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…

Teachers often promote care in doing calculations, but for most students a single mistake rarely has major consequences. This article presents several real-life events in which relatively minor mathematical errors led to situations that ranged from public embarrassment to the loss of millions of dollars' worth of equipment. The stories here…

In the context of a department of applied mathematics, a program assessment was conducted to assess the departmental goal of enabling undergraduate students to recognize, appreciate, and apply the power of computational tools in solving mathematical problems that cannot be solved by hand, or would require extensive and tedious hand computation. A…

A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill…

We describe a college math course and summer research project in which students used their math skills to analyze sustainability issues on campus and in the wider community and how these projects contributed to bringing about change in the community. Staff members at the college played an important role in developing and supervising the student…

In the Fall semester of 2009, I taught a first-year course that focused on skills required to successfully complete undergraduate research. This paper will discuss the Simpson College first-year course requirements, my course goals, the graph theory topics covered, student feedback, and instructor reflection.

Over the last four years of the senior capstone seminar at Western Carolina University, we have redesigned the course substantially to comply with our institutional Quality Enhancement Plan for engaged student learning and to follow the guidelines proposed by the Mathematical Association of America's Committee on Undergraduate Programs in…

We discuss a mathematics capstone course designed to help students grow in mathematical independence. We describe how the course is structured to support this goal and the major assignments: a course wiki, a group expository project, and an individual problem to solve and extend. Students learn to ask and answer their own questions, helping them…

Constructivism is currently a hotly debated topic, with proponents and opponents equally adamant and emotional with respect to their viewpoints. Many misconceptions exist on both sides of the debate, and misuses of terminology and attribution are rampant. Constructivism is a theory of learning, not a particular approach to instruction and not a…

This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…

Studies show that more students fail or withdraw from college mathematics courses than any other. To address this concern, the Mathematics Department at the University of North Dakota opened its Mathematics Learning Center (MLC) in the fall of 2000. In this study, the effectiveness of the MLC and the free tutoring offered for students in freshman…

This article reports on an innovative approach to teaching Calculus I which was initiated in a two-semester course designed for students at risk of failing Calculus I. The treatment consisted of voluntary oral assessments offered before every written examination. Analyses showed that the treatment students did significantly better than the control…

In education theory, Bloom's taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is…

We describe our approach to incorporating a civic engagement component into a quantitative literacy (QL) course and the resulting gains in student learning, confidence, and awareness of local civic issues. We revised the existing QL course by including semester-long group projects involving local community issues that students could investigate…