Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…

The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…

This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)

The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form y = u[subscript 1]y[subscript 1] + u[subscript 2]y[subscript 2], a sum of function products using solutions to the homogeneous equation y[subscript 1] and…

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

This study investigates the effects of applying an inverted classroom model in a second-semester calculus course at a large regional university in the southwest during the Spring of 2013. The sample consisted of four class sections with the same instructor, with a total of 173 students; two class sections were in the experimental group, whereas…

Traditionally, research on technology in mathematics education focuses on interactions between the user and the technology, but little is known about how technology can facilitate face-to-face interaction among students. We will explore the role that iPads versus traditional laptops play in shaping the learning spaces in which students explore…

This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

In this article I use Sfard's theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point…

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Over a period of six years, three different types of recitation sessions were implemented into the large enrollment section of a college calculus course. During the fall semesters, the results on the departmental final examination, the DFW rates, and the one-year retention rates of students as STEM majors were examined by the type of recitation…

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…