Polynomials with rational roots and extrema may be difficult to create. Although techniques for solving cubic polynomials exist, students struggle with solutions that are in a complicated format. Presented in this article is a way instructors may wish to introduce the topics of roots and critical numbers of polynomial functions in calculus. In a…

Our students experience difficulties in working on non-routine mathematical problems. They cannot see the general through special things or instead see things that are special through common things when dealing with mathematical concepts and examples. They cannot see the essential features of the way or recognize it when presented in various…

Over the past 10 years, the authors of this paper have implemented a series of project-based and inquiry-based learning initiatives in the calculus sequence at our institution. These initiatives took place in a department with an existing strong culture supporting teaching innovation and improvement. In this paper, we describe three initiatives in…

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 study consisted of two stages. In stage A, 38 students were divided randomly into an experimental and a control group. The experimental group received lectures assisted by dynamic geometry software (DGS) and the control group received lectures using chalk and blackboard. The effects of DGS on metacognition and its components were…

Improving students' performance in Calculus is a challenge for many colleges and universities. One way of improving students' performance as well as their metacognition and study skills is to provide opportunities for them to receive support outside of the lecture. A modified version of the Motivated Strategies for Learning Questionnaire (MSLQ)…

To remain competitive in a global economy, it is important that institutions of higher education provide equitable teaching practices to support female students in STEM (Joseph et al., 2017). Despite this need, teacher-centered teaching practices in calculus courses have become a roadblock for female students passing the course and STEM degree…

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear…

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the…

The purpose of this dissertation is to investigate the relationships between student persistence and students' attributes or perceptions of instructional pedagogies, as well as to examine whether the identified relationships are moderated by three different instructional settings. Improving student persistence in science, technology, engineer, and…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

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…

Investigations into attrition of STEM-intending students indicate that poor experiences in introductory courses are at least partly to blame, specifically the students' frustration with lecture-driven teaching methods. In this research, hierarchical linear modeling is used to identify the individual and situational characteristics of instructors…

Recent years have seen a resurgence of interest in using virtual reality (VR) technology to benefit instruction, especially in physics and related subjects. As VR devices improve and become more widely available, there remains a number of unanswered questions regarding the impact of VR on student learning and how best to use this technology in the…