Research with first year engineering students on an extended programme at the University of Pretoria indicates that competence in mathematics can be enhanced through academic support that combines the development of mathematical and non-mathematical skills. This paper investigates the effect of this approach on students' performance in mathematics…

At their final exam in linear algebra students at the author's university were given the possibility to choose between two types of proofs to be done. They could either prove two short statements by themselves or they could explain four steps in a given proof. This paper reports on investigations of students' responses to the choice option…

It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that…

"Imagine a tenth of a mile of river front with an unbroken line of trees with fireflies on ever leaf flashing in synchronism. ... Then, if one's imagination is sufficiently vivid, he may form some conception of this amazing spectacle." So wrote the naturalist Hugh Smith. In this article we consider how one might model mathematically the…

Combinatorial identities are proved by counting the number of arrangements of a flagpole and guy wires on a row of blocks that satisfy a set of conditions. An identity is proved by first deriving and then equating two expressions that each count the number of permissible arrangements. Identities for binomial coefficients and recursion relations…

We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.

The fraction 10000/9801 has an intriguing decimal expansion, namely 1.02030405... In this paper, we investigate the properties of this fraction via an arithmetical approach. The approach also yields a class of fractions whose decimal expansions involve higher-dimensional analogues of the integers, the n-dimensional pyramidal numbers, thereby…

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

This paper describes 25 National Science Foundation supported projects that have innovations designed to improve education for students majoring or minoring in statistics. The characteristics of these projects and the common themes which emerge are compared with the American Statistical Association's (ASA) guidelines for developing statistics…

In this article we discuss an approach to the critical problem of student retention and the high school-college transition. The context of the discussion is centered on science and engineering students for whom calculus in the first year in college is an essential requirement for on-time graduation. This transition/retention problem has become…

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

This article presents questions and answers about ACT's College Readiness Benchmarks. ACT's College Readiness Benchmarks are the minimum ACT test scores required for students to have a high probability of success in credit-bearing college courses--English Composition, social sciences courses, College Algebra, or Biology. Colleges can use the…

Effectiveness was operationalized as a combination of successful developmental course completion, high student satisfaction at the end of the course, and high academic achievement in a subsequent college-level math course. Instructional methodologies were similar to the extent that the instructional delivery systems allowed. With a sample size of…

Teaching mathematics in real-word contexts is a strategy to make math relevant for undergraduate students. However, very little research exists on students' methods of integrating contextual and mathematical knowledge through writing. This study uses an interdisciplinary writing assignment to investigate the relationship between students' written…