Some years ago when I was co-editor of the German periodical Mathematik lehren we decided to prepare an issue on the history of mathematics. To secure the interest of our usual readership, we planned to elaborate a few hints, recommendations, or suggestions on how to include historical items in the ordinary teaching of mathematics in school. It soon became clear however that this methodological problem would be the critical point of our project. It turned out, as I had feared from the beginning, that only a very few of my colleagues could be talked into writing about this feature of the subject. It was easy to get papers on historical facts or on hypothetical developments, but everyone found it hard to write about practical ways of teaching history in the mathematics classroom.

The idea of using history of mathematics in school practice is becoming more and more popular : Arcavi (1987), Steen (1989) and the French experiences described in Fauvel (1990) offer significant examples on tiiis point. At the same time in many works, such as Freudenthal (1981), Arcavi, Bruckheimer and Ben-Zvi (1982 and 1987), the importance of enhancing the teachers' literacy in the history of mathematics is recognised. We agree with this attitude in mathematics education and in the present paper we offer some hints aimed at an activity which may contribute to the renewing of mathematics teaching and, at the same time, may offer teachers stimuli to reflect on historical development of mathematical ideas.

Teaching mathematics has never been easy. There is no reason to imagine that it ever will be. Yet it is still worth asking whether there might not be relatively simple ways of improving our teaching of particular topics and of particular groups of pupils. History of mathematics has much to offer on both counts, and can enrich ordinary teaching in many ways and on many levels. But it also has its problems and its pitfalls. This article focuses on two issues: the temptation to enlist the support of ‘history’ when trying to change social attitudes; and the uncritical way in which intelligent students respond to such pseudohistory.

There are questions which have only personal answers. One such question is the one in the title; another, which is intricately bound up with it, is: Why teach mathematics? On the following pages you will find my personal answers to both questions; a selection of other people's answers to one or both are listed at the end. Much longer lists could be made, and very long ones if one included also papers in other languages than English. As you will see, my list contains papers from different parts of the world and from different times in this century; it seems that many people agree, for different reasons, that one really should teach history of mathematics, but that it has to be said again and again.

This article describes some of my experiences of using the mathematics of the Old Babylonian period in my classes. It will not be a connected account of Babylonian mathematics – for that readers can turn to the excellent and easily available book The exact sciences in antiquity [1] and the article will make little sense unless you have read that book or others like it, or know a little about cuneiform mathematics already. I have got to stress that reading a book like Neugebauer's is the minimum preparation before presenting the material that this article discusses. I have neither the time nor the ability to discuss the context in which these materials should be placed. Indeed, placing these materials into their exact historical context is not really possible: even professional historians do not agree about what might seem to the amateur quite simple matters. So in this article I shall be offering readers some nice resources that I have enjoyed using with classes, I shall discuss how they might be used at various places in the curriculum, and indicate some of my faltering attempts to integrate this material into my pupils' general education.

The title is a section heading from the lovely biography [1] by Florian Cajori of the English mathematician William Oughtred (15647-1660). Though Cajori was writing history he chose his subject and style to give modern readers (of 1916), and especially teachers of mathematics, something to think about.

Oughtred was a fine amateur mathematician and a thoughtful teacher. John Aubrey in his brief lives (quoted in [1p12]) wrote: