A Knack for Numbers?
Erik Stokstad 撰，domi 譯
By Erik Stokstad
ScienceNOW Daily News
8 September 2008
一台擁擠的巴士與你是否有能力學習數學有什麼關聯？一項新的研究顯示，如果你瞥一眼便發現前面還是後面的人比較多，那麼你與數字打交道可能更為輕鬆。數學上 的成功已經證明與一些因素(如：短期記憶)有關。許多專家也猜測這些因素對略估數位系統(ANS)也有一定作用 ，這是一種能夠使我們判斷各種物體相對數量(如：一輛巴士裡在前面或後面的人)的思維能力。但沒有人研究過這種能力在不同人群中在何種程度上呈現不同，或 是否確實涉及到數學能力。
What does a crowded bus have to do with your ability to learn math? If you can tell by a quick glance whether more people are in the front or the back, chances are you had an easier time with numbers in school, a new study reveals.
Success in mathematics has already been linked to factors such as short-term memory. Many experts also suspected a role for the approximate number system (ANS), a sort of mental sense that allows us to judge the relative quantities of various objects, such as people in the front or back of a bus. But no one had studied the extent to which this ability varies in people, or whether it relates to math proficiency.
馬里蘭州巴爾的摩市約翰斯霍普金斯大學的心理學家Justin Halberda和他的同事在14歲兒童中進行了一項測試。64名兒童觀測電腦螢幕上顯示瞬間閃爍的不同比例的藍色和黃色小點。少數兒童在該測試中得到高分：他們可以輕易地辨認出更豐富的色彩，其正確比率高至 9:10。而另外一些兒童辨認比率則低至2:3。“我們驚訝地看到該差異的顯著度。”Halberda說。
Psychologist Justin Halberda of the Johns Hopkins University in Baltimore, Maryland, and his colleagues tested the ANS in 14-year-olds. The 64 children watched a computer screen that flashed split-second images of blue and yellow dots in various ratios. A handful aced the test; they could easily identify the more abundant color in ratios as fine as 9:10. Others had trouble with ratios as low as 2:3. "We were surprised to see this very wide variation," Halberda says.
研究者更驚訝於發現ANS 敏銳度與學生的考試成績(甚至可以追溯到幼稚園)之間有著很強的關聯性。ANS解釋了在兩個國家考試TEMA-2和WJ- RCALC中三年級的表現有著高達28%至32%的差異度。“這真是令人驚訝，” Halberda說。甚至當他們控制智商、空間推理、短期記憶體，以及13個其他因素，仍舊存在此關係。該小組的報告線上發表於本周《自然》雜誌上。目前 尚不清楚究竟ANS如何提高數學能力;或許有利於判斷一個數學問題的答案是否確實。
The researchers were even more surprised to see how strongly the acuity of the ANS correlated with the students' test scores, going as far back as kindergarten. The ANS explained a whopping 28% to 32% of the variation of third-grade performance on two national tests, called the TEMA-2 and WJ-RCALC, for example. "This was really astounding," Halberda says. The relationship held even when they controlled for IQ, spatial reasoning, short-term memory, and 13 other factors, the team reports online this week in Nature. It's not clear exactly how the ANS might improve skill in formal mathematics; possibly it helps one judge whether an answer to a math problem is even plausible.
法國Gif-sur-Yvette INSERM的認知神經科學家Stanislas Dehaene則強調，該實驗是對ANS與數學能力之間關係的“美麗的證明”。不過他指出，研究只顯示了ANS和數學高分之間的關係;這並不證明ANS與 其他數學能力相關。Halberda表示他所在團隊正在對一組兒童進行測試以幫助回答這個問題。
Cognitive neuroscientist Stanislas Dehaene of INSERM in Gif-sur-Yvette, France, calls the experiment a "beautiful demonstration" of the link between the ANS and mathematical ability. Still, he notes that the study only shows a relationship between ANS and high math scores; it doesn't prove that one causes the other. Halberda says his team is now following a group of children to help answer that question.
Other experts say the finding could lead to ways to help boost academic performance. "An exciting possibility is that you might be able to train your ANS and improve your acuity," says psychologist Elizabeth Brannon of Duke University in Durham, North Carolina. "And that might translate into better math ability."