It seems self-evident that there is a significant gap between secondary school and university mathematics, even though the gap may take different forms, which vary with different education systems in different places and at different times. This paper attempts to capture some common forms of this gap, and in particular, it discusses some core…

Current e-learning environments are ill-suited to college mathematics. Instructors/students struggle to post diagrams and math notation. A new generation of math-friendly e-learning tools, including WebEQ, bundled with Blackboard 6, and NetTutor's Whiteboard, address these problems. This paper compares these two systems using criteria for ideal…

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's…

The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…

We report on implementations of online homework systems at two moderately-sized state universities. These implementations were created with the intention of supporting student engagement outside of the classroom by mimicking the attempt-feedback-reattempt sequence of events which often occurs in a teacher's presence. Evidence is presented which…

This study investigates students' experiences of group work, in mathematics, at both school and university, along with their current attitudes towards group work. Three groups of students from different universities were involved, and data was gathered using a questionnaire and semi-structured interviews. Results revealed some significant…

Diagnostic testing in mathematics has become a favoured tool at many universities. In this paper we report on a novel method of diagnostic testing which incorporates a paired question approach, with two questions being set on each of 20 different topics. It was introduced at Loughborough University for use with first year engineering students in…

College students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort assignment containing 18 long three-digit ? two-digit (3?2) multiplication problems with all numerals in each problem being equal to or greater than four and a moderate-effort assignment that contained nine long problems and nine…

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…

This note, which is based on a final year project for a BSC degree, presents an investigation on the Olympic decathlon. It shows that the existing non-linear transformation which is used to assign points to athletes' performance gives practically identical results to that of a simpler linear one. In addition, the paper presents evidence to support…

Since 1959, ACT has collected and reported data on students' academic readiness for college. Because becoming ready for college is a process that occurs throughout elementary and secondary education, measuring academic performance over time in the context of college readiness provides meaningful and compelling information about the college…