During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

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…

This design/problem-solving activity challenges students to design a replacement bridge for one that has been designated as either structurally deficient or functionally obsolete. The Aycock MS Technology/STEM Magnet Program Virtual Bridge Design Challenge is an authentic introduction to the engineering design process. It is a socially relevant…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

The Native Species and Natural Processes certificate at the University of Victoria is an advanced-level online program of four courses to introduce students to state-of-the-art topics in the field of ecological restoration. The program posed some unique challenges for course developers. The development team needed to find ways to create online…

The process of creating child-developed board games in a counseling setting may promote social, emotional, and behavioral development in children. Using this creative approach, counselors can actively work with children to address referred concerns and build skills that may generalize outside of counseling sessions. A description of the method is…

Efforts to promote self-determination have been a principal focus of transition planning in support of students with disabilities for nearly two decades. However, research and recommendations related to self-determination have been primarily centered on promoting student participation in the IEP process and ensuring broader preparation for…

Inequality in education and other domains of life stands in the way of economic and civic progress in the United States. It forestalls social mobility and economic productivity and impairs social cohesion. As a result, national and international leaders--from big-city mayors to Pope Francis--recognize that, as President Obama (2013) put it,…