Students' proof abilities were explored in the context of an inquiry-based learning (IBL) approach to teaching an introductory proofs course. IBL is a teaching method that puts the responsibility for proof on students and focuses on student discussion and exploration. Data collected from each of the 70 participants included a portfolio consisting…

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

This paper reports on mathematics remediation efforts at a public 4-year institution. Specifically, it describes redesign efforts that led to the implementation of co-requisite mathematics remediation. Data on this program were collected and analyzed with respect to completion rates, length of time to earn college mathematics credit, and factors…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or…

In this study we aimed to understand who was struggling in freshman calculus courses, and why. Concentrating on the Fall sections of the class, the best predictors for success (R[superscript 2] = 0.4) were placement test results, the student's own appraisal of the quality of mathematics teaching they received in high school, and the Motivated…

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…

In the mid-1990s, Mercer University's undergraduate schools placed incoming freshmen in their first mathematics course, using only their scores on the mathematics portion of the SAT (SATM). This placement policy was strongly supported by the admissions office because it did not require additional testing of the freshmen in their on-campus summer…

Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during…

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Recent "math wars" have drawn attention to how well various high school mathematics curricula prepare students for college-level mathematics. The purpose of this study was to investigate the relationship between the high school mathematics curricula and students' post-secondary mathematics placement recommendation, specifically how…

When thinking of models for sinusoidal waves, examples such as tides of the ocean, daily temperatures for one year in your town, light and sound waves, and certain types of motion are used. Many textbooks [1, p. 222] also present a "Ferris wheel description problem" for students to work. This activity takes the Ferris wheel problem out of the…

Teaching preparatory mathematics to first-time college students--who come from economically impoverished high schools that have not prepared their students to do college level mathematics--can be a daunting task for teaching assistants (TAs). The preparation of TAs to assist such students in the mastery of mathematical content is a complex…

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…

Remediation of incoming college freshman students is a national concern because remediated students are at higher risk of failing to complete their degrees. Some Oklahoma higher education institutions are working to assist K-12 systems in finding ways to reduce the number of incoming college freshman students requiring remediation. This study…