Students often view their role as that of a replicator, rather than a creator, of mathematical arguments. We aimed to engage our students more fully in the creation process, helping them to see themselves as legitimate proof creators. In this paper, we describe an instructional activity (i.e., the "group proof activity") that is…

Increasing evidence supports the use of small group instruction to enhance student learning in undergraduate mathematics. However, effectively enacting such learning methods requires instructors to develop new skills as educators. This paper provides a practical guide for group work in undergraduate mathematics, describing key aspects of group…

The purpose of this paper is to explain a newly implemented interactive delivery model for students at the Colorado School of Mines (Mines) repeating Calculus for Scientists & Engineers I during the spring of 2017. Since calculus is a necessary component for so many STEM degrees, it will continue to be a gateway to obtaining such degrees and…

Our traditional model of calculus instruction at a large public research university emphasized factual knowledge and procedural fluency with few realistic applications, leaving a chasm between classroom mathematics and disciplinary practice. Amid an ongoing effort by our department to improve undergraduate learning outcomes, we replaced…

Active learning techniques, such as peer instruction and group work, have been gaining a lot of traction in universities. Taking a natural next step in re-evaluating current practices, many institutions recently started experimenting student-centred group exams. In order to assess the feasibility and effectiveness of collaborative assessments, we…

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…

One goal of our Discovering the Art of Mathematics project is to empower students in the liberal arts to become confident creators of art and imaginative creators of mathematics. In this paper, we describe our experience with using string art to guide liberal arts students in exploring ideas of calculus. We provide excerpts from our inquiry-based…

The recent introduction of a new course in mathematical modeling at Manhattan College has provided students with a valuable opportunity to gain practical experience utilizing tools in applying their mathematical abilities to a real-world problem. This paper describes the steps taken to create this class, from obtaining a real-world partner…

This paper describes the results of a two-semester-long study of the effects of student-centered instruction on Precalculus courses. We also describe our teaching approaches centering around students, which include a mixture of lectures, student presentations, group work, discussion, and guided investigations. Students were taught with either the…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

Equivalence relations and partitions are two interconnected ideas that play important roles in advanced mathematics. While students encounter the informal notion of equivalence in many courses, the formal definition of an equivalence relation is typically introduced in a junior level transition-to-proof course. This paper reports the results of a…

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…

We describe our approach to incorporating a civic engagement component into a quantitative literacy (QL) course and the resulting gains in student learning, confidence, and awareness of local civic issues. We revised the existing QL course by including semester-long group projects involving local community issues that students could investigate…

The purpose of this article is to describe a general procedure for implementing group poster projects in lower and upper division mathematics courses. The authors have found that students who complete projects gain a deeper understanding of the mathematics they study, refine their ability to communicate mathematically, and engage in an activity…