For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

There has been a broad wave of change in tertiary calculus courses in the past decade. However, the much-needed change in tertiary pre-calculus programmes--aimed at bridging the gap between high-school mathematics and tertiary mathematics--is happening at a far slower pace. Following a discussion on the nature of the gap and the objectives of a…

The d'Arbeloff Interactive Mathematics Project or d'AIMP is an initiative that seeks to enhance and ultimately transform the teaching and learning of introductory mathematics at the Massachusetts Institute of Technology. A result of this project is a suite of "mathlets," a carefully developed set of dynamic computer applets for use in the…

We report on a two-year NSF-funded project to strengthen connections among science, technology, engineering, and mathematics (STEM) disciplines. One component of this project was to produce some initial data on the effectiveness of Interdisciplinary Lively Applications Projects (ILAPs) in teaching science and engineering undergraduates. ILAPs are…

This article examines a "calculus graphing schema" and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus…

We describe a program that provides structured practice of prerequisite material to students in an ordinary differential equations course using an existing automated homework system originally designed for precalculus and calculus classes. The goal of the program is to improve students' comprehension of material presented in class by timing the…

This study investigates the effect of the preparatory year program courses on the first calculus course (Calculus I) at King Fahd University of Petroleum and Minerals (KFUPM). The data consists of more than 2,000 bilingual Arab university students studying in the English language, tracked over seven semesters. These students represent over 70% of…

This paper describes two uses of the software package TEMATH (Tools for Exploring Mathematics) with calculus students: (1) as a demonstration tool in the classroom to visually explore with students the many mathematical models introduced in a first year calculus course; and (2) as a part of a lab where students use a set of laboratory explorations…

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

The emphasis is on so-called "best solution" problems to questions that frequently arise in practical situations, such as finding an answer for the least amount of time, greatest volume, least amount of work, maximum profit, and minimum cost. One of this module's purposes is to help users become acquainted with the types of calculations necessary…

This report discusses how a computer was used to enhance the curriculum of a college calculus course. Problems with a calculus adjunct course in computer science are detailed, along with the nature of changes in the new program. The changes moved from student use of the computer as an automatic typewriter to use as a tool with instructional…

REPORTED ARE THE FINDINGS AND RECOMMENDATIONS OF A PANEL ESTABLISHED BY THE ADVISORY COUNCIL ON COLLEGE CHEMISTRY (ACCC) WORKING COOPERATIVELY WITH THE COMMITTEE ON THE UNDERGRADUATE PROGRAM IN MATHEMATICS (CUPM). THE FUNCTION OF THIS PANEL WAS TO DETERMINE THE APPROPRIATENESS OF RECOMMENDATIONS FOR CHANGES IN THE UNDERGRADUATE MATHEMATICS…

The individualized community college calculus course described here was developed to accomodate differences in student learning rates. It consists of three units: (I) limits and continuity; (II) the derivative with applications; and (III) the integral with applications. There are three sections in Unit I, four sections in Unit II, and five…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…