A teacher can make a great deal out of some of the questions which pupils and friends put to him from time to time. In an article in Mathematics in School a few years ago [1] I listed a number of such questions and discussed one, which involved a geographical application of matrices, in detail. The present article continues this theme, but its main aim is to stimulate discussion of the place of “mathematical modelling” in the curriculum. For it is felt by some that, in spite of the opportunities offered by (say) linear programming, mechanics and probability, insufficient emphasis is placed on modelling in the secondary school. It has been said too that we have not been notably successful in finding good applications of topics new to our syllabuses and incorporating them into our teaching [2].

During my year as President of The Mathematical Association the government began a review of the curriculum across all subjects taught in school. Given the constant tinkering with the education system by every government, this is probably a sentence that any MA president could write during their tenure. But 2013 saw government really trying to layout their vision for what education should deliver in the coming decade.

In English, an aim of the curriculum review is to develop a student's love of literature through widespread reading for enjoyment. Students will get to read Shakespeare, romantic poetry, the great novels of the nineteenth century together with seminal works of world literature. It is hoped that this will expose students to the great works of literature and allow them to acquire an appreciation of ‘our rich and varied literary heritage’ [1, p. 13].

In science, by building on fundamental ideas and concepts, the curriculum review aims to foster in students ‘a sense of excitement and curiosity about natural phenomena’ [1, p. 99]. Students will study the fundamental mechanics of the cell, learn about stem cells, photosynthesis and genomics; they will be exposed to radiation (in a theoretical sense) and the evidence for the Big Bang. Such fundamental ideas will give students the scientific knowledge to be able to understand the uses and implications for the impact of science on society.

The following treatment is perhaps easier than, and is in son respects an expansion of, that given by Professor H. F. Baker in h Principles of Geometry, vol. ii, pp. 58-60.

1. A,B,C,O are four given points ; AO meets BG in D, BO meet CA in E, CO meets AB in F. Then DEF is the diagonal point triangle of the quadrangle ABCO. Take this as triangle of reference for areal coordinates and let O be (u, v, w). Then A is (-u, v, w) B is (u, - v, w) and C is (u, v, -w).

For many years candidates (and teachers) involved in A-level work have quoted Newton’s experimental law of restitution as one of the principles enabling collision problems to be solved. It had always seemed to me that it is fortunate that such a simple law holds and also that it is a great pity that there is no simple relationship between the initial and final kinetic energies. Recently, however, I realised that, viewed in terms of invariance, the law is not at all surprising and also that there is a very simple way of dealing with the loss of kinetic energy.

Ladies and Gentlemen,

There are many different forms of Presidential Address. To glance back at those delivered to this Association is at once an exhilarating and a humbling procedure. Indeed, at one stage during it I toyed with the notion of filling this session with an amalgam of abstracts. You might have been better served had I done so; as it is I shall be quoting from three only and the reasons for that particular selection should become apparent before long.