of which encompass NCTM's Content Standards. Students…

The emergence of Web 2.0 and some of its ascendant tools such as blogs and wikis have the potential to dramatically change education, both in how we conceptualize and operationalize processes and strategies. We argue in this paper that it is a change that has been over a century in coming. The promise of the Web 2.0 is similar to ideas proposed by…

What's democracy got to do with teaching? To answer this question, the author recollects the personal experiences through which she came to understand the connections between democracy and teaching. Sustaining democracy requires its citizens--teachers, parents, and students, in the case of schooling--to fight for it intelligently. The way teachers…

The widespread adoption of the Common Core State Standards (2010) has caused mathematics and special educators to reconsider instructional methods. The Common Core introduces eight Standards for Mathematical Practice that outlines the dispositions that should be fostered in students. Most notable are those that push students to analyze problems,…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

A course in system dynamics has been included in the first year of our university's six-year medical curriculum. System Dynamics is a discipline that facilitates the modelling, simulation and analysis of a wide range of problems in terms of two fundamental concepts viz. rates and levels. Many topics encountered in the medical school curriculum,…

Problem solving is an essential skill for nuclear engineering graduates entering the workforce. Training in qualitative and quantitative aspects of problem solving allows students to conceptualise and execute solutions to complex problems. Solutions to problems in high consequence fields of study such as nuclear engineering require rapid and…

Recently, many educational institutions across the globe have implemented engineering leadership programmes either as a part of a formal engineering curriculum or where leadership development is embedded into separate in-house programmes. This shows the clear intent of these educational institutions to prepare their engineering students for…

As a high school physics teacher, Kim Geddes is constantly searching for new experiences to challenge, motivate, and engage students. Last year, she incorporated ExploraVision into the energy unit of her school's physics curriculum with the help of their media specialist (Elease Franchini). ExploraVision is a competition offered through a…

To counteract disempowerment frequently experienced in education, in 2001 the authors initiated a "Problem Solution Project" (PSP) in the second year a two-year urban certification and Master's program. The PSP, designed to promote empowerment of first-year urban teachers and their students, involves both service learning. In 2004, the authors…

An interesting change has been occurring in the author's middle school mathematics classes. Some students have become creative, free-thinking inventors. If they have had little experience with an operation, they invent strategies of their own. Sometimes these strategies have been well informed and supported by strong mental math skills and a good…