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2012 年第

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2 期 亨利・ 庞加莱 (Poincaré , Jules-Henri, 1854C1912) 《上海 HPM 通讯》第2期编委会名单 主编:汪晓勤 副主编:彭刚邹佳晨 编委(按姓氏字母序): 高渊露 胡晓娟 黄友初 黄婷刘攀柳笛陆琳琰 彭刚蒲淑萍 沈春辉 屠靥韵 汪晓勤 王科王莹颖 吴骏吴晨昊 谢正敏 姚瑾赵东霞 邹佳晨 目录刊首语

1 经典选读 USING HISTORY IN MATHEMATICS EDUCATION.

JOHN FAUVEL

2 文献研究 数学归纳法的历史演变 王科 汪晓勤

9 时空隧道 和差术:从历史到课堂 王芳 汪晓勤

16 数学文化 啊哈, \PI DAY.LIU PAN

27 他山之石 实无穷概念的演变及大学生之理解 黄友初(编译)34 温故知新 历史的片段―欧几里得与 素数有无穷多个 彭刚

45 教学反思 HPM 视角下的高中数学教学:实践与思考.张小明

52 思想交流 走进 HPM 研究希望的田野―义乌教育纪行 蒲淑萍

59 丰富生动演绎数学史的教育价值―有感于华师大 HPM 读书报告会 宁锐

63 1 刊首语 江南三月, 草长莺飞. 在各位作者和编委会的共同努力下,《上海HPM通讯》第2期终于与大家见面了. 与第1期一样, 本期继续努力为HPM爱好者打造一个思想交流的平台, 在这里大家可以畅 所欲言, 谈古论今: 论理论方法, 谈感想体会, 共同驰骋在HPMD希望的田野上‖. 今年是2012年, 既是《上海HPM通讯》创刊之际, 也恰逢法国著名数学家亨利・ 庞加莱逝世 100周年.在出版于1908年的《科学与方法》(Science et Mé thode)一书中, 庞加莱的名言D预 见数学之未来的正确方法是研究它的历史和现状‖常常为我们所引用, 来说明古为今用之举 足轻重. 因此, 谨以此刊纪念这位伟大的数学家, 他那深刻的思想将永远激励我们前行.

2 经典选读 Using History in Mathematics Education JOHN FAUVEL* For decades if not centuries now, a few voices in each generation have urged the value and importance of using history in teaching mathematics―but so far without this insight taking firm and widespread root in the practice of teaching. This can be most starkly seen by comparing the content and guidance for the UK National Curriculum in mathematics, laid down for state schools by the British government in 1989, with some views held earlier in the century. * John Grant Fauvel (1947-2001)是英国数学史家,曾 任英国数学史学会主席(1991-1994), 国际 HPM 主席(1992-1996).本文刊于 For the Learning of Mathematics, Vol. 11, No. 2, Special Issue on History inMathematics Education (Jun., 1991), pp. 3-6, 排版 时尽量保持原文样式, 略有调整. The teacher who knows little of the history of Mathematics is apt to teach techniques in isolation, unrelated either to the problems and ideas which generated them or to the further problems and ideas which generated them or to the further developments which grew out of them. [...] A knowledge of the arguments and dissensions between great mathematicians might induce healthy skepticism and discussion in the classroom and lead to a firmer grasp of principles. [...] One of the most valuable assets which the teacher can acquire from a knowledge of the history of his subject is an appreciation of the influence of current traditions. [...] It is important to convey to the pupils the knowledge that much of what is taught today as a finished product was the result of centuries of groping or of spirited controversy. [...] Mathematics can be properly taught only against a background of its own history. Ministry of Education,