Provides evidence of differences in students' ability to solve problems with and without a computer algebra system. Indicates that almost without exception, the TI-92 students were more successful at symbolically solving problems than comparison students. Observes improved performance on all three levels of problems: (1) directive computational;…

The purpose of this study is to determine differences in mathematics self-efficacy between students enrolled in a developmental mathematics course and those enrolled in a calculus course. Data from a sample of 185 freshmen students at a single 4-year institution using the Mathematics Self-Efficacy Scale are analyzed. Results indicate that calculus…

Score equity assessment (SEA) is introduced, and placed within a fair assessment context that includes differential prediction or fair selection and differential item functioning. The notion of subpopulation invariance of linking functions is central to the assessment of score equity, just as it has been for differential item functioning and…

This paper addresses the issue of collegiate mathematics achievement of underrepresented minority students as it investigates the impact of a cooperative learning calculus programme on the first-year calculus experience of non-Asian ethnic minority engineering students. The Emerging Ethnic Engineers Programme in the College of Engineering at the…

Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…

As part of a first-year college Introductory Physics course, I have students construct an Excel[R]: spreadsheet based on the differential equation for pendulum motion (we take a pendulum having a light bar rather than a string, so it can go "over the top"). In extensive discussions with the students, I find that forcing them to make the…

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done a historic and epistemological study aimed at clarifying the role and the meaning of the differential in…

A calculus-free approach is offered for determining the equation of lines tangent to conics. Four types of problems are discussed: line tangent to a conic at a given point, line tangent to a conic passing through a given point outside the conic, line of a given slope tangent to a conic, and line tangent to two conics simultaneously; in each case,…

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

The tedium that characterizes many routine calculus activities necessary for average students often results in the loss of the most talented to the field of mathematics. One way to overburden teacher to nurture mathematical talent within a typical calculus class is to encourage student research. This article illustrates how student research…

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. (Contains 2 figures.)

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

The article begins by highlighting recent trends and concerns in post-secondary Calculus and Precalculus education. The main purpose of the article is to discuss the transition to a new Precalculus/Calculus I two-semester course at Wabash College, a small liberal arts college for men. Three years of data from the earlier, traditional, sequence are…

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…