This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to sampling distributions and their properties to increase student understanding of the concepts and methods in elementary statistics courses. The article considers such sampling distributions as the…

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

All advocates of curriculum reform talk about an increased emphasis on conceptual understanding in mathematics. In this article, the authors use many examples to address the following issues: What does conceptual understanding mean, especially in introductory courses such as college algebra, precalculus, or calculus? How do we recognize its…

In this article, the author describes an individualized term project that is designed to increase student understanding of some of the major concepts and methods in multivariate calculus. The project involves having each student conduct a complete max-min analysis of a third degree polynomial in x and y that is based on his or her social security…