Discusses the lack of calculus textbook improvements even though there have been complaints about them from students and professors. Argues against using commercial textbooks in calculus instruction. (ASK)

Suggests that many students with A-level mathematics, and even with a degree in mathematics or a related subject, do not have an understanding of the basic principles of calculus. Describes the approach used in three textbooks currently in use. Contains 14 references. (Author/ASK)

Discusses the role of context problems as they are used in the Dutch approach known as realistic mathematics education (RME). Uses an RME design for a calculus course to illustrate that theory based on the design heuristic using context problems and modeling, which was developed for primary school mathematics, also fits advanced topics such as…

Presents a study that examines how two teachers taught differentiation using a hand-held computer algebra system. Finds that students of the teacher who privileged conceptual understanding and student construction of meaning were more able to interpret derivatives. Highlights the fact that within similar overall attainment on student tests, there…

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

A simple and practical application of mathematics is for fairly resolving the dispute of division of items for which two parties have equal claim. Basic properties of fair division are explained, which would enable students to learn concepts on optimization without introducing calculus.

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Despite the ready availability of computer algebra packages, from a pedagogical point of view, the authors still feel that integration should be taught extensively the classical way, by means of carefully selected examples which combine as many fundamental techniques as possible for their evaluation. Furthermore, whenever possible, these examples…

Disparities in curricular offerings between poor, inner-city schools and their more affluent counterparts leave urban students at a disadvantage in terms of preparation for higher education and future job opportunities. Introducing more rigorous academic coursework into traditionally low-performing schools is one way to close this gap; however,…

It is an eye opening experience for students to find out that even a great mathematician like Leibniz made mistakes, forgot to check carefully his calculations, and was temporarily misled by user-friendly but incorrect formulas. From Leibniz's mishap with the derivation of the rules of differentiation students can learn the importance of spending…

Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.

The paper is based on extensive research carried out on students of mathematics who had completed a university course of calculus. The basic purpose of the research was to determine the students' images of the concept of limit, that is to find out their associations, conceptions and intuitions connected with limits and to determine the degree of…

This article is a short introduction on how to use Modellus (a computer package that is freely available on the Internet and used in the IOP "Advancing Physics" course) to build physics games using Newton's laws, expressed as differential equations. Solving systems of differential equations is beyond most secondary-school or first-year college…

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…