In the Spring of 2011, two of the authors of this paper taught number theory courses at their respective institutions. Twice during the semester, students in each class submitted proofs of two to three theorems to be peer reviewed by students in the other class. Each student wrote anonymous and formal referee reports of the submitted theorems,…

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

The current manuscript is a reflective case study that describes the emerging design of the author's first online mathematics course. The case study addresses how expectations associated with teaching in a live setting can raise conflicts in designing online courses. The author reframes the conflicts into questions; explores the questions and…

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…

This article discusses the creation of a student project about linear difference equations using primary sources. Early 18th-century developments in the area are outlined, focusing on efforts by Abraham De Moivre (1667-1754) and Daniel Bernoulli (1700-1782). It is explained how primary sources from these authors can be used to cover material…

Some challenges to increasing actuarial science program size through recruiting broadly among potential students are identified. Possible solutions depend on the structures and culture of the school. Up to three student cohorts may result from partition of potential students by the levels of academic progress before program entry: students…

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we…

The Mathematical and Theoretical Biology Institute (MTBI) is a successful summer research experience for undergraduates, with a strong record of mentoring Ph.D. graduates, particularly, underrepresented minority students. However, the MTBI program was designed for education in research, not for research in education, and the mechanisms of the…

Understanding the effects of a service-learning component on the classroom culture, socially and academically, brings a novel perspective to designing, executing, and assessing these types of active-learning projects. This paper evaluates the success of a service-learning project from a perspective of social networks by investigating the question:…

Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…

The purpose of this paper is to present results of a recent study in which students voted on multiple choice questions in mathematics courses of varying levels. Students used clickers to select the best answer among the choices given; in addition, they were also asked whether they were confident in their answer. In this paper we analyze data…

Service-learning can be a valuable educational enterprise with both course-specific and general education benefits, as well as contributions to the community. These potential merits and key considerations in achieving them are discussed with special attention to the mathematical sciences.

As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…