In this study, we evaluate an innovative method to improve the teaching of linear algebra. The use of peer instruction in conjunction with a seminar strategy and supported by didactic engineering is proposed as a means to facilitate the mastery of abstract concepts, the undertaking of innovative research in problem solving, and the practical…

Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K-12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra…

As higher education institutions focus on increasing mathematics success, it is important to consider the experiences and needs of structurally disadvantaged identities. In this article, an asset-based framework was used to examine how eight first-generation, low-income, Students of Color perceive their mathematics placement experience. Although…

The purpose of this article is to provide a deeper understanding of the natural rhythm of a typical semester, as observed in students' reflections in journals kept during the semester. Our analysis of students' writings rendered a breakdown of the semester into four distinct periods that were independent of the particular semester or section the…

The emergence of non-Euclidean geometries in the 19th century rocked the foundations of mathematical knowledge and certainty. The tremors can still be felt in undergraduate mathematics today where encounters with non-Euclidean geometry are novel and often shocking to students. Because of its divergence from ordinary and comfortable notions of…

In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…

Florida Atlantic University implemented a number of changes in the College Algebra course in an attempt to improve student success. We summarize these changes, and how they have affected the course. We also discuss possibilities for future improvements. (Contains 3 figures and 1 footnote.)

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…

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

During the last two years we have developed a precalculus course customized around biology by using the scientific method as a framework to engage and motivate biology students. Historically, the precalculus and calculus courses required for the Suffolk County Community College biology curriculum were designed using examples from the physical…

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

Games are a useful and fun way to review material in class, and encourage students to actively participate in review sessions. In fact, researchers have concluded that playing games can be an effective learning tool, especially in mathematics, in situations where the goal is to reinforce specific ideas or concepts. Two places this type of…

This study reports the effects of an integrated instructional program (the Keystone Method) on the students' performance in mathematics and reading, and tracks students' persistence and retention. The subject of the study was a large group of students in remedial mathematics classes at the college, willing to learn but lacking basic educational…

The careful use of notation and language in the statement of both the definitions and problems of calculus can begin the process of making students mathematically literate while allowing them to enjoy working on challenging problems and applications without the aid of numerous examples. Engaging the students to participate in the precise use of…

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)