Compiles observations from a multivariable calculus class in which computers were used extensively. Results show that visualization skills can be improved and that students use technology in very innovative ways. (Author/MM)

The aim of this essay is to build a bridge between two intersecting areas of research, social indicators research on the one hand and health-related quality of life research on the other. The first substantive section of the paper introduces key concepts and definitions in the social indicators research tradition, e.g., social indicators,…

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…

The general perception is that high school teaching of mathematics in South Africa tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems rather than conceptual. This study compares the conceptual and procedural skills of first-year calculus students in life sciences. Also…

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational…

As a precursor to lessons on prime decomposition and reducing fractions, rules are generally presented for divisibility by 2, 3, 5, 9, and 10 and sometimes for those popular composites such as 4 and 25. In our experience students often ask: "What about the one for 7?" and we are loathe to simply state that there isn't one. We have yet to see a…

In terms of modern pedagogy, having visual interpretation of trigonometric functions is useful and quite helpful. This paper presents, pictorially, an easy approach to prove all single angle trigonometric identities on the axes. It also discusses the application of axial representation in calculus--finding the derivative of trigonometric functions.

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…

The standard derivative tests for extrema and inflection points from Calculus I can be revisited subsequently from the perspective of Taylor polynomial approximations to provide additional insights into those tests, as well as to extend them to additional criteria. (Contains 3 figures.)

We introduce a cooperative learning, group lab for a Calculus III course to facilitate comprehension of the gradient vector and directional derivative concepts. The lab is a hands-on experience allowing students to manipulate a tangent plane and empirically measure the effect of partial derivatives on the direction of optimal ascent. (Contains 7…

Especially in their first upper-division mathematics courses, students often have trouble with proofs; and sometimes they object, "This is hard. I do not get it. Why am I doing this?" Though symptomatic of emotional reaction to difficulty, at its heart this is a legitimate question and it deserves a legitimate answer. This article offers one such…

A new transform proposed by Oyelami and Ale for impulsive systems is applied to an impulsive fish-hyacinth model. A biological policy regarding the growth of the fish and the hyacinth populations is formulated.

In many elementary calculus textbooks in use today, the definition of a "smooth curve" is slightly ambiguous from the students' perspective. Even when smoothness is defined carefully, there is a shortage of relevant exercises that would serve to elaborate on related subtle points which many students may find confusing. In this article, the authors…