In recent years, changes in the Brazilian economic and social scenario have generated a growing demand for higher education in the country. In response to this new context, the federal government launched in 2007 a programme aiming at expansion of the enrolment to public higher education. In such environment of changes, several proposals have…

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…

It is common for freshmen students to enter Calculus I with a wide range of levels of preparation and mastery of background material. In addition, many of the students struggle with the adjustment from high school to college. In an effort to help the students to solidify their understanding of concepts as they progress through the course, as well…

Successful science and engineering programs require proficiency and dynamics in mathematics classes to enhance the learning of complex subject matter with a sufficient amount of practical problem solving. Improving student performance and retention in mathematics classes requires inventive approaches. At the University of Central Florida (UCF) the…

This article presents several of the challenges facing postsecondary mathematics education and describes how the undergraduate Learning Assistant (LA) program has been used as a catalyst to engage faculty and students in redesigning opportunities to learn mathematics. Characteristics of the LA program that have been used to transform introductory…

The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

In this paper we examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce an informal argument and then use this as a basis for constructing a formal proof. The work of students who produce such informal arguments during proving activities was analyzed to distill three…

Mathematical fallacies have an embedded sense of awe and mystery that can be used effectively in a classroom to inspire students to tackle a fallacy and find the "hidden" violation. In doing so, the student may discover the consequence of a rule violation in a stimulating manner, thus making a lasting impact of the rule as well as providing the…

We present the quotient rule version of integration by parts and demonstrate its use.

Those who come to Cambridge soon learn that the fastest route between Harvard and MIT is by the subway. For many students, this short ride is a quick and easy way to link physics and calculus. A simple, homemade accelerometer provides all the instrumentation necessary to produce accurate graphs of acceleration, velocity, and displacement position…

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…

We began by observing a variety of properties related to the tangent and normal lines of three conic sections: a parabola, an ellipse, and a hyperbola. Some of these properties include specific relationships between the x- and y-intercepts of the tangent and normal lines. Using these properties, we were able to form several differential equations.…

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting students' postsecondary success as STEM majors. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. In the present study, the connections…

Existing research on limits documents many difficulties students encounter when learning about the concept. There is also some research on teaching of limits but it is not yet as extensive as the research on student learning about limits. This study explores the discourse on limits in a beginning-level undergraduate calculus classroom by focusing…