At Manhattan College, secondary mathematics education students take a capstone course designed specifically for them. In this course, students revisit important topics in the high school curriculum from a mathematically advanced perspective; incorporating the mathematical knowledge they have attained in their college mathematics classes to an…

In this paper we demonstrate how video game mechanics can be used to help improve student engagement with online mathematics homework. Specifically, we integrate two common video game systems, levels and achievements, with the online homework program "WeBWorK." We describe the key features of the implementation of these systems and…

This article describes a quantitative and qualitative assessment from a study done on the possible effectiveness of including an online homework component in first-semester calculus. Two instructors, each teaching two sections of Calculus I, agreed to treat one of their sections as an experimental group and the other as a control group. Students…

We describe the use of browsing and searching (in libraries, online, inside sources, at meetings, in abstracts, etc.) as a way to stimulate the teacher of undergraduate mathematics, specifically in differential equations. The approach works in all other areas of mathematics. Browsing can help build new and refreshing teaching materials based on…

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

Mathematical induction is one of the major proof techniques taught to mathematics students in the first years of their undergraduate degrees. In addition to its importance to mathematics, induction is also required for computer science and related disciplines. However, even if the concepts of a proof by induction are taught and understood, many…

In this article the author describes her experiences in an effective, and cost-efficient way of teaching developmental mathematics online in a course that runs on its own once it is set up. The online course described here was created and implemented at Ramapo College. The course is an innovative method of teaching developmental mathematics in…

The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…

A detailed description is provided of a 200-level 3-credit course introducing ways in which mathematics may be explored with the use of a computer. This may serve as a template for such courses or be taken piecemeal for use in other classes. The original course was aimed at mathematics and mathematics education majors. (Contains 2 tables, 21…

This article describes key elements for faculty development programs to prepare mathematics teachers for technology-rich environments. We offer practical examples from our experiences in teaching mathematics with technology and in teaching others to incorporate technology-based pedagogies. We address challenges faced by faculty using technology,…

In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

We describe two classes of sequences that give rise to accessible problems for undergraduate research. These problems may be understood with virtually no prerequisites and are well suited for computer-aided investigation. The first sequence is a variation of one introduced by Stephen Wolfram in connection with his study of cellular automata. The…

Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…