PDF《上海 HPM 通讯》

s ideology is so clear to us now that this kind of analysis is hard to sustain with such innocence, even though at the time it was a powerful and effective model. The cause of invoking history in mathematics education may have suffered a setback through being tarred, however unfairly, with the brush of a racist ideology (from which the history of mathematics itself has not been free). Nor is this an abstract intellectual consideration. Notice something else which has not made it to the Mathematics National Curriculum;

not only is any sense of historical perspectives and opportunities missing, but also the social, moral, spiritual and cultural contexts which have managed to gain a toehold in the Science Curriculum (further Pupils should develop their knowledge and understanding of the ways in which scientific ideas change through time and how the nature of these ideas and the uses to which they are put are affected by the social, moral, spiritual and cultural contexts in which they are developed. Science in the National Curriculum,

1989 4 discussed in Pumfrey [1991]). There may still be something too dangerous about the combination of history and mathematics. The potential subversiveness of history is always a constant threat to authorities who need to control the past, and its conjunction to a mathematics which embodies quite other qualities may be an unsettling and provocative programme. But there are other factors too behind the neglect of history in mathematics education. History is not just some kind of lubricant or additive that comes in a tube and can just be poured in at the right time, like fabric conditioner into one'

s washing machine. Making use of history is hard for pupils, whose historical framework and sense of the past can be very erratic, if it exists at all;

and it is hard for teachers―who have usually learned little or no mathematical history during their training, let alone received training on how to use history with their pupils. Historians of mathematics, too, have not always found it easy to accommodate their sense of the complexity and subtlety of history to the somewhat cavalier way with historical accuracy and truth which may be a feature of some classroom presentations or even popular historical texts. Furthermore, the message that using history is a good idea is worthy, but incomplete. It is not hard to produce many good reasons for using history in math teaching and to detail the benefits it can bring. Many worthwhile and interesting papers have been written over the past decades drawing up lists such as this and exploring the arguments and illustrations which justify these claims―but there is a danger that this is seen as the end of the argument, and the changes will then miraculously happen, on account of their inherent persuasiveness. It is important to move beyond this stage, to take it as read, for the moment, that using history is a good thing―for numerous reasons―and to show how it might be incorporated into some classroom activities, how it might make the teaching of various specific things easier, how the extra work which may be needed at first has a long-term pay-off in improving the attainment........