只有中国人是数学天才?请看来自美国的数学老师的回答

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2019年1月23日 16:58
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柯斯理学校中美老师研究发现:用英文学数学,能同时提高英文与数学。现引用美国数学联盟创始人之一的 Dan Flegler 的一段话,希望给家长及学生提供参考,同时引用了中国数学胡博士的观点,引发家长思考。

 

the Math League program - co-founder Dan Flegler :

I believe that contests such as ours instill a love of mathematics in students and spur them on in their study of mathematics. The best math student I ever taught was getting Cs in the honors ninth-grade math course I was teaching when his father bribed him with a $5 bill to join the math team. On the first contest he ever took, he missed 5 of the 6 questions, but got the very hardest question correct. I was amazed since the problem he got correct was a geometry question that I thought he lacked the requisite knowledge to solve. It turned out that he found a novel way to solve the problem that was completely different from the way I thought it should be done. He went on to complete algebra 1, geometry, algebra 2 and trigonometry in about four months, studying independently under my direction. He eventually won virtually every high school math competition in New Jersey and later got his Ph.D. from Stanford University in applied mathematics. But this never would have happened if he hadn’t been inspired by a math contest.

I also asked about the speed test. The goal for this test is a fast, correct answer — rather different from the poking and prodding we do on Numberplay. Nevertheless I did enjoy racing through the sixty questions, which are much easier than they look at first. Finding the simple hook for each — in about ten seconds — is exhilarating: a series of sixty bite-sized riddles. At the same time, I didn’t get them all right. Do many students score 100%? Here’s Mr. Flegler:

The only students who ever got perfect scores on the speed round were two fraternal Chinese twins (a boy and a girl). Neither I nor any of my colleagues can get a perfect score on the speed round when we take the speed round for fun (even when I write many of the questions myself!). Trying to do 60 questions in 45 minutes isn’t an easy task for anyone. The speed round is really very different from anything else we do in our competitions — we save it for last since it’s like dessert after a heavy meal.

 

数学大联盟杯赛联合创始人丹·弗雷格勒(Dan Flegler)的回答:

 

我觉得,我们举办的这类竞赛,向学生们灌输了对数学的热爱,激励了他们的数学学习。我见过的一名最好的数学学生,他在我教的九年级(相当于中国高一)数学优等班里的成绩只是C,后来他父亲用5美元贿赂他加入了数学竞赛。他首次参赛时,6道题做出了5道,但答对了最难的一道。我很惊讶,因为他做对的那道是几何题,我以为他缺乏必要的解题知识。原来,他发现了一种全新的解题方法,与我认为应该用的方法截然不同。他在我的指导之下,在四个月的时间里,独立完成了代数1、几何、代数2和三角的学习。他后来还在新泽西州的几乎所有高中数学竞赛中获胜,并最终获得斯坦福大学的应用数学博士学位。然而,如果不是因为他的灵感在一次数学竞赛中被激发,这一切也许永远不会发生。

有史以来,只有两名学生做速答题得了满分,他们是来自中国的一对异卵双胞胎(一个男孩和一个女孩)。无论是我、还是我的任何同事,我们为了好玩做速答题时,都得不了满分(尽管其中有不少道题是我自己出的!)。试图在45分钟内做60道题对任何人来说都不是一件容易的事。速答题与我们竞赛中的其他试题完全不一样,我们将速答题保留到最后,因为它们像是一顿大餐后的甜点。

Rui Hu, coach of the China team response:

The Math League and the Stanford International Youth Program enable Chinese students to view and learn math and science from a completely different perspective from what is available in China.

I find two major problems with current Chinese education. The first is math education. All students are forced to study Math Olympiad problems, very hard problems, even though a lot of these students have no interest in studying these hard problems designed only for math geniuses. This makes Chinese students the least happy students in the world. But Math League contests are well-known math competitions in North America and in the world, with more than 30 years’ history. They present fun and creative problems that promote critical thinking and problem-solving skills, the two most important skills that Chinese students are missing in the current exam-oriented, cram education system in China. It is much more fun working on Math League questions than on extremely hard math problems. Math League contests present a complement to the current Chinese math education. To me, I think the best way is American-style math plus Chinese-style rigorous practice and sound, systematic curriculum.

The second problem is English education. Chinese students spend a lot of time on studying English. But Chinese teachers teach students English with the goal to help them achieve high scores in various English tests, such as the TOEFL (Test of English as a Foreign Language) and SAT, not the goal to use English in daily life. So Chinese students achieve very high scores on English tests, but can’t communicate with English speakers. This is true in math education, too. The goal is scoring high in contests like Math Olympiad, not developing students’ true interests in math. So ironically, Chinese students hate math and English, although they spend a lot of time studying math and English. And this is where Math League can help as well. Students can learn native English and have fun solving Math League problems.

Here’s Dr. Hu:

The current Gaokao system, which was restored in the winter of 1977 by Chinese leader Deng Xiaoping, played the most important and critical role in lifting China from poverty and making China the second-largest economy in the world. Thanks to the Gaokao, millions of quality students are able to enter universities in China; most are trained to be the quality engineers who helped create modern China. But the Gaokao and the education system in both K-12 and university levels have their shortcomings. It is basically a cram system. It doesn’t really encourage critical thinking, creative thinking or intuitive problem-solving. This partially explains why China is very good at copycatting, but not necessarily good at innovation or creativity.

China has produced many, many quality engineers, but not enough innovators or independent thinkers. The Chinese government realizes this problem, so do Chinese parents and teachers. But it is extremely hard to change the current Gaokao system. No one expects the current Gaokao system will change in foreseeable future. So they (Chinese parents, students and teachers) are looking at alternatives or complementary, and the United States is their first choice, as it is the most powerful and innovative country in the world.

Not all the students who participate in Math League contests in China are planning to go to non-Chinese universities. I would say more than half of them are still planning to go to Chinese universities. But these Chinese students want to try something new, something that is innovative and creative, something that is complementary to the current Chinese education system.

 

中国胡锐博士觉得目前中国的教育存在两个主要问题

1)数学教育:

所有的学生都被迫学习奥林匹克数学竞赛试题,这些题非常难做,尽管学生中很多人对这些专门为数学天才设计的难题毫无兴趣。这让中国学生成了世界上最不幸福的学生。而数学大联盟杯赛是北美和全球有名的数学竞赛,有30多年的历史。他们出的题既有乐趣,又有创意,有利于提高批判性思维和解决问题的能力,这是在目前中国以考试、应试为主的教育体系中,中国学生所缺少的两个最重要的技能。做数学大联盟杯赛的试题,比做极难的数学题有趣多了。数学大联盟杯赛对目前中国的数学教育是一种补充。在我看来,我认为最好的结合是美国式的数学,加上中国式的严谨练习和完善的系统性课程。

2)英语教育 :

中国学生花很多时间学习英语。但中国老师教授学生英语,是以帮助他们在诸如托福(Test of English as a Foreign Language的中文简称)和SAT等各种英语考试上得高分为目标,不是以在日常生活中使用英语为目标。因此,中国学生的英语考试得分很高,但不能与说英语的人交流。在数学教育中也有这个问题。我们的目标是在如奥林匹克数学竞赛上得高分,而不是激发学生对数学学习的真正兴趣。因此有一种讽刺性的后果,那就是中国学生讨厌数学和英语,虽然他们花了很多时间学习数学和英语。而这也是数学大联盟杯赛能提供帮助之处:学生能在学习纯正英语的同时,享受解决数学竞赛试题的乐趣。

集中精力高考的学生真能抽出时间来参加像数学大联盟杯赛这样的活动吗?下面是胡锐的回答:

目前的高考制度是中国(已故)领导人邓小平在1977年冬季恢复的,这个制度在让中国脱离贫困、成为世界第二大经济体中起了重要和关键的作用。由于高考,中国数以百万计的优秀学生得以进入大学读书;他们中的大多数都成为中国现代化过程中训练有素的工程师。但高考、以及中小学和大学教育体制也有自己的缺点。基本上是一种应试教育。没有真正鼓励批判性思维、创造性思维,以及直觉地解决问题的能力。这也部分解释了为什么中国能非常好地山寨别人的东西,但创新能力或创造力不一定行。

中国已经产生了很多很多训练有素的工程师,但没有足够多的创新者和独立思考者。中国政府意识到了这个问题,中国的家长和老师也意识到了。但是,很难改变目前的高考制度。没有人认为目前的高考制度会在可预见的未来能有改变。因此,他们(中国家长、学生和老师)正在寻找提供替代或补充的东西,美国是他们的第一选择,因为美国是世界上最强大、最有创新力的国家。

并非所有参加数学大联盟杯赛的中国学生打算去国外上大学。我觉得他们中一半以上的人仍打算在中国上大学。但是,这些中国学生想试试新的东西,试一些具有创新性和创造性的东西,一些为目前中国的教育体系提供补充的东西。

 

 

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数学大联盟杯赛年度竞赛样题参考 :(有兴趣家长可以让孩子试试,最后用英文版本,适合初一孩子)

1、如果24年前我是24岁,那么24年后我多大?

2、一间屋子里至少要有多少人才能确保至少有3个人是在同一个月份出生的?

3、如果三个质数之和为20,那么这三个质数中可能的最大值是多少?

4、如果我的大脑的重量等于0.90千克加上其一半的重量,那么我的大脑究竟有多重?

5、一个水泵独自工作需要3天充满一座空水池。如果加上第二个水泵,两个水泵一起两天就可以充满这座空水池。那么,倘若第二个水泵独自工作的话,需要几天才能充满?

 

英文版本 : Math League Competition (Sample Questions):   

1、If my age 24 years ago was 24, what will my age be 24 years from now?

2、What is the minimum number of people needed in a room to be certain that at least 3 of them were born in the same month?

3、If the sum of three prime numbers is 20, what is the largest possible value of one of the three primes?

4、If my brain weighs 0.90 kilogram plus half its weight in kilograms, how many kilograms does my brain weigh?

5、Working alone, a pump fills an empty pool in 3 days. If it works with a second pump, the two pumps together can fill an empty pool in 2 days. In how many days can the second pump, working alone, fill an empty pool?