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2012年7月28日,美国纽约时报发表了一篇题为“代数是必需的吗?(Is Algebra Necessary?)”的短文~1.作者是一位名叫Andrew Hacker的政治学的教授.他认为“不需要”.这篇短文很快引起了美国数学界的反响,两个关国数学学会(MAA和AMS)于同年8月2—4日举行了一次联合会议,就此事进行讨论.同时,前MAA主席,著名数学家A·斯梯恩(Lynn Arthur Steen)为1999年的NCTM年刊所撰写的一文“关于数学推理的20个问题(Twenty Questions about Mathematical Reasoning)~2”重新成为许多人关注的话题.数学的演绎推理,以及教学中使用“情境学习”、“合作学习”等手段一向为国内数学教育学界所重视.然而,斯梯恩却对此提出了一系列的质疑性思考.我们应该怎么看?值得认真思索.本文还提出了许多前瞻性的课题,包括脑科学对未来数学教育、特别是数学推理的影响,极具启发性.我们常常称道国外数学教育研究使用的实证方法,用数据说话.但是,高水平的数学教育研究,也需要高屋建瓴地,借助科学进步作深层次的论说.这方面,我们还远远落后.本文是一个值得仿效的范例.为了阅读方便,请译者将斯特恩的文章做了一些小的删节,故称编译.此外,我们在各个段里插入了一些评注.由于文章较长,本刊分两期刊出.
On July 28, 2012, the New York Times of the United States published an essay titled “Is Algebra Necessary?” 1 The author is a professor of political science named Andrew Hacker . “He did not think ” This essay quickly aroused the response of the American mathematical community. Two math societies (MAA and AMS) held a joint meeting on August 2-4 of the same year, The same time, the former MAA chairman, the famous mathematician Lynn Arthur Steen wrote for the NCTM Annual 1999 article “20 questions about mathematical reasoning (Twenty Questions about Mathematical Reasoning) ~ 2 ”Again become a topic of concern to many people.Mathematical deductive reasoning, as well as the teaching of the use of“ situational learning ”, “ cooperative learning ”and other means has always been valued for the domestic mathematics education academics However, This presents a series of questionable thinking.What should we look at? It is worth pondering seriously. This article also proposes many forward-looking topics, including the impact of brain science on math education in the future, especially mathematical reasoning. Often praised the use of foreign mathematics education Method, using data to speak.However, the high level of mathematical education research, but also need to build high places, with scientific progress for the depth of argument.To this aspect, we are still far behind.This article is a worthy example.For the convenience of reading, Please translator Stern’s article made a few small deletions, so called compilation .In addition, we have inserted in a number of paragraphs commentary .As the article is longer, the Journal published in two issues.