A method is presented for constructing infinite series with prescribed rates of convergence. The method is presented as being an aid to improving the student's understanding of how the partial sum of an infinite series can be used to approximate the sum of the series, as well as being of interest in itself. The focus of the paper is the degree of…

A major source of challenging problems for students is the use of higher mathematics to derive elementary problems. Several examples are given. (MP)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

This book, written for students of calculus, is designed to augment the explanations of concepts covered in a calculus class. It consists of an overview of calculus divided into basic ideas and vocabulary, the process of differential calculus, and integral calculus. The book is intended as a resource to explain the concepts of calculus in everyday…

The systems approach to teaching is briefly discussed and then applied to teaching undergraduate calculus. The implementation procedure, specifications of the learning units, program of study and experimentation, and the various types of expenses are also outlined. (Author/MK)

Included are a detailed example of a calculator demonstration, the general principles to be followed in preparing a calculator demonstration, a list of demonstration topics for a calculus course, and some suggested topics for other courses. (MK)

Examines the effects of two teaching techniques on college liberal arts majors' ability to solve calculus problems; concludes that instruction involving a modified directed reading-thinking activity followed by peer tutoring may improve problem-solving ability in calculus. (DD)

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

Several mathematicians have expressed their criticism of calculus instruction and some have developed innovations. This paper reviews the criticism and innovations and then questions the approach and the emphasis of the reformers. (Contains 34 references.) (Author)

Genre analysis is a form of discourse analysis that can provide useful and sometimes surprising new perspectives on understanding teaching and learning. Uses two examples to illustrate the application of genre analysis in mathematics education. (Contains 23 references.) (ASK)

Reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to learning and teaching of collegiate mathematics using differential equations as a specific case. Focuses on the RME design heuristic of guided reinvention as a means to locate the starting point for an…