This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

This article describes the authors' experiences developing and implementing an innovative curriculum connecting mathematics and the biological sciences. It describes the original plan, the modifications that were necessary, and some advice to readers who might want to develop comparable programs.

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or…

This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…

This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…

Data analysis methods, both numerical and visual, are used to discover a variety of surprising patterns in the errors associated with successive approximations to the derivatives of sinusoidal and exponential functions based on the Newton difference-quotient. L'Hopital's rule and Taylor polynomial approximations are then used to explain why these…

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.

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)

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…

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.)

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…

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…