Saint Joseph's University, a small comprehensive university, implemented a one-credit capstone project for the mathematics major beginning in 2002. After expansion to three credits in 2007, the capstone, although successful, had unintended consequences. In 2010, for both programmatic and practical reasons, the department decided to remove the…

In this introduction to the Special Issue on Capstone Courses we describe a range of models for the capstone course, common goals for these different courses, popular teaching methods, the use of capstone courses in program assessment, and issues related to course maintenance and faculty development.

Over the last four years of the senior capstone seminar at Western Carolina University, we have redesigned the course substantially to comply with our institutional Quality Enhancement Plan for engaged student learning and to follow the guidelines proposed by the Mathematical Association of America's Committee on Undergraduate Programs in…

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…

We discuss a mathematics capstone course designed to help students grow in mathematical independence. We describe how the course is structured to support this goal and the major assignments: a course wiki, a group expository project, and an individual problem to solve and extend. Students learn to ask and answer their own questions, helping them…

This paper describes the student-driven Senior Seminar Program at Hamilton College, giving a brief history, a list of past and current seminars, and illustrative details about one of the seminars.

Faculty often wish to allow for guided exploration or a deeper view of at least one topic in a bridge course. However, when the time allotted to such a course is only seven to ten weeks, it can be difficult to avoid moving quickly from one topic to another--leaving little opportunity for students to see a unified context in which the structures…

Initially designed to be an interdisciplinary experiment that would change attitudes about mathematics, the semester-long collaboration between a writing instructor and a mathematics instructor yielded unexpected long-term results. The collaboration served as an immersion in methods and techniques used by writing instructors. Description of…

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

Successful outcomes for a "Transition Course in Mathematics" have resulted from two unique design features. The first is to run the course as a "survey course" in mathematics, introducing sophomore-level students to a broad set of mathematical fields. In this single mathematics course, undergraduates benefit from an introduction of proof…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

We study how different sections voted on the same set of classroom voting questions in differential calculus, finding that voting patterns can be used to identify some of the questions that have the most pedagogic value. We use statistics to identify three types of especially useful questions: 1. To identify good discussion questions, we look for…

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Constructivism is currently a hotly debated topic, with proponents and opponents equally adamant and emotional with respect to their viewpoints. Many misconceptions exist on both sides of the debate, and misuses of terminology and attribution are rampant. Constructivism is a theory of learning, not a particular approach to instruction and not a…

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…