美國人數學差表現在語言里的一個例證

美國人數學差好像已是件地球人都知道的事情， 2012 年一項針對 20 個國家 16-65 歲人口的比較研究也確實發現，美國人的算術能力排在最後 5 名。按 1-5 的等級衡量，29% 的美國人得分在等級 1 或更低，表明他們會做基本的算術，但碰到兩步或兩步以上的運算就不會了。

A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy. On a scale of 1 to 5, 29 percent of them scored at Level 1 or below, meaning they could do basic arithmetic but not computations requiring two or more steps.



針對醫藥處方差錯的一項分析研究發現，17% 的失誤源於醫生或藥劑師的數學錯誤。一項調查發現，四分之三的醫生對於常見手術的死亡率和主要併發症發病率存在錯誤估計，即使在他們自身的專業領域也不例外。

One study that examined medical pres**tions gone awry found that 17 percent of errors were caused by math mistakes on the part of doctors or pharmacists. A survey found that three-quarters of doctors inaccurately estimated the rates of death and major complications associated with common medical procedures, even in their own specialty areas.



有個詞叫half friend就是關係一般，但是quarter friend關係就很特殊，並沒有因為數變小了，就更差。你要是不信，就看下面這個案例：

1980 年代初，當時 A&W 連鎖快餐為與麥當勞的 「1/4 磅漢堡」 競爭，推出了一種新漢堡，裡面有 1/3 磅牛肉，比麥當勞的 「1/4 磅」 要多。在品嘗活動中，顧客也更喜歡 A&W 漢堡。而且它還更便宜。A&W 在電視和廣播上做了大量市場推廣活動，宣傳這些優點。然而對這樣的超值之物，並沒增加美國人購買興趣。

直到 A&W 公司開展了消費者焦點組調研，事情的原因才搞清楚。「1/3 磅漢堡」給美國公眾出了道分數題，我們卻沒有答對。消費者誤解了 1/3 的數值，認為這種漢堡價格過高。他們問調研人員，憑什麼要他們為三分之一磅肉支付那麼多錢，而同樣的錢在麥當勞可以買到四分之一磅肉。「1/4」中的 「4」 大於 「1/3」 中的「3」，這導致他們理解錯誤。

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald』s. The 「4」 in 「¼,」 larger than the 「3」 in 「⅓,」 led them astray.



很多美國人是按分母大小來比較分數大小的。同理quarter friend > half friend.



認知科學研究表明，美國人患上數盲症的原因竟然是學校數學教育。

The cognitive-science research suggested a startling cause of Americans』 innumeracy: school.

用一位數學教育者的話說，學生們學的不是數學，而是解題。比如，教師們不是試圖去傳授做分數減法的實質意義，而是告訴學生們先畫蝴蝶，然後將蝴蝶對角翅膀上的數字做乘法，再把兩個觸角上的數字做加法，最後，如果需要，再化簡分數。

Students learn not math but, in the words of one math educator, answer-getting. Instead of trying to convey, say, the essence of what it means to subtract fractions, teachers tell students to draw butterflies and multiply along the diagonal wings, add the antennas and finally reduce and simplify as needed.



一個案例表明，受過教育的美國人，數學能力下降了。

在 1970 年代和 1980 年代，認知科學家對一個失學人群——即沒有或幾乎沒有受過正式教育的人群——進行了研究。通過考察 80 年代巴爾的摩乳品廠的工人，心理學家 Sylvia Scribner 發現，即使最基本的工作也要求掌握大量數學。

比如，負責將牛奶成誇脫成加侖地裝入大貨箱的工人，所受教育均不超過六年級。但為了高效裝箱，他們能做數學，裝箱 「就相當於在不同的基本數字系統之間進行換算」。

For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was 「equivalent to shifting between different base systems of numbers.」

在這種心算過程中，「基本不存在」 錯誤。而當這些工人因病休假，由乳品廠受過更好教育的辦公室職員來頂缺時，生產率就會下降。

Throughout these mental calculations, errors were 「virtually nonexistent.」 And yet when these workers were out sick and the dairy』s better-educated office workers filled in for them, productivity declined.

雖然相比受過專門教育的人來說，失學人群進行複雜數學運算的能力更強，但一旦處於學校環境中，他們卻被沒上學的時候就會的數學問題難住了。

The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew.