双语：如何教出一个数学天才

　　Parents who hate math often fear raising kids who will feel the same.
　　对数学感到头痛的父母常常害怕这样一件事情：教育同样厌恶这个科目的孩子。

　　Tammy Jolley is one of them - 'a horrible math-phobic,' she says. After struggling through algebra and statistics in high school and college, helping her 9-year-old son Jake with math homework makes her 'feel like saying, 'Aaarghh, this is hard! I know why you don't get it,' 'says the Madison, Ala., state-court official. Instead, she forces herself to encourage Jake.
　　塔米·乔利（Tammy Jolley）是阿拉巴马州麦迪逊县（Madison）的一名法院官员，她说自己就是患有“严重数学恐惧症”人群中的一员。在高中、大学时代好不容易熬着学完了代数学与统计学的课程后，乔利现在又得给自己九岁的儿子杰克辅导数学作业了。她说，这么做会让她“想要发出这样的感慨，‘啊哈，数学真难，我知道你为什么学不明白了。’”但乔利还是硬着头皮、强迫自己去鼓励儿子学数学。

　　Ongoing research is shedding new light on the importance of math to children's success. Math skill at kindergarten entry is an even stronger predictor of later school achievement than reading skills or the ability to pay attention, according to a 2007 study in the journal Developmental Psychology.
　　目前正在进行的研究进一步揭示了数学对孩子成功的重要性。2007年刊发于《发展心理学》（Developmental Psychology）期刊的一篇研究论文指出，学生在幼儿园时表现出来的数学能力是他们在日后学习中能否取得好成绩的一个预报器，其预示作用甚至超过了集中注意力的能力和阅读能力。

　　The issue is drawing increasing attention as U.S. teens continue to trail their global peers in math, performing below average compared with students in 33 other industrialized nations, based on the most recent results of the Program for International Student Assessment in 2010.
　　由于美国青少年在数学成绩上继续落后于全球其他国家的同龄人，这个问题也日益受到人们的关注。2010年国际学生评估项目（Program for International Student Assessment）的最新结果显示，与其他33个工业化国家的学生相比，美国孩子的数学成绩低于平均分。

　　Parents play a pivotal role in kids' math attitudes and skills, starting in toddlerhood. Those who talk often to their youngsters about numbers, and explain spatial relationships in gestures and words, tend to instill better math skills at age 4, according to a long-term, in-home study of 44 preschoolers and their parents led by Susan C. Levine, a professor of psychology and comparative human development at the University of Chicago.
　　从孩子蹒跚学步开始，父母就在他们学习数学的过程中扮演着不可或缺的角色：从对这个科目的态度到掌握数学技能都是如此。芝加哥大学（University of Chicago）心理学和比较人类发展学教授苏珊?C.莱文（Susan C. Levine）针对44名学龄前儿童和他们的父母进行了一项长期的家庭研究。该研究发现，那些经常跟孩子谈论数字，用肢体语言和文字语言解释空间关系的父母常常在子女四岁的时候就给他们灌输了更强的数学观念。

　　Yet many parents unconsciously teach children to fear math. A parent who reacts to a child's math questions or homework by saying, 'I have never been good in math,' or, 'I haven't done math in 20 years,' conveys to kids that math is daunting and they probably can't do it either, says Bon Crowder, a Houston-based teacher, tutor and publisher of MathFour.com, a website on math-teaching strategies.
　　Jason Schneider但很多父母却在无意中令孩子对数学心生畏惧。休斯顿教师、数学教育指南网站MathFour.com的出版人邦?克劳德（Bon Crowder）说，当孩子问到一个数学题目或家庭作业时，那种回答说“我对数学一窍不通”或者“我都有20年没碰过数学”的父母其实是在向孩子传达这样一个观念：这个学科是令人生畏的，他们很可能也将无法攻克它。

　　It is possible for a math-phobic parent to raise a quant, but parents need to change their behavior, researchers and educators say. This means halting negative talk, mixing math games and questions into daily life just as they do reading and spelling, and encouraging kids to dive into tough math problems and not be afraid to struggle.
　　研究人员和教育专家称，那些患有数学恐惧症的父母也能教出一位数量分析家，但前提是他们得先改变自己的行为。这就意味着，家长要停止消极的对话，并将数学游戏和问题揉进日常生活中，就像他们教孩子读写那样。父母还得鼓励子女要勇于钻研数学难题，不要害怕费脑子。

　　Encouraging children's instinctive curiosity is a good place to start. Adam Riess, who won the 2011 Nobel Prize in physics, peppered his parents with questions about math as a child, and they treated his curiosity as natural. On car trips with his family at age 8, 'instead of asking the proverbial, 'Are we there yet?' I'd look at mile markers and the speedometer and figure out how much time we needed to get there,' says Dr. Riess, a professor of astronomy and physics at Johns Hopkins University. 'Math seemed powerful to me.'
　　教数学可以从激发孩子天生的好奇心开始。约翰?霍普金斯大学（Johns Hopkins University）天体物理学教授、2011年诺贝尔物理学奖得主亚当?里斯（Adam Riess）小时候就喜欢向他父母问东问西，常常都是一些数学问题，而他们觉得这是孩子好奇的天性，所以都一一耐心解答。里斯回忆道，八岁那年，他和家人一起驾车出游，“我没有像别的孩子那样问：我们快到了吗？我是看了里程路牌和车速仪表盘然后算出了到达那里所需的时间。”里斯博士说，“数学于我而言很有用。”

　　Parents don't have to know math to help kids get off to a good start. Teaching youngsters to make connections between numbers and sets of objects - think showing a child three Cheerios when teaching the number three - helps children understand what numbers mean better than reciting strings of numbers by memory, Dr. Levine says. Doing puzzles together or using gestures to help describe spatial relationships such as 'taller' and 'shorter,' can instill spatial abilities, which are linked to better math skills, she says.
　　父母也不是非得都懂数学，然后才能帮助孩子在这个科目的学习上有良好的开端。莱文博士说，家长可以教孩子在数字与实物间建立一种联系──在教三这个数字时，可以给孩子三个Cheerios麦圈──帮助他们更好地理解数字的含义，这比让他们背诵一串数字强多了。父母还可以和孩子一起玩拼图游戏，或者借助肢体语言向他们表述像“更高”和“更矮”这样的概念。这些都能逐渐强化孩子的空间认知能力，而这又与习得更强的数学技能息息相关。

　　Something as simple as playing with blocks side-by-side and encouraging a child to replicate your stacks and structures can teach spatial skills, says Kelly Mix, a professor of educational psychology at Michigan State University.
　　密歇根州立大学（Michigan State University）教育心理学教授凯利?米克斯（Kelly Mix）说，父母和孩子一起玩积木游戏，鼓励孩子模仿着堆建你砌好的房屋，用这样简单的方法来培养孩子对于空间的认知。

　　Although Fiona Cameron struggled with math in school, she is trying to teach her children Iain, 5, and Mhairi, 3, to enjoy it. Snuggling with them at bedtime, she encourages them to spot patterns in picture books, such as the 'stripe-stripe-dot' on an eel, says Ms. Cameron, a Pasadena, Calif., financial adviser. She also poses daily problems from Bedtime Math, a nonprofit website launched last February to help parents integrate math into their children's lives.
　　菲奥娜·卡梅隆（Fiona Cameron）是加利福尼亚州帕萨迪纳市（Pasadena）的一名财务顾问，她在自己的学生时代曾备受数学的折磨，但如今她仍在试着培养两个孩子──五岁的伊恩（Iain）和三岁的梅莉（Mhairi）──对数学的兴趣。卡梅隆说，她会让孩子们在睡前翻看图形书并认出那些图形，像一条鳗鱼身上的“条-条-点”之类的。卡梅隆还会从“睡前数学”网站（Bedtime Math）上挑选一些日常问题来问自己的孩子。“睡前数学”是一家专门帮父母将数学知识融于孩子日常生活中的非盈利网站，建于去年2月份。

　　The site posts a playful math question each day related to daily life and current events, such as the Olympics, and pushes 'kids to wrestle with it in their heads, while talking with their parents about how to do it,' says founder Laura Bilodeau Overdeck of Summit, NJ, a former high-tech strategy consultant.
　　这家网站的创始人劳拉?毕洛多?欧文德克（Laura Bilodeau Overdeck）曾是新泽西州萨米特市（Summit）的一名高科技策略顾问，她说，睡前数学网站每天都会发布一个好玩儿的、与日常生活和时事相关的数学问题，像奥运会之类的，然后促使孩子们一边动脑筋想办法解答，一边和父母谈论解决方式。

　　Baking in the kitchen, Ms. Cameron explains fractions while having each of her children crack half the eggs. Filling muffin cups becomes a subtraction problem: 'If we fill eight muffin cups and there are 12 in all, how many more do we have to fill?' Thanks to this 'stealth math' approach, her kids are having fun solving problems, she says.
　　在厨房烘焙糕点时，卡梅隆让两个孩子将鸡蛋敲开一分为二，在这个过程中，她向孩子解释了分数的概念。而给玛芬纸杯蛋糕加馅儿也演变成了一个减法问题，“如果一共有12个玛芬纸杯蛋糕，我们已经给八个加了馅儿，我们还需要再加几个？”卡梅隆说，多亏了这种嵌入式数学教学法，她的孩子在解决问题的同时也收获了快乐。

　　When kids start bringing math homework home, many parents have to break old habits of emphasizing good scores and grades, and praise them instead for trying hard and using multiple approaches to figure out problems. In Dr. Levine's study, 9-year-old children were more eager to tackle new math challenges if their parents focused on the process of problem-solving, rather than correct answers.
　　当子女将数学作业带回家做时，许多家长必须冲破分数和排名至上的窠臼，鼓励孩子努力尝试、用多种方法解答问题。莱文博士的研究发现，如果父母将关注的焦点放在问题解决过程中而非正确答案上，九岁的孩子会更有热情去应对新的数学挑战。

　　Struggling alongside your child can actually be helpful, says Suzanne Sutton, a Rockville, Md., math consultant and founder of NewtonsWindow.com, a website to help parents and students with math. A parent who is comfortable with trying and failing can teach a child how to look up things and grapple with challenges.
　　马里兰州洛克维尔市（Rockville）的数学教育顾问、NewtonsWindow.com网站（一家帮助父母和学生学数学的网站）创始人苏珊娜·萨顿（Suzanne Sutton）称，父母陪在孩子身边一起钻研其实很有用。那些在尝试中失败、又能从失败中站起的家长能教会子女这样一件事情：凡事往好的方面看、竭尽全力去应对挑战。

　　If you haven't a clue how to help, Ms. Crowder says, avoid voicing your anxiety or frustration. Instead, tell your child your time together would better be spent in other ways, and offer to get a tutor or another person to help.
　　克劳德说，如果你还是不知道该如何出手帮助孩子，那起码不要朝他们表达出你内心的焦虑和沮丧。相反，你需要做的是告诉孩子，你会在别的时候换种方式陪伴他们，那样会更好。而在学数学的时候，你该为他们找一位家教或别的什么人来指导。

　　Another option: Hire your child to tutor you in math. A parent asked Ms. Sutton years ago how to help her teenage son tackle a tough algebra course when she couldn't even understand the syllabus. Ms. Sutton told her to pick the toughest topic and offer to pay her son for writing a report on it and teaching it to her. The mother picked logarithms.
　　还有一种选择：花钱雇你的孩子来教你数学。多年前就曾有一位家长问萨顿，在自己对教学大纲都无法理解的情况下，该怎样帮助她青春期的儿子学习艰深的代数课程。萨顿告诉这位家长，让她选出最难的问题，然后花钱雇儿子就此写一份报告并教会她。后来，这位妈妈选了对数这一章。

　　When her son gave her only a superficial explanation, Ms. Sutton says, the mother told him, 'You didn't meet the terms of our agreement. I don't understand what it means.' The teen dug deeper and tried again, and finally got the concept across to his mom, Ms. Sutton says.
　　萨顿说，当这个儿子只给出了流于表面的解释时，他妈妈回应道，“你没有履行我们的协议。我不明白对数的含义。”儿子又深挖下去，再试着讲解了一次。终于，在儿子的辅导下，这位妈妈弄清了对数的概念。

　　Secure knowing that he had already mastered one of the toughest topics in the course, the teen went on to do well in the class.
　　在确认自己已经掌握了代数课程中最艰深的章节后，这位少年后来的学习一直都不错。