BSHM Bulletin Volume 25 Number 3 (2010)
The aims of the British Society for the History of Mathematics (BSHM) are ‘to promote research into the history of mathematics and to encourage its use at all levels of mathematics education.’ While BSHM encourages a wide range of research, there has always been a place for the use of history in mathematics teaching and in the 1990s especially the society ran a series of very successful conferences on the theme of history in mathematics education (HIMED). In 2004 the society’s Newsletter metamorphosed into a more professional journal, the Bulletin and from 2006 was published by Taylor & Francis, with Jacquie Stedall as editor. The first Taylor & Francis issue (volume 21, number 1) contained feature articles on mathematical textbooks and thus exemplified the society’s interest in the teaching of mathematics. The range of articles in the Bulletin is quite astonishing as much in wide historical periods and civilisations as in the spread of mathematical topics. The articles in the most recent issue, volume 25, number 3, all written by teachers, will give a flavour of what the Bulletin has to offer.
Kathleen M Clark’s article Connecting local history, ancient history and mathematics is both an example of how local history can inspire classroom mathematics and an example of producing usable classroom material from ancient mathematics, here using Babylonian cuneiform tablets. The link with the past is intriguing and described in more detail in an earlier article by Clark and Eleanor Robson (BSHM 23-3, 2008). Twenty-five clay tablets, mostly Ur III administrative records (late third millennium BCE), are held at Florida State University. They came into the possession of the university’s forerunner, Florida State College for Women, in 1922 having been purchased from a dealer. Nothing seems to have been done with the collection and Clark happened to notice one of the tablets displayed in a cabinet. Eleanor Robson agreed to examine the texts and a catalogue of all twenty-five tablets appears in Clark & Robson (BSHM 23-3, 2008). There is also a full transcription by Robson of FSU 22, which is an account of agricultural labour, as well as a description of the context. Clark has since worked with elementary school teachers to prepare classroom materials based on the FSU tablets. In the BSHM Bulletin 25-3 she describes some mathematics lessons where the teachers and their students used the information from the tablets to work on problems such as: ‘A field is 2 bur and it must be harrowed three times. When one eshe is ploughed per day, how many days of work will it to complete the harrowing?’ This was a pilot study on the use of historical texts. Clark describes the project and some the results.
Concern about the contents of the mathematical curriculum are by no means new. Jenneke Krüger from the Netherlands tells of curriculum development in the Netherlands in the early seventeenth century. The newly emerging Dutch republic between 1600 and 1650 faced new challenges to security and defences and a growing skilled artisan class. Mathematics training, particularly in geometry, needed a focus on practicality and new text books of the time, such as Pracktijck des Lantmetens (Practice of surveying) and Van het gebruyck der Geometrische instrumenten (On the use of geometrical instruments) by Johan Sems and Jan Pitersz Dou published in 1600 remained in use for much of the seventeenth century. Jenneke Krüger’s informative article is illustrated by many pages from text books and students’ copy books. We seem to be continually revisiting the question of what the curriculum should contain (a lively debate here in Britain). Today it is less clear what skills are needed than in 17th century Netherlands.
Whatever the future mathematical needs of our students, statistics is certain to be among them. A subject that did not start to be taught in schools before the middle of the 20th century is now an essential component of even elementary mathematics courses. The need for intelligent interpretation of data is evident but standard deviation, the most common, and very useful, measure of spread, is little understood by students. Kourkoulos and Tzanakis report a study of four tertiary institutions in the USA where students who had just completed an introductory statistics course were examined. All students had gained top grades but their understanding of SD was slender. In fact they had not formed the simple idea that SD is a kind of average distance from the mean. The real problem for any teacher at an elementary level is to try to justify why the squares of distances should be used. The authors turned to the history of using the mean of the squares of deviations and found the idea used in moments of inertia of systems of masses and in the dispersion energy of a physical system. Here using squares of distances arises naturally from the physical problem and makes sense. Kourkoulos and Tzanakis tried out using physical models in introductory statistics classes with two groups of students and say that the majority understood the interpretation of variance in these physical contexts. The historical background described by the authors is detailed and the article is a very nice example of how historical research may inform current teaching.
The fourth article in BSHM 25-3 is by Garrod Musto, a secondary school mathematics teacher from Bath, who worked with a colleague teaching art. The stimulus was to brighten the walls of the corridors leading to the mathematics rooms. The solution was to get the art students to paint pictures of mathematicians. The mathematicians were chosen from those which appear in the four part BBC television series The story of maths, created by Marcus de Sautoy. In the mathematics class, the students were given a mathematician to research and had to write a short biography. In the art class, each student was assigned a mathematician and asked to produce a portrait in the style of one of the artists they had been studying. Musto quotes G. H. Hardy’s remark that: a mathematician like a painter or a poet is a maker of patterns… Four of the portraits, in the styles of Frida Kahlo, Picasso (blue period), Stanley Spencer and Chuck Close illustrate Musto’s article.
The Bulletin also carries reviews, brief reports of meetings and usually a useful list of recent publications (not present in issue 25-3). The Bulletin comes with membership of BSHM and individual copies can be bought from Taylor & Francis. You can also ask for a free sample copy from the publishers. The relevant websites are:
Please note that there is a special promotion whereby all articles mentioned above, and more, can be read freely throughout 2011.