把數學變有趣


       

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把數學變有趣

譯者:李威霖 William, Excellence

Making Math Fun
作者:Jennie Harris
 

How a professor combines his passion for math and magic in showstopping stunts.
一個教授如何結合數學和魔術,讓其教學像表演廣受歡迎

 

Did anyone happen to bring a calculator? With this simple request, tuxedo-donned Arthur Benjamin sets the stage to wow his audience. His international show, Mathemagics,blends math and magic in the form of astonishing mathematical calculations. These include squaring three-digit numbers in his head faster than you can say abracadabra. Tell him you were born on August 27, 1957, and hell immediately announce it was a Tuesday. Toast masters can learn a great deal from this math expert who can communicate a complicated subject in a clear way and effectively connect with his audience.
「誰有帶計算機?」簡單的詢問,這位身穿燕尾服的亞瑟•班傑明,他的國際表演「數學魔術」融合數學和魔術,用一種難以置信的數學運算,讓現場的觀眾發出陣陣驚嘆,他的表演包括3位數的平方運算表演。而他解題的速度快到讓你都還來不及反應。如果你告訴他,你的生日是1957827日,他就能立即說出那天是星期二。這位數學專家能夠把原本很複雜的題目用一種清晰又有效的方法來和觀眾溝通,我們演講會會員可以從這位數學專家學到許多。

A professor at Harvey Mudd College in Claremont, California, Benjamin teaches courses such as calculus, probability, statistics, discrete mathematics, combinatorics, number theory and game theory. When students ask if theyll need a calculator for one of his tests, this professor jokes, Well, I didnt need one when I made the exam. Amazingly, everyone laughs. Recent graduate Elizabeth Reiland says Benjamins passion for math is infectious. He makes the material fun by breaking down subject matter in ways that are easy to understand and remember.
現在是加州可拉蒙哈維穆德學院的教授,班傑明教授許多課程,包括微積分、或然率、統計學、離散數學、組合學、數字理論和遊戲理論等。如果學生要求考試帶計算機時,這位教授會開玩笑說:「呃,我考試時不需要帶計算機。」讓人非常訝異的,學生都開懷大笑。最近畢業的學生依麗莎白•麗蘭說班傑明「對數學的熱愛有感染性的。他把教材變得有趣,並且將一些題目分解,讓它變得容易懂、也容易記。」

Fame is part of his equation. Named Americas Best Math Whiz by Reader’s Digest, Benjamin has appeared on The Colbert Report, The Today Show and CNN, and was profiled in The New York Times and Scientific American. He not only is a math whiz; he also is a dynamic presenter in the classroom as well as on the international stage, as evidenced by the standing ovation he received at the 2005 TED conference. [http://bit.ly/mathemagicianart] He gained even more fans when the conference speakers sessions were made available online a few years later.
他的名氣非常響亮。讀者文摘稱他「美國最好的數學高手」。班傑明接受過柯爾伯特報導、今日秀和美國CNN電視網的訪問,紐約時報科學美國也都介紹過他。他不只是一個數學高手,也是一個在教室甚至於國際舞台充滿活力的表演者。2005年的TED(技術、娛樂和設計)年會邀請他來表演,現場觀眾起立為他鼓掌。〔http://bit.ly/mathemagicianart〕幾年後,這個年會的演講者相關資料可上網瀏覽時,他獲得更多粉絲的支持。

Toastmaster
magazines Jennie Harris asked Benjamin about his experiences.
國際演講協會雜誌的珍妮•哈里斯訪問了班傑明並請教了一些有關他的經驗 

How did your learn to perform rapid calculations?
你的快速運算是如何辦到的?

It definitely came with practice. Most of my methods were self-taught, and I enjoyed putting in the time and practice, because for me it was a form of play, not work. Its one of those skills, like riding a bicycle, that doesnt require too much practice once youve mastered it. Now I give more than 50 presentations per year and I get enough practice from my performances.
那當然是要透過練習。我的大部分的方法都是自學的。而且我也不斷的花時間練習。對我來說,它就是一種形式的表演,而非工作。而這種技巧就像騎腳踏車,一旦你騎腳踏車的技術純熟後,就不需要再花太多時間練習。現在我每年至少有超過50場的表演,因此我可以從每次的表演中得到充分的練習。

How did you become a “mathemagician”?
你是如何成為數學魔術師的?

As a kid, I enjoyed doing magic tricks. In high school, I performed at childrens birthday parties throughout the Cleveland, Ohio, area as The Great Benjamini. Independently of this, I had developed this skill of doing rapid mental calculations. When I started doing shows for older audiences, my father suggested that I put some of my mathematical tricks into the show. To my surprise, it got a huge reaction. This gave me the incentive to do even bigger and faster calculations. Thus, I became a mathemagician.
當我小的時候,我就很喜歡耍魔術。高中時,我就經常在克里夫蘭、俄亥俄和大班傑明地區的兒童生日宴會上表演。除此之外,我也展現了快速心算的技巧。當我開始為一些年紀大的人表演時,我爸爸建議我把一些數學上的技巧加在表演中。出乎我意料的,獲得了很大的迴響。這給了我更大的動力來做更大數字和更快的計算。也因此,我成了「數學魔術師」。

Were you always comfortable speaking in front of an audience?
在觀眾面前,你是否都能輕鬆自在的演講?

Looking back, I actually think I was too comfortable in front of audiences. I can remember when I was a kid, my parents would take me to the theater, and I would stand on my head in the lobby during intermission. I argued that the people were there to be entertained and thats what I was doing. But I think it was that same uninhibited quality, and my willingness to react to my audience and think on my feet (or my head), that made me successful as a kids magician and, ultimately, as a college professor. In fact, I would attribute most of my success as a speaker and professor to what I learned about entertaining an audience through magic.
回顧過去,我真的想我在觀眾前面太輕鬆自在了。我仍記得我小時候父母親會帶我到戲院,而在中場休息時我就在大廳表演倒立。我那時認為人們到戲院就是要得到娛樂,而我就是要娛樂他們。不過我心想也就是因為這樣毫無顧忌的特質和我願意做給觀眾看並用我的腳想(或我的頭),讓我成為一個成功的小魔術師,最後當上了大學教授。事實上,我所以能成功當演講者和教授,大部份應歸功於我所學藉由魔術來娛樂觀眾的技巧。

Are there other “mathemagicians”?
有其他的數學魔術師嗎?

Im sure that there are thousands of other people who can calculate as quickly as I do. Ive met mathematicians, accountants, stock traders, cab drivers and others with similar skills, but they tend to be introverted and shun the footlights. I dont think there are too many others who do it professionally. Although, in the last few years, a number of kids have read my book Secrets of Mental Math, watched my videos (produced by The Great Courses series) and have started giving mathemagical presentations in their neighborhoods.
我相信有其他數以千計的人可以算的跟我一樣快。我曾遇到過數學專家、會計人員、股票營業人員、計程車司機和其他的人有類似的技巧,但是他們似乎比較內向又對舞台心生恐懼。因此,我認為並沒有很多人能作專業性的表演。雖然過去幾年有不少小朋友讀過我寫書名叫心算數學的奧秘的書,也看了我的影帶(偉大課程系列製作)並且在他們的附近地區開始做數學魔術的表演。

Which mathematicians have influenced you?
哪位數學家對你產生影響?

First on my list would be Martin Gardner, author of more than 70 books on subjects like recreational mathematics, magic, puzzles, science, critical thinking and poetry. He wrote a Scientific American column called Mathematical Games for more than 25 years. He might have been the first person to use the term mathemagician. Martin had a way of making advanced mathematics clear, fun and magical.
影響我的人的名單中,第一位是馬丁•迦得納。他寫的書超過70本,寫的範圍有娛樂數學、魔術、謎猜、科學、批判式的思考和詩集等。他在科學的美國專欄持續寫了「數學遊戲」文章達25年之久。他也可能是第一位使用「數學魔術師」這個名詞的人。馬丁能將高級數學用清晰、有趣和神奇魔術的方法來教學。

What does it take to speak at a TED conference?
TED年會上你演講的是什麼?

Generally, to speak at TED, you need to be recommended by other TED speakers. Back then, I had never heard of the TED conferences, but one of the speakers told me that if I ever received a call from them to just say yes. When they called, they told me that they were happy to fly me to the conference, even though I was on sabbatical in Australia at the time.
通常,在TED演講,你必須要有TED的其他演講者推薦才有機會。回想當初,我根本沒聽過什麼TED年會。但是有一個演講者告訴我說如果我接到他們打來的電話,「只管說是」。當他們打給我時,他們告訴我說他們非常高興請我飛去參加年會,縱使那時我正在澳洲享受一年的帶薪休假。

Originally, TED talks were only seen by people who attended the event. Around 2007, they began to gradually put most of the TED talks online for free. Mine came out in December 2007 and it was viewed by more than a million people in one year. I used to give about 40 speaking engagements per year, but in 2008, I did 80.
本來,TED的演講只能現場參加大會的人才可以看到。大約2007年左右,他們開始逐漸把TED演講內容PO上網,人們可免費自由點閱。我的演講在200712月在網站上出現,自那時起每年超過一百萬的人點閱。過去我每年大約有40場的演講邀約,但是2008年時我共做了80場演講。

My wife Deena, who is a Distinguished Toastmaster, District 12 Secretary and member of the Expresso club in Upland, [California], made a T-shirt for me that year, saying Mathemagics World Tour 2008, and listed 35 cities where I performed that year.
我太太狄娜是國際演講會傑出演講員,12區的秘書和加州阿布蘭地區Expresso演講會的會員。那年她為我做了一件T-恤,上面印有「2008數學魔術世界之旅」,並把那年我去表演過的35個城市列出。

How do you teach advanced math in a clear and entertaining way?
你是如何用清晰而帶娛樂的方式來教高級數學?

I always try to identify those aspects of the subject that turned me onto it. Just as every joke needs a punch line, every class needs to have a WOW moment where the students are glad they decided to show up that day. I find that students really respond to relevance and elegance. In other words, show them something useful or something beautiful.
我總是會對那些我要講主題的各個面向試著做分析。就如同每個笑話都需要一個關鍵妙句,每個班級需要有「驚奇時間」一樣。讓學生高興那天能來上這個課。我發現學生真的會對教學內容是否「適切」和「優雅」做回應。換句話說,身為老師的要秀給學生有用的東西和優美的東西 

Could you teach Toastmasters one of your mathemagics tricks?
能否教演講會會員一種你的數學魔術技巧?

I would describe my process in three words: Left to Right. On paper, we learn to do math from right to left, but when doing it mentally, it is much more natural, and ultimately faster, to do it from left to right. For example, to do 365 x 4, start with 4 x 300 = 1200. Next do 4 x 60 = 240, then add those numbers (from left to right) to get 1440. Finally, add 4 x 5 = 20 to get the answer of 1460. With practice, you can do a problem like this in seconds.
我把我的方法用三個字來形容:「左到右」。在紙上,我們學到的數學運算是從右到左,但是當用心算時,從左到右會比較自然也比較快。舉例來說,365×4,從4×3001200開始,然後4×60240,把兩個乘積加起來(從左到右),得到1440。最後,加上4×520就得到答案1460。只要多加練習,你也能在幾秒內算出類似這樣的數學題目。

Do people from different cultural backgrounds share the same reaction to your shows?
是否來自不同文化背景的觀眾對你的表演都有相同的反應?

I have presented my shows throughout the world, and the audience reaction has been consistently strong. My goal has always been to bring mathematics to the masses through my classes, books, DVD courses and live presentations, and I hope to be able to continue to do that for a long time.
在全世界,我已經做過多場表演。觀眾的反應都非常熱烈。我的目標一直就是想把數學透過我的班級教學、書本、DVD課程和現場表演帶給民眾。我也希望我的表演能長長久久。

To learn more about Arthur Benjamin, visit BenjaminMath.com.
想要更了解亞瑟•班傑明,請上其網站 BenjaminMath.com

Jennie Harris is a junior writer of the Toastmaster magazine. Reach her at jharris@toastmasters.org.
珍妮•哈里斯是國際演講會雜誌的初級撰寫員。

翻譯:李威霖