Poincaré, dans sa conférence prononcée au Musée pédagogique de Paris en 1904, déclarait déjà qu'ily avait lieu de penser en dérivées non en différentielles. II me semble utile pour l'enseignement de se conformer résolument à ce principe et d'abandonner les explications assez compliquées qui sont classiquement données sur le symbole d. Pour la différentielle premiére, passe encore : Je puis comprendre l'égalité accroissements infiniment petits.

Take a look at the ‘string’ (or finite sequence)

6,2,1,0,0,0,1,0,0,0.

Count the occurrences of the numbers:

Notice that the bottom row is the string we started with! In fact the above string is the unique answer to the popular question (posed, for example, in a recent edition of the Trans World Airlines magazine, The Ambassador, August 1978) to find a string

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.

There is no need to recommend to teachers in this country, familiar with Dobbs’ School Course and with later books of the same tendency, the free use of the ideas of displacement, rotation, and reflection. In the course of a paper read at the Zürich Congress last year, Prof. Thomsen, of Rostock, gave some striking examples of the effective introduction of the language and notation of the theory of groups into work of this kind, and afterwards he agreed willingly to contribute to the Gazette an article on the subject. For applications to their own problems we must refer readers elsewhere, since Prof. Thomsen has paid them the compliment of explaining a point of view that would be quite unsuitable in the school. To some of our readers we must apologise for replacing the original article by a translation, but since there are no familiar symbols or recognisable formulae to facilitate the grasping of a novel theory, we think that a substantial minority will be grateful for this assistance. In making his version, Prof. Neville has taken one or two liberties with the author’s notation.

The crisis in applicable maths for schools

In the first paper in this series I remarked that there have been three successive paradigms which have dominated school mathematics since 1960: three “eras” of predominant pedagogy –“traditional” maths, “new” maths and “applicable” maths. The main theme of the first paper was, however, that the new degree of involvement of school mathematics with applications – which came about as a result of the third paradigm – can hardly be unlearned. It will be very difficult, if not impossible, to disengage from paradigm 3. Society is most unlikely ever to let school mathematics revert to a condition of explicit, high-academic, mandarinstyle leadership, whether of the traditional pure mathematics or the modem pure maths allegiance. Yes, the third paradigm looks as if it may be beginning to falter, but the reason, I suggest, is that we are not getting the full pedagogic benefit from the particular genre of applications we are using, and from the particular style of application-mindedness we are building into our teaching.