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与中国现有数学竞赛的比较

中国从1985年开始派选手参加国际数学奥林匹克竞赛 (IMO), 至今共参加25届,共有154人参赛,其中120人获得金牌, 取得的成绩令世人瞩目,傲视群雄。 奥数竞赛在选拔人才、增强自信心和激发数学学习兴趣上成绩斐然,功不可没。 但是同时很多专家认为,随着奥数成为普及型、大众性的活动, 它的作用已逐渐被异化。 原本是培养学生对数学的学习兴趣、提高学生的逻辑推理能力、发现和选拔数学精英的竞赛, 却变成了比拼解题技巧、机械大量做题的强化训练。 这种强迫式的学习,最后不仅不会让学生爱数学, 反而会恨数学。达到目的以后,数学就会在他们的追求中“退场”。 在数学奥赛上获奖以后,却很少有人继续从事数学研究。 据统计,我国154位国际数学奥林匹克竞赛(IMO)参赛者中, 将数学作为终身研究职业的仅在10位左右, 其中一多半在国外发展。 中国为什么会有“钱学森之问”?为什么建国60多年了,创新还是难题? 原因就是我们的教育对于创新型人才的培养是不利的。 中国的青少年几乎是世界上学习负担最重、最没有欢笑的。 让青少年长期处于慢性压力之中,是损害青少年身心健康的。 过早的慢性压力逐渐抹杀了青少年学习数学的兴趣,导致他们到了大学后劲不足。 但奥数竞赛的功利性并非与生俱来,美国、俄罗斯以及欧洲各国都没有这种现象。

美国“数学大联盟杯赛”竞赛试题灵活、生动, 富有趣味性和挑战性,同时贴近生活。 让学生理解数学、欣赏数学,激励学生创新, 激发学生学习数学的兴趣,培养学生主动探索的精神。 使孩子们体会到学习数学会使人有创造性和灵感,会使用逻辑推理, 有理性, 灵活、快乐地生活、工作和做决策。

在美国和加拿大每年有超过一百万名学生参与, 对比美国和加拿大的学生总数,这是一个相当大的数字, 由此可见美国“数学大联盟杯赛”影响之广泛。 对中小学生来讲,参与和兴趣是最重要的。 在中国推广美国“数学大联盟杯赛”可以让中国的学校、 老师、学生、家长、教育工作者领略美国最为普及、最受欢迎的数学竞赛的原貌, 希望对中国教育制度改革的探索、提高学生素质和创新能力的培养贡献一份力量。




Steven(美国“数学大联盟杯赛”创始人 Steven Conrad)的两个孩子是如何考取哈佛大学和普林斯顿大学的?

美国“数学大联盟杯赛”创始人Steven Conrad的两个孩子分别毕业于哈佛大学和普林斯顿大学数学系。 他们在小学和中学阶段没有参加过很多的数学竞赛。 比如:他们没有参加过国际数学奥林匹克竞赛 (IMO)。 他们参加了每年的美国“数学大联盟杯赛” (因为他们的父亲是创始人) 和每年夏天的 Ross Mathematics Program。 Ross Mathematics Program 是一个六周的数学强化夏令营, 这个夏令营不是针对某一个竞赛的强化训练营, 而是专注于培养孩子们正确的科学探索的能力和方法。 这些能力和方法的培养对于Steven的两个孩子录取哈佛大学和普林斯顿大学起了至关重要的作用。

The first year course in the Ross Program is organized around a series of daily problem sets in number theory. These sets invite the participants to contemplate a variety of seemingly simple questions about numbers and their relationships. As the summer progresses the students are encouraged to investigate these questions in increasing depth, and to return to them periodically as their skill at abstract reasoning and their collection of available tools become more powerful.


This spiraling of concepts is summarized in the Ross Program's motto:

"Think deeply about simple things."


To realize this idea, we concentrate on one central theme, rather than touching lightly on many disjoint mathematical topics. Ross students spend the entire summer focusing their attention on integers and their properties.


The term begins with investigations of topics involving prime numbers and modular arithmetic. Participants observe curious numerical properties and search for satisfactory explanations of them. Starting from a list of "axioms", they learn how to write proofs that are rigorous and complete. Even the simplest of those proofs might become important later in the term, when similar ideas are investigated in other contexts.


After examining concrete numerical examples, students identify patterns and then formulate general algebraic statements that include those numerical examples as special cases. They work to prove that those statements are true, and then use those proofs to help explain new observations. Eventually they encounter versions of the original questions in other contexts and begin to appreciate them from a deeper perspective. Some of these investigations lead to significant insights into the structure of number systems and the underpinnings of algebraic formalism. By considering simply stated questions from several directions, participants attain some understanding of how professional mathematicians and scientists work: gathering data, looking for patterns and analogies, making conjectures, and finally testing and proving those conjectures.


Students should expect to get deeply involved in intensive, mathematical work. Although formal classes take up only eight hours per week, Ross participants work hard during the many hours of unstructured time. They think about the many mathematical problems, and struggle with the difficulties. After a lot of effort they finally develop methods of thought that will prove useful in many aspects of their scientific lives.




美国人对教育终极目标的阐述:
  • "The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education." - Martin Luther King, Jr.
  • "What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?" - Benjamin Franklin
  • “We must teach our students what no one knew yesterday, and we must prepare our schools for what no one yet knows.” - Margaret Mead
  • “The most beautiful thing we can experience is the mysterious.” – Albert Einstein
  • “Mistakes are the portals of discovery.” - James Joyce
  • "...most students in a school would benefit from high quality curriculum that authentically reflects the nature of the discipline it is designed to teach, engages students in complex thought, and work representative of what an expert in the field would do, and helps them organize and understand...a topic and discipline." -Carol A. Tomlinson
  • "Challenging and nurturing mind, body, and spirit, we inspire boys and girls to lead lives of purpose, faith, and integrity."
  • "Be the change you wish to see in the world."
  • "We can not solve problems with the same level of thinking that created them." - Albert Einstein
  • "It is the supreme art of the teacher to awaken joy in creative expression and knowlege." - Albert Einstein
  • “May you get all your wishes but one so you always have something to strive for.”
  • Learn with Joy. Live with Purpose.
  • An educational journey that prepares students to inspire, lead, act, and make a difference in the world.
  • "The value of an education is not in the learning of many facts, but in training the mind to think. " - Albert Einstein
  • "Mathematics, rightly viewed, possesses not only truth, but supreme beauty capable of a stern perfection such as only the greatest art can show." - Bertrand Russel
  • "Anyone who has never made a mistake has never tried anything new." - Albert Einstein
  • “If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.” - Albert Einstein