如何教出一個數學天才 Raising a Math Genius
Parents who hate math often fear raising kids who will feel the same.
對數學感到頭痛的父母常常害怕這樣一件事情：教育同樣厭惡這個科目的孩子。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·喬利（Tammy Jolley）是阿拉巴馬州麥迪遜縣（Madison）的一名法院官員，她說自己就是患有“嚴重數學恐懼症”人羣中的一員。在高中、大學時代好不容易熬着學完了代數學與統計學的課程後，喬利現在又得給自己九歲的兒子傑克輔導數學作業了。她說，這麼做會讓她“想要發出這樣的感慨，‘啊哈，數學真難，我知道你爲什麼學不明白了。’”但喬利還是硬着頭皮、強迫自己去鼓勵兒子學數學。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.
目前正在進行的研究進一步揭示了數學對孩子成功的重要性。2007年刊發於《發展心理學》（Developmental Psychology）期刊的一篇研究論文指出，學生在幼兒園時表現出來的數學能力是他們在日後學習中能否取得好成績的一個預報器，其預示作用甚至超過了集中注意力的能力和閱讀能力。
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.
由於美國青少年在數學成績上繼續落後於全球其他國家的同齡人，這個問題也日益受到人們的關注。2010年國際學生評估項目（Program for International Student Assessment）的最新結果顯示，與其他33個工業化國家的學生相比，美國孩子的數學成績低於平均分。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.
從孩子蹣跚學步開始，父母就在他們學習數學的過程中扮演着不可或缺的角色：從對這個科目的態度到掌握數學技能都是如此。芝加哥大學（University of Chicago）心理學和比較人類發展學教授蘇珊?C.萊文（Susan C. Levine）針對44名學齡前兒童和他們的父母進行了一項長期的家庭研究。該研究發現，那些經常跟孩子談論數字，用肢體語言和文字語言解釋空間關係的父母常常在子女四歲的時候就給他們灌輸了更強的數學觀念。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 , a website on math-teaching strategies.
Jason Schneider但很多父母卻在無意中令孩子對數學心生畏懼。休斯頓教師、數學教育指南網站的出版人邦?克勞德（Bon Crowder）說，當孩子問到一個數學題目或家庭作業時，那種回答說“我對數學一竅不通”或者“我都有20年沒碰過數學”的父母其實是在向孩子傳達這樣一個觀念：這個學科是令人生畏的，他們很可能也將無法攻克它。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.
研究人員和教育專家稱，那些患有數學恐懼症的父母也能教出一位數量分析家，但前提是他們得先改變自己的行爲。這就意味着，家長要停止消極的對話，並將數學遊戲和問題揉進日常生活中，就像他們教孩子讀寫那樣。父母還得鼓勵子女要勇於鑽研數學難題，不要害怕費腦子。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.'
教數學可以從激發孩子天生的好奇心開始。約翰?霍普金斯大學（Johns Hopkins University）天體物理學教授、2011年諾貝爾物理學獎得主亞當?里斯（Adam Riess）小時候就喜歡向他父母問東問西，常常都是一些數學問題，而他們覺得這是孩子好奇的天性，所以都一一耐心解答。里斯回憶道，八歲那年，他和家人一起駕車出遊，“我沒有像別的孩子那樣問：我們快到了嗎？我是看了里程路牌和車速儀表盤然後算出了到達那裏所需的時間。”里斯博士說，“數學於我而言很有用。”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數學，然後才能幫助孩子在這個科目的學習上有良好的開端。萊文博士說，家長可以教孩子在數字與實物間建立一種聯繫──在教三這個數字時，可以給孩子三個Cheerios麥圈──幫助他們更好地理解數字的含義，這比讓他們背誦一串數字強多了。父母還可以和孩子一起玩拼圖遊戲，或者藉助肢體語言向他們表述像“更高”和“更矮”這樣的概念。這些都能逐漸強化孩子的空間認知能力，而這又與習得更強的數學技能息息相關。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.
密歇根州立大學（Michigan State University）教育心理學教授凱利?米克斯（Kelly Mix）說，父母和孩子一起玩積木遊戲，鼓勵孩子模仿着堆建你砌好的房屋，用這樣簡單的方法來培養孩子對於空間的認知。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.
菲奧娜·卡梅隆（Fiona Cameron）是加利福尼亞州帕薩迪納市（Pasadena）的一名財務顧問，她在自己的學生時代曾備受數學的折磨，但如今她仍在試着培養兩個孩子──五歲的伊恩（Iain）和三歲的梅莉（Mhairi）──對數學的興趣。卡梅隆說，她會讓孩子們在睡前翻看圖形書並認出那些圖形，像一條鰻魚身上的“條-條-點”之類的。卡梅隆還會從“睡前數學”網站（Bedtime Math）上挑選一些日常問題來問自己的孩子。“睡前數學”是一家專門幫父母將數學知識融於孩子日常生活中的非盈利網站，建於去年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.
這家網站的創始人勞拉?畢洛多?歐文德克（Laura Bilodeau Overdeck）曾是新澤西州薩米特市（Summit）的一名高科技策略顧問，她說，睡前數學網站每天都會發佈一個好玩兒的、與日常生活和時事相關的數學問題，像奧運會之類的，然後促使孩子們一邊動腦筋想辦法解答，一邊和父母談論解決方式。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.
在廚房烘焙糕點時，卡梅隆讓兩個孩子將雞蛋敲開一分爲二，在這個過程中，她向孩子解釋了分數的概念。而給瑪芬紙杯蛋糕加餡兒也演變成了一個減法問題，“如果一共有12個瑪芬紙杯蛋糕，我們已經給八個加了餡兒，我們還需要再加幾個？”卡梅隆說，多虧了這種嵌入式數學教學法，她的孩子在解決問題的同時也收穫了快樂。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.
當子女將數學作業帶回家做時，許多家長必須衝破分數和排名至上的窠臼，鼓勵孩子努力嘗試、用多種方法解答問題。萊文博士的研究發現，如果父母將關注的焦點放在問題解決過程中而非正確答案上，九歲的孩子會更有熱情去應對新的數學挑戰。Struggling alongside your child can actually be helpful, says Suzanne Sutton, a Rockville, Md., math consultant and founder of , 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.
馬里蘭州洛克維爾市（Rockville）的數學教育顧問、網站（一家幫助父母和學生學數學的網站）創始人蘇珊娜·薩頓（Suzanne Sutton）稱，父母陪在孩子身邊一起鑽研其實很有用。那些在嘗試中失敗、又能從失敗中站起的家長能教會子女這樣一件事情：凡事往好的方面看、竭盡全力去應對挑戰。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.
克勞德說，如果你還是不知道該如何出手幫助孩子，那起碼不要朝他們表達出你內心的焦慮和沮喪。相反，你需要做的是告訴孩子，你會在別的時候換種方式陪伴他們，那樣會更好。而在學數學的時候，你該爲他們找一位家教或別的什麼人來指導。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.
還有一種選擇：花錢僱你的孩子來教你數學。多年前就曾有一位家長問薩頓，在自己對教學大綱都無法理解的情況下，該怎樣幫助她青春期的兒子學習艱深的代數課程。薩頓告訴這位家長，讓她選出最難的問題，然後花錢僱兒子就此寫一份報告並教會她。後來，這位媽媽選了對數這一章。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.
薩頓說，當這個兒子只給出了流於表面的解釋時，他媽媽迴應道，“你沒有履行我們的協議。我不明白對數的含義。”兒子又深挖下去，再試着講解了一次。終於，在兒子的輔導下，這位媽媽弄清了對數的概念。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.
在確認自己已經掌握了代數課程中最艱深的章節後，這位少年後來的學習一直都不錯。
