Approximate Number Sense托福聽力原文翻譯及問題答案

Approximate Number Sense托福聽力原文翻譯及問題答案

一、Approximate Number Sense托福聽力原文：

NARRATOR:Listen to part of a lecture in a psychology class.

FEMALE PROFESSOR:For some time now,psychologists have been aware of an ability we all share.It's the ability to sort of…judge or estimate the numbers or relative quantities of things.It's called the approximate number sense or ANS.

ANS is a very basic,innate ability.It's what enables you to decide at a glance whether there are more apples than oranges on a shelf.And studies have shown that even six-month-old infants are able to use this sense to some extent.And if you think about it,you'll realize that it's an ability that some animals have as well.

MALE STUDENT:Animals have number…uh approximate…

FEMALE PROFESSOR:Approximate number sense.Sure.Just think:would a bird choose to feed in a bush filled with berries,or in a bush with half as many berries?

MALE STUDENT:Well,the bush filled with berries,I guess.

FEMALE PROFESSOR:And the bird certainly doesn't count the berries.The bird uses ANS—approximate number sense.And that ability is innate…it's inborn…Now,I'm not saying that all people have an equal skill or that the skill can't be improved,but it's present,uh,as I said it-it’s present in six-month-old babies.It isn't learned.

On the other hand,the ability to do symbolic or formal mathematics is not really what you'd call universal.You'd need training in the symbols and in the manipulation of those symbols to work out mathematical problems.Even something as basic as counting has to be taught.Formal mathematics is not something that little children can do naturally,an-and it wasn't even part of human culture until a few thousand years ago.

Well,it might be interesting to ask the question,are these two abilities linked somehow?Are people who are good at approximating numbers also proficient in formal mathematics?So,to find out,researchers created an experiment designed to test ANS in fourteen year olds.They had these teenagers sit in front of a computer screen.They then flashed a series of slides in front of them.Now these slides had varying numbers of yellow and blue dots on them.One slide might have more blue dots than yellow dots—let's say six yellow dots and nine blue dots;the next slide might have more yellow dots than blue dots.The slide would flash just for a fraction of a second,so you know,there was no time to count the dots,and then the subjects would press a button to indicate whether they thought there were more blue dots or yellow dots.

So.The first thing that jumped out at the researchers when they looked at the results of the experiment was,that between individuals there were big differences in ANS proficiency.Some subjects were consistently able to identify which group of dots was larger even if there was a small ratio—if the numbers were almost equal,like ten to nine.Others had problems even when differences were relatively large—like twelve to eight.

Now,maybe you're asking whether some fourteen year olds are just faster.Faster in general,not just in math.It turns out that's not so.We know this because the fourteen year olds had previously been tested in a few different areas.

For example,as eight year olds they'd been given a test of rapid color naming.That's a test to see how fast they could identify different colors.But the results didn't show a relationship with the results of the ANS test:the ones who were great at rapidly naming colors when they were eight years old weren't necessarily good at the ANS test when they were fourteen.And there was no relationship between ANS ability and skills like reading and word knowledge.…

But among all the abilities tested over those years,there was one that correlated with the ANS results.Math,symbolic math achievement.And this answered the researchers'question.They were able to correlate learned mathematical ability with ANS.

FEMALE STUDENT:But it doesn't really tell us which came first.

FEMALE PROFESSOR:Go on,Laura.

FEMALE STUDENT:I mean,if someone's born with good approximate number sense um,does that cause them to be good at math?Or the other way around,if a person develops math ability,you know,and really studies formal mathematics,does ANS somehow improve?

FEMALE PROFESSOR:Those are very good questions.And I don't think they were answered in these experiments.

MALE STUDENT:But wait.ANS can improve?Oh,that's right.You said that before.Even though it's innate it can improve.So wouldn't it be important for teachers in grade schools to...

FEMALE PROFESSOR:…Teach ANS?But shouldn't the questions Laura just posed be answered first?Before we make teaching decisions based on the idea that having a good approximate number sense helps you learn formal mathematics.

二、Approximate Number Sense托福聽力中文翻譯：

旁白：在心理學(xué)課上聽一節(jié)課的一部分。

女教授：一段時(shí)間以來，心理學(xué)家已經(jīng)意識(shí)到我們都有一種能力。它是一種……判斷或估計(jì)事物數(shù)量或相對(duì)數(shù)量的能力。它被稱為近似數(shù)感覺或ANS。

ANS是一種非?；镜?、與生俱來的能力。它使你能夠一眼就決定貨架上的蘋果是否比橘子多。研究表明，即使是六個(gè)月大的嬰兒也能在一定程度上使用這種感覺。如果你仔細(xì)想想，你就會(huì)意識(shí)到這也是一些動(dòng)物的一種能力。

男學(xué)生：動(dòng)物有數(shù)字……呃，大概…

女教授：近似數(shù)字意義。當(dāng)然試想一下：一只鳥會(huì)選擇在長滿漿果的灌木叢中覓食，還是選擇在漿果數(shù)減半的灌木叢中覓食？

男學(xué)生：嗯，我想灌木叢里種滿了漿果。

女教授：鳥當(dāng)然不會(huì)數(shù)漿果。這種鳥使用近似的數(shù)字感覺。這種能力是與生俱來的……它是與生俱來的……現(xiàn)在，我并不是說所有人都有相同的技能，或者說這種技能無法提高，但它是存在的，呃，正如我所說的，它存在于六個(gè)月大的嬰兒身上。這不是后天習(xí)得的。

另一方面，符號(hào)或形式數(shù)學(xué)的能力并不是你所說的普遍性。你需要接受符號(hào)方面的培訓(xùn)，以及如何運(yùn)用這些符號(hào)來解決數(shù)學(xué)問題。甚至像數(shù)數(shù)這樣的基礎(chǔ)知識(shí)也必須教。正規(guī)數(shù)學(xué)不是小孩子天生就能做的事情，直到幾千年前，它甚至還不是人類文化的一部分。

問這個(gè)問題可能很有趣，這兩種能力是否有某種聯(lián)系？擅長近似數(shù)字的人也精通形式數(shù)學(xué)嗎？因此，為了找到答案，研究人員設(shè)計(jì)了一個(gè)實(shí)驗(yàn)，旨在測(cè)試14歲兒童的ANS。他們讓這些青少年坐在電腦屏幕前。然后，他們?cè)诿媲胺帕艘幌盗谢脽羝，F(xiàn)在這些幻燈片上有不同數(shù)量的黃色和藍(lán)色圓點(diǎn)。一張幻燈片上的藍(lán)點(diǎn)可能比黃點(diǎn)多，比如說六個(gè)黃點(diǎn)和九個(gè)藍(lán)點(diǎn)；下一張幻燈片中的黃點(diǎn)可能比藍(lán)點(diǎn)多?；脽羝粫?huì)閃爍幾秒鐘，所以你知道，沒有時(shí)間數(shù)點(diǎn)，然后受試者會(huì)按一個(gè)按鈕指示他們是否認(rèn)為有更多的藍(lán)點(diǎn)或黃點(diǎn)。

所以當(dāng)研究人員看到實(shí)驗(yàn)結(jié)果時(shí)，他們首先想到的是，個(gè)體之間的ANS水平有很大差異。一些受試者始終能夠識(shí)別哪一組點(diǎn)更大，即使在數(shù)字幾乎相等的情況下（如10比9）有一個(gè)小比例。其他人甚至在差異相對(duì)較大（如12到8）時(shí)也有問題。

現(xiàn)在，也許你在問一些14歲的孩子是否跑得更快。一般來說，速度更快，不僅僅是在數(shù)學(xué)方面。事實(shí)并非如此。我們之所以知道這一點(diǎn)，是因?yàn)檫@些14歲的孩子此前曾在幾個(gè)不同的領(lǐng)域接受過測(cè)試。

例如，在八歲時(shí)，他們接受了快速顏色命名測(cè)試。這是一個(gè)測(cè)試，看看他們識(shí)別不同顏色的速度有多快。但結(jié)果并沒有顯示出與ANS測(cè)試結(jié)果的關(guān)系：那些在八歲時(shí)擅長快速命名顏色的人在十四歲時(shí)不一定擅長ANS測(cè)試。而且，ANS能力與閱讀和單詞知識(shí)等技能之間沒有關(guān)系?！?/p>

但在這些年測(cè)試的所有能力中，有一項(xiàng)與ANS結(jié)果相關(guān)。數(shù)學(xué)，象征性的數(shù)學(xué)成就。這回答了研究人員的問題。他們能夠?qū)⑺鶎W(xué)的數(shù)學(xué)能力與ANS聯(lián)系起來。

女學(xué)生：但它并沒有告訴我們哪個(gè)先來。

女教授：繼續(xù)，勞拉。

女學(xué)生：我的意思是，如果一個(gè)人天生就有很好的近似數(shù)感覺，那么這會(huì)導(dǎo)致他們擅長數(shù)學(xué)嗎？或者反過來說，如果一個(gè)人發(fā)展了數(shù)學(xué)能力，你知道，并且真正學(xué)習(xí)了形式數(shù)學(xué)，那么ANS是否會(huì)有所提高？

女教授：這些都是很好的問題。我認(rèn)為在這些實(shí)驗(yàn)中沒有得到答案。

男學(xué)生：但是等等。ANS可以改進(jìn)嗎？哦，沒錯(cuò)。你以前說過。盡管這是天生的，但它可以改善。那么，小學(xué)教師是否有必要。。。

女教授：……教ANS？但是，勞拉剛才提出的問題不應(yīng)該首先得到回答嗎？在我們做出教學(xué)決定之前，我們的想法是，擁有良好的近似數(shù)字意識(shí)有助于你學(xué)習(xí)形式數(shù)學(xué)。

三、Approximate Number Sense托福聽力問題：

Q1:1.What is the main purpose of the lecture?

A.To explain a mechanism behind the ability to approximate numbers

B.To explore the connection between ability in symbolic mathematics and the ability to approximate numbers

C.To show the importance of new research into the ability to solve complex mathematical problems

D.To demonstrate that children,adults,and animals have a similar ability to approximate numbers

Q2:2.Why does the professor mention six-month-old infants?

A.To emphasize that ANS is largely innate

B.To refute the claim that symbolic mathematics is learned

C.To point out the difficulty of testing mathematics ability in very young children

D.To contrast the way infants learn with how older children learn

Q3:3.Why does the professor stress that the dots in the experiment flashed on the computer screen for only a fraction of a second?

A.To emphasize that humans'ANS ability is more developed than that of animals

B.To point out that it was not possible to complete the task using formal mathematics

C.To show a contrast between the dot experiment and the color-naming experiment

D.To explain,in part,how subjects were chosen for the experiment

Q4:4.What did researchers observe in the study of fourteen-year-old children?

A.The children with strong ANS skills also scored well on color-naming tests

B.The children were more likely to make mistakes when there were small numbers of blue and yellow dots

C.The ANS skills of the children had improved over time.

D.There were large differences in the ANS skills of the children tested.

Q5:5.Why does the professor mention that the subjects of the experiment were also tested in reading and word knowledge?

A.To show that ANS skills are not linked with abilities in those areas

B.To emphasize the thoroughness of the researchers

C.To point out that ANS and other skills are learned in a similar way

D.To contrast learned skills with innate abilities

Q6:6.What is the professor's opinion of using instruction in ANS to improve children's performance in formal mathematics?

A.It is likely that instruction in ANS would lead to improvement in areas other than formal mathematics.

B.It would be important for the instruction in ANS to begin when children are very young.

C.It is unclear whether instruction in ANS would improve performance in formal mathematics.

D.it is more likely that instruction in formal mathematics would improve children's ANS ability.

四、Approximate Number Sense托福聽力答案：

A1:正確答案：B

A2:正確答案：A

A3:正確答案：B

A4:正確答案：D

A5:正確答案：A

A6:正確答案：C

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