I have always disagreed with government ministers who assert that it is a good idea to separate teaching from research at the universities. For I believe that with mathematics, research and good teaching go hand in hand. And if we interpret ‘research’ in its widest terms of questioning, discovery, involvement, etc, then I believe that the same holds true at the school level. Mathematics needs to be taught as a vibrant, living subject which challenges the intellect and the imagination, not as a dusty collection of historical facts. Further, asking questions is just as much fun as answering them!

Planarity is a concept that appears in most discrete mathematics courses (in particular, it is a syllabus item in all A level Discrete mathematics syllabuses). I have recently taught a unit in graph theory to a group of BEd students and, when I came to the concept of planarity, I decide to approach it in a different way – through the context of Cabri Géomètre, a dynamic geometry package. In the article I would like to share some of my ideas and reflections on this approach to teaching this topic, paying particular attention to the role of Cabri Géomètre in scaffolding the important ideas involved in an understanding of planarity.

It is common today for students in elementary calculus to possess a powerful graphics calculator, such as the TI-82. These machines have had a dramatic impact on how teachers present the subject. The teacher population is clearly divided when it comes to the emphasis on the use of the calculators. There are instances, though, where it is difficult to argue with the calculator's effectiveness as a teaching tool in calculus. One such case is in using Newton's method to find the roots of an equation, for once the algorithm is presented, it is merely a matter of performing the numerical calculations for the sequence of iterates, and this is an operation that the TI-82 does very well.

On 6 October 1997 NASA plans to launch a space probe named Cassini which, if all goes to plan, will follow a convoluted path which will take it past Venus in April 1998 and again in June 1999 before it repasses close to Earth in August 1999. By then it will have gained enough speed to set out to more distant planets and after passing Jupiter at the end of the millennium (i.e. at the end of the year 2000) it should reach Saturn on 25 June 2004, where it will spend four years studying that planet and its satellites.