Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…

Describes a simple cooling experiment that can be conducted in class at the college algebra, precalculus, calculus, or differential equations level whose aim is to determine the best exponential function to fit the experimental data. (Author/ASK)

Online assessment in mathematics is becoming more prominent as mathematics and the internet become more compatible. This paper is based on a case study of a web-based calculus course in which a combination of paper and online assessment is used for assessing various activities. The paper first investigates what student assessment preferences are…

A study of undergraduate actuarial graduates found that math SAT scores, verbal SAT scores, percentile rank in high school graduating class, and percentage score on a college mathematics placement exam had some relevance to forecasting the students' grade point averages in their major. For both males and females, percentile rank in high school…

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

It is widely attested that university students face considerable difficulties with reasoning in analysis, especially when dealing with statements involving two different quantifiers. We focus in this paper on a specific mistake which appears in proofs where one applies twice or more a statement of the kind "for all X, there exists Y such that R(X,…

It is generally agreed that the ability to read mathematics is an important skill--one that few of our students possess. A number of people have published some suggestions for helping students learn to read their mathematics textbooks. What these have in common is suggestions for getting students more active while reading. Using these resources as…

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

A deliberate attempt is made in Business Mathematics oriented text books as well as in some reform calculus oriented text books to interpret the derivative f[prime](a) of a function y = f(x) at the value x = a as the change in the y-value of the function per "unit" of change in the x-value. This note questions the above interpretation and suggests…

Forty-two studies comparing students with access to graphing calculators during instruction to students who did not have access to graphing calculators during instruction are the subject of this meta-analysis. The results on the achievement and attitude levels of students are presented. The studies evaluated cover middle and high school…

In response to low completion rates in a calculus course for a biology, management, and social sciences program at California's Orange Coast College (OCC), a project was undertaken to develop a revised course outline for the college's pre-calculus course to better prepare students for success in calculus. Specifically, the project sought to…

This paper presents a laboratory exercise in which an integration problem is applied to cinematography, without the need for apparatus. The problem situation is about the oscillation control of a camera platform to attain the contrast angular rate of objects. Wave equations for describing the oscillations are presented and an expression for…

A laboratory experiment, based on a simple electric circuit that can be used to demonstrate the existence of real-world "related rates" problems, is outlined and an equation for voltage across the capacitor terminals during discharge is derived. The necessary materials, setup methods, and experimental problems are described. A student laboratory…

The use of linear regression to identify variables that predict grades of black students in precalculus and calculus I was studied at Xavier University of Louisiana, a historically-black institution. The predictive power of the variables for black males and females was also assessed. These two mathematics courses are prerequisites for students…

This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory,…