This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

The number of undergraduates placing into developmental or "remedial" coursework continues to increase. This rise is concerning because developmental or "remedial" coursework creates barriers for many students. This mixed method study examines a holistic approach to placement. After one-on-one interviews with mathematics…

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

Texas A&M University-Commerce has implemented supplemental instruction (SI) for Calculus since the fall of 2013. A direct display of the ABC rates from fall 2005 to spring 2021 only presents fluctuation from semester to semester, and one can hardly deduce that the ABC rates are increasing. In this paper, the "moving average"…

This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors.…

This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student…

Higher education's interest in remedial college coursework and its bumpy impact on student success drove this collaboration between the mathematics department and institutional research at a small, private 4-year university. For first-time freshmen needing math remediation, national research shows that these students struggle with earning required…

Homework completion and self-regulatory ability have both been extensively studied to examine their impact on learning achievement. Moreover, the reciprocal nature of how these two qualities affect one another is also an area of research. While evidence shows that voluntary completion of assigned homework predicts self-regulation in students, a…

The University of Minnesota Talented Youth Mathematics Program (UMTYMP) is a selective, five-year accelerated mathematics program for students in grades 6-12. During the program, students take college mathematics courses on University of Minnesota campuses, starting with algebra and continuing through logic and proofs, linear algebra, and…

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

Using clickers in the statistics classroom can help students identify and understand common errors and misconceptions through a combination of surprise and discussion. Students are presented with multiple-choice questions that they discuss with each other and then vote on; a class-wide discussion follows. Questions for which many students vote for…

Universities have drawn on an assortment of strategies to address the learning challenges and high attrition rates of developmental mathematics students. One of those strategies has been utilizing computer adaptive instruction (CAI) mathematics software. Reports about the efficacy of CAI vary from glowing to unfavorable. This article presents an…

We present a model for professional development of instructional faculty. Though initially conceived for accreditation compliance as a credentialing process for adjunct faculty, this project led to increases in participants' collaboration on lesson design, investment in curricular decisions, and adoption of active learning methods. In this paper,…

Developmental mathematics is often a barrier to student progress and success in college. As a result and for this reason, this research study describes the redesign of a developmental mathematics course at a U.S. East Coast university to decrease the amount of time it takes for students to complete their developmental requirement and increase the…

Cornell University has long offered a Calculus for Life Sciences course. In this case study, we report on how a team of pure mathematicians has modernized both the content and teaching methods of this course. The content went from a standard calculus course with few genuine applications in the life sciences to a course focusing on dynamical…