Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the…

We describe a project to restructure the way Applied Calculus is taught at our university to improve student success rates. Eliminating large lecture sections, re-evaluating the needs and expectations of our students, developing uniform course delivery and grading systems, incorporating active learning teaching methods, and focusing on conceptual…

This article describes a system of specifications-based grading used in an introduction to proofs course. The system was introduced to address two issues that arose in the course: how to spend less time grading and how to encourage use of feedback. We describe the implementation of the system and the results on grading and on students.

Dennis Pearl is Professor of Statistics at Pennsylvania State University and Director of the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE). He is a Fellow of the American Statistical Association. This interview took place via email on November 18-29, 2016, and provides Dennis Pearl's background story, which describes…

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply…

In this paper, we discuss the Experimental Mathematics course taught at Valparaiso University since 2009. We focus on aspects of the course that facilitate students' abilities to ask and explore their own research questions.

In the age of the internet, it is increasingly difficult to write homework assignments in a way that encourages students to struggle with a problem on their own without seeking answers from other sources. This is especially true in lower-level courses, where students often start with the attitude of "I can't do this." In this article, I…

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A…

This work outlines a model for creating momentum for active learning at the departmental level through a Community of Practice. This approach focuses on empowering members of the community by providing easy access to active learning tasks, pacing guide, and teaching tips for the course.

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…

The purpose of this paper is to provide issues related to student understanding of logical components that arise when solving word problems. We designed a logic problem called the King and Prisoner Puzzle--a linguistically simple, yet logically challenging problem. In this paper, we describe various student solutions to the puzzle and discuss the…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction:…

We present a short-term class project used in an introductory linear algebra course, designed to engage students in matrix algebra. In this activity, students responded to a survey of their pop culture tastes. Using the survey responses, they worked to design a series of matching algorithms, using matrices, with the goal of matching the students…