The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to…

We examine the equant model for the motion of planets, which was the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity, which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal…

Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in "Principles of Optics" by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer…

According to Poincare, a geometry cannot be an object of experience since any geometrical experiment must be realized with physical objects, such as rulers and light rays, and it is only their properties that can be tested. This position was apparently refuted by general relativity and the successful confirmation of its predictions by astronomical…

The objective of this study is to facilitate progressive transitions in chemistry teachers understanding of nature of science in the context of historical controversies. Selected controversies referred to episodes that form part of the chemistry curriculum both at secondary and university freshman level. The study is based on 17 in-service…

Pedagogical content knowledge (PCK) has been described as an assemblage of the most powerful analogies, demonstrations, examples and illustrations that make content knowledge understandable to students, together with an understanding of the preconceptions and alternate conceptions that students bring with them to the classroom (Shulman, 1986). In…

This study explored the influence of a Saturday Science program that used explicit reflective instruction through contextualized and decontextualized guided and authentic inquiry on K-2 students' views of nature of science (NOS). The six-week program ran for 2.5 hours weekly and emphasized NOS in a variety of science content areas, culminating in…

There have been substantial reform efforts in science education to improve students' understandings of science and its processes and provide continual support for students becoming scientifically literate (American Association for the Advancement of Science in Benchmarks for science literacy, Oxford University Press, New York, 1993; "National…

Working at scientists' elbows is one suggestion that educators make to improve science education, because such "authentic experiences" provide students with various types of science knowledge. However, there is an ongoing debate in the literature about the assumption that authentic science activities can enhance students' understandings…

Selection bias is a problem for mathematics education researchers interested in using observational rather than experimental data to make causal inferences about the effects of different instructional methods in mathematics on student outcomes. Propensity score methods represent 1 approach to dealing with such selection bias. This article…

This article presents a simple activity using Archimedes' principle that helps students to develop their scientific thinking and also to identify and correct their misconceptions. The exercise consists of linear and reverse processes.

An introductory approach to black holes is presented along with astronomical observational data pertaining to the presence of a supermassive black hole at the center of our galaxy. Concepts of conservation of energy and Kepler's third law are employed so students can apply formulas from their physics class to determine the mass of the black hole…

When a ball bounces elastically against a floor, the vertical component (v[subscript y]) of the velocity of the ball's mass-center changes sign. This is a special case of the elastic collision of two balls (i.e., two objects, neither of which is much more massive than the other), in which case the balls' post-collision relative velocity (=…

On Dec. 27, 2006, we drove with our children and their families to a cabin we rented on the grounds of the "YMCA of the Rockies" in Estes Park, CO, for a few days of winter relaxation and recreation. On the night of the 27th a snowstorm dropped over half a meter of new snow, creating a beautiful winter wonderland. For the next couple of days the…

We have found that a simple demonstration experiment using a match or a cotton swab and a drinking straw or an acrylic pipe serves as an effective introduction to dynamics. The most basic apparatus has a cotton swab serving as a dart and the straw as the blowgun. When blown from a starting point near the exit end of the straw, the cotton swab does…