Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

Idealized models are often used in introductory physics courses. For one, such models involve simple mathematics, which is a definite plus since complex mathematical manipulations quickly become an obstacle rather than a tool for a beginner. Idealized models facilitate a student's understanding and grasp of a given physical phenomenon, yet they…

For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

The Onsager reciprocal relations are essential to multicomponent transport theory. A discussion of the principles that should be used to derive flux laws for coupled diffusion is presented here. Fluctuation theory is employed to determine the reciprocal relation for transport coefficients that characterize coupled mass and heat transfer in binary…

Ask a graduating chemical engineering student the following question: What makes one reactor different from the next? The answers received will often be unsatisfactory and will vary widely in scope. Some may cite the difference between the basic design equations, others may point out a PFR is "longer," and still others may state that it…

Background: Developmental dyscalculia is a heterogeneous disorder with largely dissociable performance profiles. Though our current understanding of the neurofunctional foundations of (adult) numerical cognition has increased considerably during the past two decades, there are still many unanswered questions regarding the developmental pathways of…

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

Learning to question is essential for determining pathways of conservation and development in southwestern Amazonia during a time of rapid global environmental change. Teaching such an approach in graduate science programs in regional universities can be done using play-acting and simulation exercises. Multiple working hypotheses help students…

The need to include proficiency with estimation and mental arithmetic as goals for the study of computation is presented. Approaches and guidelines are described for developing these skills.

The article suggests possible reasons for difficulties with verbal (word) problems and describes two remediation strategies: re-teaching the introductory sequence for an operation and having students write their own problems. (CL)

The potential uses for Chisanbop, a Korean system of using fingers for calculating, in the education of the elementary grade visually impaired student are explored. (Author/SBH)

Tips are presented for chemistry teachers on the use of acid-base half-reactions in review lessons, the use of calculators by chemistry students, significant figures, and the preparation of benzoyl peroxide from acne medicine. (BB)

Teaching the art of counting can be quite difficult. Many undergraduate students have difficulty separating the ideas of permutation, combination, repetition, etc. This article develops some examples to help explain some of the underlying theory while looking carefully at the selection of various subsets of objects from a larger collection. The…

Redox calculations have the potential to reinforce important concepts in bioenergetics. The intermediacy of the NAD[superscript +]/NADH couple in the oxidation of food by oxygen, for example, can be brought out by such calculations. In practice, students have great difficulty and, even when adept at the calculations, frequently do not understand…