This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

Finding a periodic solution to a nonlinear ordinary differential equation is in general a difficult task. Only in a very few cases can direct methods be applied to an equation to find initial values leading to a solution of the corresponding initial value problem that is periodic. Oscillatory periodic solutions have such practical importance that…

This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability. (Contains 2 tables and 10 figures.)

For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates,…

The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…

A mathematics module in the undergraduate programme for first year engineers aims to enable those with low mathematical qualifications to understand and use efficiently calculus and related topics. The teaching approach is designed to develop student's fluency, understanding and responsibility through creating an inquiry community, encouraging…

In 2000, the Massachusetts Institute of Technology (MIT) faculty first proposed putting the course materials from all 1,800 MIT classes online, free of charge. The idea behind MIT OpenCourseWare (OCW) was to use the Internet for more than just distance learning. When MIT began placing the course materials online in 2002 and 2003, the audience…

In this paper, we explore the use of isomorphic problem pairs (IPPs) to assess introductory physics students' ability to solve and successfully transfer problem-solving knowledge from one context to another in mechanics. We call the paired problems "isomorphic" because they require the same physics principle to solve them. We analyze written…

This study focused on the relationship between students' Advanced Placement Program® (AP®) performance in AP English Language, Biology, Calculus, and U.S. History, and their subsequent college success. For each AP Exam studied, students were divided into three groups according to their AP Exam performance (no AP Exam taken, score of 1 or 2, and a…

Previous research [S. J. Pollock et al., Phys. Rev. ST Phys. Educ. Res. 3, 1 (2007)] showed that despite the use of interactive engagement techniques, the gap in performance between males and females on a conceptual learning survey persisted from pretest to post-test at the University of Colorado at Boulder. Such findings were counter to…

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

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…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students' understanding of the underlying mathematical concepts. It is therefore important to study the…

This article discusses the assumptions required by the item response theory (IRT) true-score equating method (with Stocking & Lord, 1983; scaling approach), which is commonly used in the nonequivalent groups with an anchor data-collection design. More precisely, this article investigates the assumptions made at each step by the IRT approach to…