We share results from a quasi-experimental study in which we compared achievement between traditional face-to-face and computer-based sections of Intermediate Algebra on a common multiple choice exam as well as performance on open-response tasks. Students in the computer-based group performed better on the final exam and were also more likely to…

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer…

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Increased importance is being placed on statistics at both the K-12 and undergraduate level. Research divulging effective methods to teach specific statistical concepts is still widely sought after. In this paper, we focus on best practices for teaching topics in nonparametric statistics at the undergraduate level. To motivate the work, we…

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

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 article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

The inverted classroom is a course design model in which students' initial contact with new information takes place outside of class meetings, and students spend class time on high-level sense-making activities. The inverted classroom model is so called because it inverts or "flips" the usual classroom design where typically class…

History of math courses are commonly offered in mathematics departments. Such courses naturally lend themselves to writing assignments, and a growing body of research supports writing as a means to learn mathematics. This article details two such assignments, providing an overview of the course in which they are situated, and a student-led…