This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

Ongoing action research at the University of Pretoria investigates first-year students' preparedness for a study in calculus. In 2005 first-year engineering students completed a mathematics diagnostic survey at the beginning and end of the year. In this article the results of the 2005 survey are compared with the students' final school marks in…

Nonstandard Analysis gives an alternative approach to teaching elementary calculus. This paper hopes to communicate to the reader the ideas of this recent development in mathematics and its implications in teaching undergraduate students. The development of the approach is first briefly traced. Then a method of constructing on ordered field…

The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…

The author presents a technique for solving limit problems that involve polynomial or rational functions by using delta, epsilon proofs. (MN)

The behavior of certain functions in advanced calculus is discussed, with the mathematics explained. (MNS)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

The behavior of some functions near the point of origin is discussed. Each function oscillates, and as x approaches 0, the oscillations become increasingly more rapid; their behavior near the origin improves with increasing values of n. Examples for a calculus class to consider are given. (MNS)

The history of the study of dynamical systems is traced, examples are given, and the contribution of Birkhoff and Smale are described. (DT)

This paper presents an initial hypothesis of instructors' beliefs about their role in helping students learn to solve problems in an introductory calculus-based physics course. Instructors see their teaching role as primarily providing resources and making suggestions, with little mentioning of how they influence the students to use the resources…

This paper reports on the vital role that reflective thinking plays in solving problems involving the mathematics of change and variation particularly multivariable calculus. We report on how reflective thinking is one kind of self-regulatory (in the sense of metacognitive) thought mechanism. We present an outline of the results of a larger study,…