The number of students continuing with their mathematics education post GCSE level has declined in recent years and hence students entering Engineering degrees are reducing. The University of Birmingham recognized this problem and introduced the Suite of Technology programme (STP) which no longer requires students to have A-level mathematics.…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

In the last 25 years, A-level Mathematics syllabi have changed very considerably, introducing a broader range of application areas but reducing the previous emphasis on classical mechanics. This article describes a baseline survey undertaken to establish in detail the entry levels in mechanics for the cohort of students entering Engineering…

This article presents an example of skimming and skipping stone motion in mathematical terms available to students studying A-level mathematics. The theory developed in the article postulates a possible mathematical model that is verified by experimental results.

In the past 6 years changes have occurred in GCE A-levels. In particular, there have been several major changes in A-level Mathematics courses. As engineering students are usually required to have studied A-level Mathematics, or its equivalent, these changes have had an effect on their prior mathematical knowledge. Moreover, engineering students…

Knowing the mathematics relating to a problem is one thing, but producing a tool to solve a practical example is often daunting. This article describes a case study which presented an interesting implementational challenge.

Several proofs demonstrating that there are infinitely many primes, different types of primes, tests of primality, pseudo primes, prime number generators and open questions about primes are discussed in Section 1. Some of these notions are elaborated upon in Section 2, with discussions of the Riemann zeta function and how algorithmic complexity…

This article describes pedagogic issues in setting objective tests in mechanics using Question Mark Perception, coupled with MathML mathematics mark-up and the Scalable Vector Graphics (SVG) syntax for producing diagrams. The content of the questions (for a range of question types such as multi-choice, numerical input and variants such as…

Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…

This article presents an investigation carried out with a group of able mathematics students who were studying at a level 1 year in advance of their peers. The purpose was to investigate the extension of usual three peg Towers of Hanoi to four pegs and attempt to find a rule that could be used to predict the minimum number of moves required to…

There are increasing concerns about the mathematics ability of students entering higher education. This situation appears to be as a result of the perceived lowering standards of A Levels, a reduction in entry requirements on some courses with a strong mathematical component and the wide-ranging educational backgrounds of many of the students.…

It has been reported that the students' level of mathematics when entering university has changed in recent years. A surprising number of students struggle with mathematics or have a mathematics anxiety. Although this was widely reported within the UK, there was some uncertainty if colleagues in other countries were experiencing the same…

A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…

Some interesting and unusual loci are generated by a familiar mechanical system.

This article looks at the question of whether and how a geometrical cube may be determined as the solution set of a single equation. Beyond this being an interesting and surprising result for upper high school and first year college students, we argue that, as an investigative activity, it has value in refining students' images of what solutions…