We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…

It is no easy feat to engage young people with abstract material as well as push them to greater depths of understanding. Add in the extra pressures of curriculum expectations and standards and the problem is exacerbated. Projects designed around standards and having multiple entry points clearly offer students the best opportunity to engage with…

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

As an often recommended but under-utilized pedagogical strategy, writing in mathematics has many benefits for students. However, creating and grading worthwhile writing projects can be more time-consuming than utilizing more traditional forms of assessment. This paper provides a concrete example of a writing project prompt, questions, directions,…

In many post-secondary, introductory mathematics courses failure and withdrawal rates are reaching as high as 50% and average GPA is steadily decreasing. This is a problem that has been witnessed across the globe. With widespread reforms taking place in K-12 mathematics education, many innovative teaching strategies have been created, implemented,…

This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)

A program on calculus is conducted, which helps students learn about inherent differentiation through a study of mathematical functions, while simultaneously reinforcing their understanding of functional concepts. This process develops their mathematical experience in the field of calculus and in other advanced quantitative programs.

A simple and practical application of mathematics is for fairly resolving the dispute of division of items for which two parties have equal claim. Basic properties of fair division are explained, which would enable students to learn concepts on optimization without introducing calculus.

Presents problems to find the integrals of logarithmic and inverse trigonometric functions early in the calculus sequence by using the Fundamental Theorem of Calculus and the concept of area, and without the use of integration by parts. (Author/ASK)

An interdisciplinary activity in which students can see how a famous author, Leo Tolstoy, metaphorically applied the integration steps from calculus to illustrate his ideas about how history should be studied is described. The activity provides a startling and energizing conclusion to a unit on applications of integration and provokes students'…

This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches…

Describes the specific courses in a sequence along with how the writing has been implemented in each course. Provides ideas for how to efficiently handle the additional paper load so students receive the necessary feedback while keeping the grading time reasonable. (Author/ASK)

Historical background and mathematical development of Riemann's rearrangement theorem are presented. The theorem is stated and proved in two parts. (PK)