PDF《上海 HPM 通讯》

1958 In our view the mathematics teacher has the task […] of helping each pupil to develop so far as is possible his appreciation and enjoyment of mathematics itself and his realization of the role which it has played and will continue to play both in the development of science and technology and of our civilization. […][High-attaining pupils] should be encouraged, too, to read books about mathematics and to learn something of the work of the great mathematicians of the past. [...] Reference to the historical background of some of the topics which are being studied can both help to explain their importance and also add interest and depth to the A-level course. Cockcroft Report,

1982 The Historical aspect of Mathematics has never yet found its fitting place in teaching of the schools [...] Every boy [D(Throughout the report the word BOY is to be taken as referring to pupils of either sex.)‖] ought to know something of the more human and personal side of the subject he studies [...] The history of mathematics will give us some help in framing our school syllabus. [...]Recommendation: That portraits of the great mathematicians should be hung in the mathematical classrooms, and that reference to their lives and investigations should be frequently be made by the teacher in his lessons, some explanation being given of the effect of mathematical discoveries on the progress of civilization. Mathematical Association Committee report,

1919 3 It is curious that no sign of these past concerns about using history in mathematics teaching is to be seen in the apotheosis of British educational aspirations, the National curriculum. We find the historical perspective less noticeable at the beginning of the 1990s than in any official document about mathematics education for a century. How has his come about? There is no lack of enthusiasm among many teachers, and it is not that people cannot have heard the message;

there is no point in merely saying the same thing again, but louder. It is important, rather, to seek to understand why the value of using history is so hard to put across in the right quarters. What is getting in the way of this simple beneficial improvement? Then we begin to understand;

for of course the change is far from simple, and may not be universally regarded as beneficial. What is fundamentally at issue may be a deep cleavage between different ways of looking at mathematics. A mathematics which consists of timeless truths and value-free facts may be fundamentally inconsistent with one which develops through human endeavor within social contexts. It is precisely the detached abstract unsullied purity of mathematics that has been its appeal to many students down the ages. We should not lose sight of the tenacity and depth―and to some extent validity, indeed―of this emotional aesthetic response. But even a historically-conditioned mathematics may give rise to ideologies which subsequent generations find unacceptable, or at least unfashionable: one strong argument for the historical perspective in mathematics education, much in favor at the start of this century, was the biologistic one that mathematical development in the individual retraces the history of mathematics itself: an ontogeny recapitulates phylogeny kind of argument. This was the key feature of Herbert Spenser'

s influential views on education, back in the 1860s: The education of the child must accord both in mode and arrangement with the education of mankind as considered historically;

or, in other words, the genesis of knowledge in the individual must follow the same course as the genesis of knowledge in the race. and reached its apogee in the work of Benchara Branford in the early 1900s. (Diagram on page 8). But historical experiences this century have made free discussion of the development of the race less welcome, and a little knowledge of mathematical history shows the course of its development to be, in any case, much less simple and linear than this analogy would require. The deep historical context of Branford'