Examines the value of concept maps as instruments for assessment of conceptual understanding, using the maps to compare the knowledge of function that experts and two groups of students (N=28)--traditional and nontraditional--enrolled in university calculus classes hold. Discusses the differences between the student and expert groups as well as…

Presents data obtained from an 11-year study of the three phases of movement from a standard approach to a reform approach in the first year calculus sequence for mathematics and science majors. (Author/ASK)

Assesses the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts. Indicates that overall performance on the geometric related-rates problems was poor and the poorest performance was on steps linked to conceptual understanding. (Contains 34 references.) (Author/ASK)

Criticizes the method of using calculators for the purpose of selecting candidates for L, for the limit value of a function. Suggests an alternative: a working formula for calculating the limit value L of a real function in terms of infinitesimals. (Author/ASK)

Investigates the impact of the TI-89 hand-held Computer Algebra System (CAS) on student achievement in a first year college core calculus course. Analyzes data from an experimental study conducted at the United States Military Academy at West Point from 1998-2000. Results indicate that the TI-89 hand-held CAS experimental group attained a higher…

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…

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…

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…

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.