Developmental education has the mission of enabling underprepared students to acquire the capabilities necessary for college success. A growing number of research studies document its failure, however; specifically, approximately two thirds of community college students referred to a remedial mathematics sequence do not complete it. In response to…

The need for universities to achieve excellence in the services they provide has been the subject of research for several decades. The idea of involving students and recognizing the importance of their opinions has led to the creation of various models and tools. This paper focuses on teaching, a central service from which improvement actions of…

A mathematical theory of peer instruction describing the increase of the normalized number of correct answers due to peer discussion is presented. A simple analytic expression is derived which agrees with class data. It is shown that our theory is connected to the mathematical learning models proposed by Pritchard et al. It is also shown that…

Note-taking is a widespread practice used by college students to record information from lectures. Unfortunately, even successful students' notes are incomplete and, therefore, may lack the potential to positively impact their academic performance. Research suggests that instructors can help students improve their note-taking skills by using…

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

The purpose of this study was to determine if course format significantly impacted student learning and course completion rates in an introductory statistics course taught at Harford Community College. In addition to the traditional lecture format, the College offers an online, and a hybrid (blend of traditional and online) version of this class.…

We state and prove the methods of False Position (Regula Falsa) and Double False Position (Regula Duorum Falsorum). The history of both is traced from ancient Egypt and China through the work of Fibonacci, ending with a connection between Double False Position and Cramer's Rule.

This article explores the time it takes for a liquid to drain from a cylindrical container through a hole in the bottom. Using dimensional analysis and some thought experiments this time is determined and Torricelli's law derived as a consequence. Finally, the effect of pouring liquid into the container as it drains is considered.

The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

A multi-stage pre/post testing scheme is developed to gauge course effectiveness using gain and loss components of normalized change. The components, unlike normalized change itself, can be used to distinguish courses that promote acquisition as well as retention of information from courses that promote acquisition at the expense of retention or…

The mathematics placement process at the University of Northern Colorado includes brief faculty-student interviews, during which faculty members suggest mathematics courses for students in their first year at the university. Data from a sample of 1466 students admitted in the fall of 2007 were analyzed to assess the effectiveness of the placement…

This paper gives results of a study on a Personal Response System (PRS). Three sections of college algebra are compared; one section used PRS and PowerPoint, one used PowerPoint, and one was considered a control. Students were given a pretest and posttest with a retired version of a mathematics ACT test, and all students gained an average of one…

This is a preliminary study of (community) college mathematics instructors. Through interviews of twelve instructors we explore each individual's educational background and path to the college, as well as his/her preparation for and feelings about teaching. The purpose of this study is to add to the emerging research on college mathematics…

We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This…

Two related themes currently dominate discourse on open-access colleges, particularly community colleges: increasing college-going and degree attainment and improving the performance of postsecondary institutions with respect to producing graduates. Largely missing from this discourse, however, is cogency concerning the innumerable ways in which…