Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

Use of the computer program "Integrate Using Definition" can help students develop understanding of integral. Several applications of the program are discussed. (MNS)

A problem that most high school calculus students can explore is presented. It can help students understand such mathematical topics as functional notation, composition of functions, the solving of systems of equations, and the derivative. A computer program is included. (MNS)

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (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)

In this paper we study how a student begins to acquire the concept of the derivative, what kind of representations he acquires and how he connects these representations. A teaching period, in which different perceptual and symbolic representation were emphasized, was carried out and task based interviews conducted to five students. The students…

Three short articles on teaching procedures are presented. They concern: (1) a simple introduction to the derivative; (2) using derivatives to solve polynomial equations; and (3) mathematical applications in problems concerning force due to gravity. (JG)