A small class of functions is described that easily lend themselves to two-dimensional and three-dimensional visualizations at the basic calculus level. The intended audience is those educators involved in the instruction of elementary calculus. This note is an educational piece that begins with the question: "What happens if a function defined on…

A calculus-based introductory physics course, which is based on the Matter and Interactions curriculum of Chabay and Sherwood (2002), has been taught at Purdue University. Characteristic of this course is its emphasis on modeling. Therefore, I would like to investigate the effects of modeling-based instruction and interactive engagement on…

This study focuses on the long-term retention of basic mathematical techniques in a first-year calculus course, involving a sample group of engineering students at the University of Pretoria. The study investigates which and how much of the basic mathematical knowledge and rote skills acquired in the first year of study is retained after a further…

H. Wainer and L. Steinberg (1992) showed that within broad categories of first-year college mathematics courses (e.g., calculus), men had substantially higher average scores on the mathematics section of the Scholastic Aptitude Test (SAT-M) than women who earned the same letter grade. However, Wainer and Steinberg's analysis may lead to…

The Mathematics Department at Borough of Manhattan Community College (BMCC) (New York) has been actively involved since 1988 in a serious and successful program to improve instruction, understanding, and retention for women and minority students in calculus courses. One result of this work has been students creating calculus animations using…

This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

Discussion and examples of the use of computer graphics in science and calculus instruction are provided. (SD)

Four problems in which elementary mathematics can be used in constructing models are described. (SD)

This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)

An overview is provided of De Anza College's use of computerized instruction in its mathematics courses. After reviewing the ways in which computer technology is changing math instruction, the paper looks at the use of computers in several course sequences. The instructional model for the algebra sequence is based on a large group format of…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

Mathematical investigations pursued by two gifted students are presented. One is written by a boy age 9 with his follow-up at 11; he studied patterns to derive the factors for the difference of two squares. Another boy of 11 discovered formulas for slopes of tangent lines and areas under curves. (LS)

Nineteen Calculus II students were randomly sampled and divided into calculator (n=9) and noncalculator (n=10) groups. These students were asked to "think aloud" while solving 24 Advanced Placement calculus problems. Each student interview was videotaped, coded and analyzed for reasoning process as well as outcome. The results indicated…

This text is based on the idea that teachers of mathematics at any level will find it advantageous to be able to point to interesting, useful, and diverse applications of the mathematics they teach. The first chapter describes several graphing techniques used for displaying data and finding meaningful relationships as a result. Subsequent chapters…

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…