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.)

This paper describes the construction of pedagogical environments in mathematics classes, centred on mathematical modelling and denominated "investigative scenarios", which stimulate students to investigation, to formulation of problems and to political reflection, as well as the sharing of acquired knowledge with other persons in the community.…

In this note a new proof of the divergence of the harmonic series is given based on the expected life of a parallel system with independent exponentially distributed component lifetimes.

In this short note is presented an easy and instructive proof of l'Hopital's Rule in both the 0/0 and [infinity]/[infinity] cases, obtained by translating the theorem into a simple geometric statement about paths in the plane. (Contains 4 figures.)

This study focused on the relationship between students' Advanced Placement Program[R] (AP[R]) 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,…

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…

See JC 690 392 above. [Not available in hard copy because of marginal reproducibility of original.]

Reasons for using Rolle's Theorem in calculus are discussed, with comparisons to the theorems of Lagrange and Cauchy. (MNS)

Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)