Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

At Binghamton, Calculus 1 is taught to over 1000 students each fall in sections of about 30-40 students, with graduate student instructors teaching most sections. Despite having small classrooms instead of lecture halls, the satisfaction and performance of students has historically been poor. We had hoped to improve student success by changing how…

The art of teaching freshmen students is undergoing a rapid paradigm change. Classical forms of teaching are not applicable any more and an unmanageable offer of new multimedia tools and concepts is glutting the market. Moreover, compared to previous courses, the class size triples. In view of these challenges, we implemented a new teaching…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students' strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students…

This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…

A hands-on activity can help multivariable calculus students visualize surfaces and understand volume estimation. This activity can be extended to include the concepts of Fubini's Theorem and the visualization of the curves resulting from cross-sections of the surface. This activity uses students as pillars and a sheet or tablecloth for the…

We generalize a standard example from precalculus and calculus texts to give a simple description in polar coordinates of any circle that passes through the origin. We discuss an occurrence of this formula in the context of medical imaging. (Contains 1 figure.)

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

Peer-led Team Learning (PLTL) is an instructional method reported to increase student learning in STEM courses. As mathematics is a significant hurdle for many freshmen engineering students, a PLTL program was implemented for students to attempt to improve their course performance. Here, an analysis of PLTL for freshmen engineering students in…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Colleges and universities remain attentive to developing and supporting ways to foster student academic success. These efforts have taken on more importance as student success, commonly measured by student learning achievement, has failed to meet expectations. For colleges and universities, the flipped classroom represents a student-centered…

This paper presents instructive interdisciplinary applications of constrained mechanics calculus in economics on a level appropriate for undergraduate physics education. The aim of the paper is (i) to meet the demand for illustrative examples suitable for presenting the background of the highly expanding research field of econophysics even at the…