In this paper the authors report on a qualitative investigation into service mathematics carried out in Irish universities against a backdrop of major concerns nationally and internationally embodied in the so-called "Mathematics problem". The enquiry involved a close inspection of how service mathematics is perceived, planned,…

This paper discusses the curriculum and students' and teachers' conceptions of proof. It goes on to discuss university students' difficulties with proving related to understanding and using definitions and theorems, understanding the structure of a proof, knowing how to read and check proofs, knowing and using relevant concepts, bringing…

This article examines a "calculus graphing schema" and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus…

Prisoner's Dilemma is a common game theory scenario in which two players must choose between acting cooperatively or out of pure self-interest. What a player decides affects not only his own outcome but also that of the other player. "Friend or Foe," a TV game show that has appeared on the cable Game Show Network (GSN), places pairs of contestants…

We describe a program that provides structured practice of prerequisite material to students in an ordinary differential equations course using an existing automated homework system originally designed for precalculus and calculus classes. The goal of the program is to improve students' comprehension of material presented in class by timing the…

This study investigates the effect of the preparatory year program courses on the first calculus course (Calculus I) at King Fahd University of Petroleum and Minerals (KFUPM). The data consists of more than 2,000 bilingual Arab university students studying in the English language, tracked over seven semesters. These students represent over 70% of…

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument.…

This paper is based on the preparatory study of a doctoral study in which we learned to consider defining in the realm of organizing. In particular, having engaged students in a situation based on "equivalence relations" (from an expert point of view), we report two different ways of organizing the given situation. One of them results in a "new"…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

We present a lottery project for lower level mathematics courses that demonstrates financial decision making in a context familiar to students. Students use elementary principals of probability and financial mathematics to compare the expected values of buying Powerball lottery tickets to some basic savings plans. Then, they compare the expected…

Most serious rock climbers are familiar with a counter-intuitive fact about their sport: The force experienced by a falling climber due to the rope as it arrests his fall does not depend simply on the length of the fall, but rather on a ratio called the fall-factor. This article explains, using elementary physics and simple differential equations,…

As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.

The authors give a rigorous treatment of the differentiability of the exponential function that uses only differentiable calculus. It can thus make "early transcendental" courses complete.

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…