The aim of this paper is to present a simple way of establishing the general solution of the linear, second-order differential equation without using complex numbers.

The number of students studying for A and AS level Further Mathematics has fallen dramatically since the early 1980s. Explains this decline and why it is vital that Further Mathematics be saved. Outlines the Gatsby-funded MEI project 'Enabling Access to Further Mathematics' which aims to show that distance learning using modern technology can…

Explores the derivation of empirical models for the stopping distance of a car being driven at a range of speeds. Indicates that the calculation of stopping distances makes an excellent example of empirical modeling because it is a situation that is readily understood and particularly relevant to many first-year undergraduates who are learning or…

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Observes four groups of mathematics undergraduates carrying out a mathematical modeling exercise of a familiar physical process (the cooling of a cup of hot water). Indicates that students neither took the time to reflect upon the physical process nor to reflect on the appropriateness of the model they produced. Recommends that classroom…

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Focuses on the use of the Internet to deliver resources directly to the secondary school teacher that can be used in the teaching of geometry and which requires a minimum of learning on the teacher's part. Considers the credibility, richness, and value of such resources. (MM)

Recounts the experiences of faculty members as they addressed some of the challenges presented in choosing and integrating a new technology, the TI-89 hand-held computer algebra system (CAS), into the core mathematics curriculum. Relates in detail deciding which instrument to choose, instructing students to use the technology, affecting the…

Examines the impact of a school-based assessment system on the implementation of an applications/modeling-based curriculum at the senior secondary level. The persistence of high task scaffolding in assessment tasks throughout the course and the concerns of teachers about the reliability and ownership of assessment in unsupervised conditions…

Investigates problems of modeling and application based on a paradigmatic case study of a classroom situation in which students deal with functions within a computer-aided learning environment. Analysis of the case study shows that computer-supported operating with functions as objects does not automatically lead to a better understanding of the…

Demonstrates the importance of expanding notions of learning beyond knowledge to the practices in mathematics classrooms. Considers a three-year study of students who learned through mathematical modeling. Shows that a modeling approach encouraged the development of a range of important practices in addition to knowledge that were useful in real…

Discusses a research tool that has the potential to identify a student's development in mathematical modeling, gauge the effectiveness of adopted teaching styles, and enhance learning. Reports on pilot applications of a questionnaire at two universities in the UK. Discusses the construction and testing of the research instrument and considers…

This article analyses the modeling approach used by one student in a business problem. It is argued that if we use previous frameworks we are not able to classify the students' approach to modeling as purely theoretical or empirical. Instead the student used a theoretical approach when constructing a real model, but abandoned it when she had to…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

Several Excel applications are presented which are part of the syllabus in the first semester of engineering studies at Haugesund College. The aim of the applications is for the students to acquire both computing skills and mathematical understanding at the same time. The applications cover numerical solution of equations, differentiation,…