The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form y = u[subscript 1]y[subscript 1] + u[subscript 2]y[subscript 2], a sum of function products using solutions to the homogeneous equation y[subscript 1] and…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

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,…

Service-learning has been shown to have benefits for both students and faculty, however, it is quite rare in the mathematics classroom. At Concordia University Irvine we have established a relationship with the Village of Hope--a local non-profit organization designed to help homeless families transition to a self-sufficient status via temporary…

This study investigates the effects of applying an inverted classroom model in a second-semester calculus course at a large regional university in the southwest during the Spring of 2013. The sample consisted of four class sections with the same instructor, with a total of 173 students; two class sections were in the experimental group, whereas…

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…

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.

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college.…

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

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…

In this study, one section of undergraduate Precalculus was taught using a modified Moore method, a student centered inquiry-based approach, and two control sections were taught in a traditional lecture format. A survey of attitudes, beliefs, and efficacy toward mathematics and Precalculus was administered at the beginning and end of the semester…

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Oulipo (Ouvroir de Littérature potentielle, or Workshop on potential literature), an over 50-year old movement that began in France, seeks to apply mathematical constraints to literature and the arts. In this article, I will give a brief survey of this movement and how I have built a learning module based on it for my mathematics for the liberal…