奇速英语创始人蔡章兵教授指出:学好英语重在“兴趣、习惯、方法、思维”。英语学习词汇是基础,阅读是核心;英语学习词汇先行,得阅读得高分。词汇量大的孩子,学英语有自信,往往阅读量也大。阅读量一大,灵活运用词汇表达的能力就会越强,英语学习就会给学生带来更多的成绩就感。这样一来,英语学习就会步入一个良性循环。词汇量、阅读量、思维量,是英语教学的精髓所在。中学词汇教学战略是:词汇和阅读两手都要抓,两手都要硬。先大量扩充阅读词汇量,让真实阅读成为可能,在大量阅读语境中再习得词汇的真实含义和准确用法。
在今年的国际数学奥赛中,参赛选手中的女孩寥寥无几,获奖的女孩则更少。女孩真的不如男孩擅长学习数学吗?
Six hundred of the cleverest people in the world are sitting in a tent in Bath,in the west of England,listening to a man standing at a wooden lectern who is extolling their achievements.
600名世界上最聪明的人坐在位于英格兰西部城市巴斯的帐篷内,聆听一个男人站在木质讲台前赞扬他们的成就。
He announces that there is a Fields medallist among them.Eager eyes try to spot the recipient of the world’s most prestigious prize in mathematics.
他宣称,他们之中有一名菲尔兹(Fields)奖得主。人们都用热切的眼神试图找出数学界世界最高奖项的获得者。
①recipient[rɪ'sɪpɪənt]n.容器,接受者;容纳者;adj.容易接受的;容纳的
例句:I felt glad that I was now a giver of pleasure,not merely a passive recipient.我很高兴,现在我是一个快乐的给予者,而不只是被动的接受者。
This is the closing ceremony of the 60th International Mathematical Olympiad,the annual world championship maths competition for secondary school-age students.It is late July,and 621 teenagers representing 112 countries are waiting for medals to be distributed.They have spent days working on mathematical problems that many university professors would fail to solve.
这是第60届国际数学奥林匹克竞赛(International Mathematical Olympiad,以下简称“国际数学奥赛”)的闭幕式,这场世界数学竞赛每年举办一次,参赛者为中学年龄段学生。时值7月末,代表112个国家的621名青少年正等待奖牌颁发。他们已经花费数天时间解决数学问题,这些问题连许多大学教授也无法解出。
The man at the lectern,a mathematician and the president of the governing body of the Olympiad,gets to his punchline.There is a Fields medallist sitting in this room,“he just doesn’t know it yet”.
讲台上的男人是一名数学家,也是国际数学奥赛组委会主席,他抖开了包袱。房间里有一名菲尔兹奖得主,“只不过他现在还不知道呢”。
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Statistically Geoff Smith is right.Half of all Fields medallists are also IMO winners who have sat through similar ceremonies.Such is the calibre of this audience that its 52 new IMO gold medallists among them are 50 times more likely to go on to win the Fields Medal—“the Nobel for mathematics”—than someone with a PhD in mathematics from the University of Cambridge.
从统计学看,杰夫•史密斯(Geoff Smith)是对的。菲尔兹奖得主有一半都是曾参加类似仪式的国际数学奥赛获奖者。这就是在座观众的水准,他们之中的52名新晋奥赛金牌得主获得菲尔兹奖——“数学界的诺贝尔奖”——的可能性是剑桥大学(University of Cambridge)数学系博士的50倍。
And though he will correct himself a few minutes later,Prof Smith is also right,at least statistically speaking,to use the masculine pronoun when he says,“he just doesn’t know it yet”.Of the 61 Fields medals awarded since 1936,only one has gone to a woman.Maryam Mirzakhani received hers in 2014 after winning gold for Iran at the IMOs of 1994 and 1995.She died two years ago.
虽然史密斯教授在几分钟之后纠正了自己,但他说“只不过他现在还不知道”时用了男性的“他”也是对的,至少从统计上看是如此。自1936年以来,61名菲尔兹奖得主中只有1名是女性。2014年菲尔兹奖获得者是玛丽安•米尔札哈尼(Maryam Mirzakhani),她曾在1994年和1995年代表伊朗获得国际数学奥赛金牌。她于两年前去世。
Looking across the audience,there are almost no girls in Prof Smith’s sightline.At the back is the UAE team of six girls and somewhere in the front sits 17-year-old Jelena Ivancic of Serbia,the only girl to score high enough on the problems that make up the competition to win a gold medal at the games.
向观众席望去,史密斯教授的视线中几乎没有女孩。后排坐着阿联酋队的6名女孩,前排某个角落坐着塞尔维亚17岁的耶莱娜•伊万契奇(Jelena Ivancic),她是唯一一名在竞赛中答题得分高到足以赢得金牌的女孩。
Most countries,particularly those in the top ranks,have a rigorous gender-blind national competition programme to pick the six members of their IMO team.Of the top 25 ranking nations at this year’s competition,148 team members were boys and two were girls.
大多数国家,特别是那些排名高的国家,都会举办严格的、不分性别的全国竞赛,挑选6名选手组建国际数学奥赛参赛队伍。今年竞赛排名前25的国家中,有148名选手是男孩,2名选手是女孩。
The divide at the top of mathematics is so stark that it is difficult to think of a comparable gender-blind data set that is global and spans 60 years.
数学顶端的性别差距如此严峻,以至于很难在不分性别的情况下再找出一个同样的全球性、跨越60年、性别差距如此之大的数据组。
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Almost no one,from neuroscientists and geneticists to educationalists and mathematicians,suggests the reason for this discrepancy is down to inherent differences in ability between the sexes.If that is correct,it means that all across the world,girls are being put off maths.
从神经科学家、遗传学家到教育学家、数学家,几乎没有人认为造成这种差距的原因是两性天生的能力差别。如果他们是正确的,那就意味着全世界女孩的数学能力都被耽误了。
That matters,not only because the top minds go on to win Fields medals and advance the field of mathematics,but because they also go on to work in computer science and write the algorithms that will define our future in an artificial intelligence-driven world.
这很重要,不但因为顶尖人才能赢得菲尔兹奖、推动数学领域的进步,而且因为他们可能会去计算机科学领域工作、写出算法定义我们未来靠人工智能驱动的世界。
Top mathematicians also follow careers in finance that will determine the stability of economies and they move into medicine and science to work on the world’s most pressing problems.When women are not present,biases are baked into systems.This is especially potent in AI.
顶尖数学家也可能进入金融业工作,他们的工作将决定经济的稳定;他们还可能进入医学和科学领域工作,解决世界上最紧迫的问题。若女性不参与其中,这些体系中就会产生偏差。在人工智能领域尤其如此。
Doug Gurr,head of Amazon UK,says mathematical skills will be important for almost all jobs in the future world of work.At Amazon,he says,“We see mathematical ability as essential to all our day-to-day work at all levels:from impact measurement to accounting,to machine learning,robotics and AI.”
英国亚马逊(Amazon UK)总裁葛道远(Doug Gurr)表示,数学技能对于未来的几乎所有工作都很重要。对于亚马逊,他表示:“我们认为数学能力在各层级的日常工作中都至关重要:从影响衡量到会计,到机器学习、机器人科学和人工智能。”
Numeracy is vital for everyone.But according to Alain Dehaze,chief executive of Adecco,the world’s biggest recruiting company,the most valuable mathematical skills in a more automated future,especially for those people who can also communicate them to generalists,are the ability to spot patterns;to problem solve logically;and to work with statistics,probability and large data sets to see into the future.
计算能力对于每个人来说都十分重要。但是,据世界最大的人才招聘企业德科(Adecco)的首席执行官阿兰•德海兹(Alain Dehaze)说,在更加自动化的未来,最有价值的数学技能——特别是对于那些能将数学技能传授给跨领域人才的人们——是发现模式的能力;运用逻辑解决问题的能力;利用统计学、概率和大数据预测未来的能力。
②generalist['dʒɛnrəlɪst]n.(有多方面知识和经验的)通才;多面手
例句:The presidency is a job for a generalist.总统的职位是一个多面手做的。
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Po-Shen Loh,a maths professor at Carnegie Mellon University in Pittsburgh,and the coach of the US IMO team,believes that there is“absolutely no difference in ability”between girls and boys.
罗博深(Po-Shen Loh)是匹兹堡卡内基梅隆大学(Carnegie Mellon University)的数学教授,也是美国的奥数队教练,他认为女孩与男孩之间“绝对没有能力差别”。
“I think that the average girl hears from various sides,various angles through their life that girls are not as good in maths and science,”he says.
他说:“我认为,普通女孩一生中会从各种方面、各种角度听说女孩不那么擅长数学和科学的观点。”
This is particularly potent in maths,where an answer is either right or wrong and everyone eventually runs into a problem they cannot solve.When one’s culture and a dearth of role models send out the message that girls are not as good at maths,it is a lot easier to give up and turn to other subjects and endeavours.
在数学领域尤为如此。在数学中,答案要么对要么错,而且每个人最终都会遇到自己无法解决的问题。当一个人的文化背景以及缺乏榜样释放出女孩相对不擅长数学的讯息时,她就更容易放弃,转向其他学科和工作。
The US team has not sent a girl to the Olympiad in 12 years and some of its members worry that the gender gap in ability is widening.So far,attempts such as girls-only competitions and camps have made little difference in the statistics.
美国队已有12年没有派女孩参加国际数学奥赛,团队中一些成员担心能力上的性别差距在扩大。到目前为止,为女孩专门举办竞赛和夏令营等尝试都没有在统计数据上带来什么改变。
Dame Celia Hoyles,one of Britain’s best known maths educationalists,says that the fear of making mistakes is holding people back,especially girls.“We’d love to change this view.It’s really quite deeply ingrained and one generation is passing it on to another.”
英国最知名的数学教育家之一西莉亚•霍伊尔斯女爵(Dame Celia Hoyles)表示,对犯错的恐惧阻止了人们前进,尤其是女孩。“我们很愿意改变这种观念。它确实根深蒂固,代代相传。”
Educationalists call this fear“maths anxiety”and have tried for decades to tackle it.
教育家把这种恐惧称为“数学焦虑症”,几十年来一直尝试解决它。
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Progress has been slow,but Dame Celia notes that there has been some improvement in the number of girls taking A level maths and choosing it at degree level.Efforts to make maths less gender biased have increased over the past decade.But cultural biases that start at birth,including expectations that undermine girls’willingness to make mistakes,are harder to change,as is the way teenage girls approach learning.
虽然进展很缓慢,但是西莉亚女爵指出,中学选修A level数学、并在读大学学位时选择数学的女生数量已有提升。在过去十年中,降低数学领域性别差异的努力增多了。但是生来就存在的文化偏见——例如让女孩不愿犯错的期望——更难改变。女孩在青少年时期的学习方式也是如此。
When asked why she thinks there are so few girls studying maths Ms Ivancic,the Serbian IMO gold medallist,says:“I worked really hard and I worked alone when I was younger because I loved it...
当被问起她认为为什么学数学的女孩这么少时,塞尔维亚的奥数金牌得主伊万契奇表示:“我真的非常努力,我小时候独自一人学数学,因为我太爱数学了……
I don’t think they[girls]are not capable.Maybe they don’t try enough or think they are not good enough.”
“我不认为她们(女孩们)做不到。也许她们只是尝试得不够多,或者自认为不够好。”
Lisa Sauermann,the most decorated female IMO contestant ever,suggests that the attitude of parents and culture can have a profound effect,especially early in life.Ms Sauermann’s mother grew up in the former DDR(East Germany)where,culturally,she says it was normal for women to be scientists and mathematicians.
得奖最多的女性国际数学奥赛选手莉萨•绍尔曼(Lisa Sauermann)认为,父母和文化的态度会产生深刻的影响,特别在一个人的人生初期。绍尔曼的母亲成长于前民主德国(东德),她说,在那里的文化中,女性成为科学家和数学家是很正常的。
A study published last year by IZA Institute of Labor Economics concludes that European socialism has had lasting benefits on girls’mathematical achievements.
德国IZA劳动经济研究所(IZA Institute of Labor Economics)去年发表的一项研究显示,前欧洲社会主义国家持续受益于女性的数学成就。
But the big rise has been that of Asia,in particularly China.Of the two winning teams,the US and China,all but one of the boys was of Asian descent.South and North Korea placed third and fourth respectively and of the top 15 nations all but the US are Asian or former socialist states,with only the Serbian and Polish teams including girls.
但是后起之秀在亚洲,特别是中国。今年的两支获胜队伍——美国队与中国队中,所有选手只有一人不是亚洲血统。韩国和朝鲜分列第三、第四名。在排名前15的国家中,除了美国以外,全是亚洲国家或前社会主义国家,只有塞尔维亚队与波兰队有女孩参赛。
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“This is not about particular ethnic groups having more capability.I think that’s bogus,”says Prof Loh,himself a child of Chinese parents.“If you want to have a very strong ability in something,it takes a lot of time and dedication.When one talks about the Chinese culture,this idea of focusing on studies has always been something that has been very pervasive.”
“这不是由于某些民族的能力更强。我认为那是无稽之谈。”父母都是中国人的罗博深表示,“如果你想要在某一领域获得很强的能力,那需要大量的时间和投入。谈到中国文化,这种专注学习的观念总是普遍存在的。”
③pervasive[pɚ'vesɪv]adj.普遍的;到处渗透的;流行的
例句:One of the most pervasive and destructive mental tendencies in the society is that of focusing on what we want instead of what we have.在社会上最普遍的、最具破坏性的心理倾向之一就是:我们关注自己想要得到的,并不是自己已经拥有的。
Prof Loh,who spends a significant amount of time trying to bring maths to the masses,notes there is a higher purpose to it than winning medals.
罗博深投入了大量时间,尝试把数学普及至大众。他指出,这样做的目的不只是为了赢得奖牌。
“Mathematics teaches you how to question,how to be very confident that you have pushed your logical conclusion through and then you actually believe in what you are doing.Then you have a world with discourse.And a world with discourse is one in which we as a society—I am talking about all 7bn of us—can get along much better.”
“数学教会你如何提问,如何获得自信——你用逻辑推导出了结论,然后你确实相信自己所做的事情。然后我们才有一个能够对话的世界。一个能对话的世界是我们作为一整个社会——我是指全球70亿人——能更加和谐相处的世界。”
The author is the former recruitment editor of the FT and is founder of the non-profit organisation Maths Teams
本文作者是前英国《金融时报》职场编辑,也是非营利组织Maths Teams创始人
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