The development of calculus and science by being permanent, didactic, demands on one part an analytical, deductive study and on another an application of methods, rhochrematics, resources, within calculus, which allows to dialectically conform knowledge in its different phases and to test the results. For the purpose of this study, the motivation…

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

An approach to polynomial approximations that leads the student to stumble on Taylor's theorem and its proof is presented, with a generalization. (MNS)

A proof for a limit is given, with a recommended presentation consisting of three lemmas followed by the theorem. (MNS)

Why calculus is taught in secondary schools is discussed, as well as how "modern mathematics" affected calculus, is calculus so difficult, and how calculus should be taught. (MNS)

An alternative approach is described for presenting the idea of the derivative through the use of chords of a graph. (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)

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)

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)

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…

How the notion of limit can be developed through a meaningful approach is discussed. Selected portions of the high school calculus course are described, and errors on a test are analyzed. (MNS)

Most presentations of mathematical ideas are suggested as being backwards from the way they evolved. Two alternatives are discussed, both emphasizing mathematical processes. (MP)