Suppose that we open a telephone directory and select any column which consists entirely of personal names. The last digit of each telephone number would seem to have no preferred value. For example, the middle column on p. 417 of the 1970 Newcastle upon Tyne directory contains 109 names, and the frequencies for 0,1,…, 9 are as follows.

A few years ago, an experiment was made at Marlborough (1) to begin the teaching of statistics with a discussion of rank correlation because “within a few periods and without any complicated arithmetic, it was possible to discuss the main items in a statistician’s philosophy”. What I want to do in this article is to show how the same can be done with one of the commonest situations in elementary statistics, when we wish to compare populations from which two samples are drawn and decide whether one is “better” than the other. In the classical approach, this is often done by Student’s t test which is highly sophisticated compared with the Mann-Whitney U test, to which I now turn.

This article does not advocate dispensing with the calculus in the least; it suggests ways in which some of the traditional problems of calculus may be studied by other methods much earlier in the school. This makes a range of very interesting problems available to a much wider audience, and also shows how some of the problems of the sixth form science course can be treated with pupils who have the misfortune to be studying science without the calculus to help them.

Every triangle can be used to tile or tessellate a plane because the 3 angles add up to 180° and so can be arranged to form a straight line. In a similar way every quadrilateral will tessellate because the 4 angles can be grouped round a point.

The aim of this paper is to illustrate developments in the teaching of mathematics of its day; emphasising, when reasonable, lines of succession. The concentration is on English teaching over the past 350 years although this is developed from its European context. The paper concerns itself with teachers rather than teaching and is intended as a modest reminder of our lineage. Much is owed to Professor Taylor’s two books on the Mathematical Practitioners, and not a little to my own Gazettes.

The article by Margaret E. Baron on the historical development of logic diagrams (The Mathematical Gazette, LIII, May 1969) aroused my interest in the infeasibility of drawing a diagram extendable to n classes. The difficulty of following Venn’s suggestion of a comb-like structure is shown in the complexity of drawing such a diagram for five classes.

Professor Geoffrey Matthews has described the scheme emanating from Ridgewaye School, Southborough, Kent, as a “Disaster Kit” and has asked me to write a description of it. This I gladly do because I am not sure about the title he has bestowed on it and you are invited to title it yourself when you have read my notes.

In any consideration of the Open University it is as well to recall the words of Lord Crowther its Chancellor. He said “We are open first as to people…. We took it as axiomatic… that no formal academic qualifications would be required for registration as a student. Anyone could try his or her hand and only failure to progress adequately would be a bar to continuation of studies…. We are open as to methods…. Every new form of human communication will be examined to see how it can be used to raise and broaden the level of human understanding…. We are open finally to ideas.”

It is dangerous to generalize from unique experience, but the season of examination results is round again. Apart from the annual surprises, the ranked order is much as our departmental meetings predicted. The range of marks is similar and the percentage qualifying to proceed to Part II of the B.Ed, degree is of the same order. No one failed, but the tail is as abysmal as in previous years. These “tail” students are perhaps the most important ones, for they will teach over a wide band of education: the spectrum may start at the reception class in an infants school and end in the higher forms of a secondary or comprehensive school. Ability as a teacher doesn’t necessarily correlate with skill as a mathematician, but the quality of their contribution is questionable. So in this summer season efforts are again directed towards finding reasons for comparative failure.