The Georgia College mathematics department has reimagined its major requirements to integrate meaningful undergraduate research experiences. We have developed and implemented a multi-year action plan to transform our major. In this article we discuss how the department has developed and implemented a year-long research experience as a capstone…

Undergraduate research experiences provide excellent examples of high-impact practices. They rely on inquiry-based learning to provide important capstone experiences for the students. However, they are time-intensive for mentor faculty. In an attempt to scale up our faculty's ability to offer such experiences, we combined a number of projects into…

The term "flipped" or "inverted" classroom includes a broad range of pedagogical innovations, and has recently received a significant amount of press. Although flipping an entire course might be a more extreme step than most are able to take, we discuss modular ideas for change that can be more easily implemented. This paper…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages…

This case study details the integration of an online grading platform in a Calculus program. Initially implemented to increase the efficiency and quality of grading written assessments in a large undergraduate program, the effects were many and surprising. Two main concerns surfaced that we needed to address, namely: (1) consistency in grading;…

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

This paper describes the development of an instructional sequence designed to allow students to reinvent the definition of sequence convergence in an introductory proof course. The sequence follows a heuristic of guided reinvention that encourages students to independently create their own mathematical definitions. This case study reports on how…

The inverted classroom is a course design model in which students' initial contact with new information takes place outside of class meetings, and students spend class time on high-level sense-making activities. The inverted classroom model is so called because it inverts or "flips" the usual classroom design where typically class…

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…

The Department of Mathematics at Bates College has offered a senior seminar capstone course for over a dozen years. In this article, we discuss the coexistence of seminar and thesis, our other capstone experience. We discuss in detail the goals of our seminar, various ways we structure the seminar to accomplish those goals, and methods of…

A capstone course is often synthetic, bringing together many components of a student's educational background. For this reason, a project-based course in mathematical modeling makes a great capstone, as modeling problems often require a broad collection of mathematical tools for their solution. The addition of a service-learning component can…

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to…