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…

The golden ratio, one of the most beautiful numbers in all of mathematics, arises in some surprising places. At first glance, we might expect that a General checking his troops' progress would be nothing more than a basic distance-rate-time problem. However, further exploration reveals a multi-faceted problem, one in which the ratio of rates…

In a college algebra course that used flipped/inverted pedagogy, students achieved learning outcomes at a significantly higher rate, as evidenced by results on the final exam. At the same time, student perception on a number of measures decreased significantly, including how interested students were in the course and whether the instructor…

Flipped learning is gaining traction in K-12 for enhancing students' problem-solving skills at an early age; however, there is relatively little large-scale research showing its effectiveness in promoting better learning outcomes in higher education, especially in mathematics classes. In this study, we examined the data compiled from both…

One of the many roles of two year community colleges in the United States is to bridge the gap between secondary school and college for students who graduate from high school with weak mathematics skills that prevent them from enrolling in college level mathematics courses. At community colleges remedial or developmental mathematics courses review…

The QEP that was implemented in this study focused on enhancing students' critical thinking skills. A pretest/posttest approach was used to assess students' critical thinking progress in freshman level core English and Math courses. An intervention was performed involving intensive instruction and assignments relating to a set of reasoning…

A variety of computerized interactive learning platforms exist. Most include instructional supports in the form of problem sets. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially to fully worked examples. Behind-the-scenes design of such systems varies as well --from static dictionaries of…

The purpose of this study was to compare student performance in online and traditional classroom based developmental math courses at Texas community colleges. This study specifically examined: (a) student performance in both delivery methods, (b) students who successfully completed the developmental math course, and (c) student performance in the…

Many technologies have changed the way individuals live and learn. Google Inc. has played significant roles in business and academic worlds. Google Apps for Education and Google Classroom have been offered to higher institutions around the globe. Although large cloud service provider such as Google do not encrypt all their stored electronic data…

This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

Office hours provide time outside of class for students to consult with instructors about course material, progress, and evaluation. Yet office hours, at times, remain an untapped source of academic support. The current study examined whether office hour attendance in combination with a learning reflection would help students learn material in an…

Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task…

In 2003, accreditation standards were revised to require coverage of management science (MS) after previously removing it in 1991. Meanwhile, increasing awareness of the value of business analytics stimulated a renewed interest in MS. To examine its present status in undergraduate core business curricula, the authors conducted two studies to…