Approximate Number Sense托福听力原文翻译及问题答案

Approximate Number Sense托福听力原文翻译及问题答案

一、Approximate Number Sense托福听力原文：

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托福听力中文翻译：

旁白：在心理学课上听一节课的一部分。

女教授：一段时间以来，心理学家已经意识到我们都有一种能力。它是一种……判断或估计事物数量或相对数量的能力。它被称为近似数感觉或ANS。

ANS是一种非常基本的、与生俱来的能力。它使你能够一眼就决定货架上的苹果是否比橘子多。研究表明，即使是六个月大的婴儿也能在一定程度上使用这种感觉。如果你仔细想想，你就会意识到这也是一些动物的一种能力。

男学生：动物有数字……呃，大概…

女教授：近似数字意义。当然试想一下：一只鸟会选择在长满浆果的灌木丛中觅食，还是选择在浆果数减半的灌木丛中觅食？

男学生：嗯，我想灌木丛里种满了浆果。

女教授：鸟当然不会数浆果。这种鸟使用近似的数字感觉。这种能力是与生俱来的……它是与生俱来的……现在，我并不是说所有人都有相同的技能，或者说这种技能无法提高，但它是存在的，呃，正如我所说的，它存在于六个月大的婴儿身上。这不是后天习得的。

另一方面，符号或形式数学的能力并不是你所说的普遍性。你需要接受符号方面的培训，以及如何运用这些符号来解决数学问题。甚至像数数这样的基础知识也必须教。正规数学不是小孩子天生就能做的事情，直到几千年前，它甚至还不是人类文化的一部分。

问这个问题可能很有趣，这两种能力是否有某种联系？擅长近似数字的人也精通形式数学吗？因此，为了找到答案，研究人员设计了一个实验，旨在测试14岁儿童的ANS。他们让这些青少年坐在电脑屏幕前。然后，他们在面前放了一系列幻灯片。现在这些幻灯片上有不同数量的黄色和蓝色圆点。一张幻灯片上的蓝点可能比黄点多，比如说六个黄点和九个蓝点；下一张幻灯片中的黄点可能比蓝点多。幻灯片只会闪烁几秒钟，所以你知道，没有时间数点，然后受试者会按一个按钮指示他们是否认为有更多的蓝点或黄点。

所以当研究人员看到实验结果时，他们首先想到的是，个体之间的ANS水平有很大差异。一些受试者始终能够识别哪一组点更大，即使在数字几乎相等的情况下（如10比9）有一个小比例。其他人甚至在差异相对较大（如12到8）时也有问题。

现在，也许你在问一些14岁的孩子是否跑得更快。一般来说，速度更快，不仅仅是在数学方面。事实并非如此。我们之所以知道这一点，是因为这些14岁的孩子此前曾在几个不同的领域接受过测试。

例如，在八岁时，他们接受了快速颜色命名测试。这是一个测试，看看他们识别不同颜色的速度有多快。但结果并没有显示出与ANS测试结果的关系：那些在八岁时擅长快速命名颜色的人在十四岁时不一定擅长ANS测试。而且，ANS能力与阅读和单词知识等技能之间没有关系。…

但在这些年测试的所有能力中，有一项与ANS结果相关。数学，象征性的数学成就。这回答了研究人员的问题。他们能够将所学的数学能力与ANS联系起来。

女学生：但它并没有告诉我们哪个先来。

女教授：继续，劳拉。

女学生：我的意思是，如果一个人天生就有很好的近似数感觉，那么这会导致他们擅长数学吗？或者反过来说，如果一个人发展了数学能力，你知道，并且真正学习了形式数学，那么ANS是否会有所提高？

女教授：这些都是很好的问题。我认为在这些实验中没有得到答案。

男学生：但是等等。ANS可以改进吗？哦，没错。你以前说过。尽管这是天生的，但它可以改善。那么，小学教师是否有必要。。。

女教授：……教ANS？但是，劳拉刚才提出的问题不应该首先得到回答吗？在我们做出教学决定之前，我们的想法是，拥有良好的近似数字意识有助于你学习形式数学。

三、Approximate Number Sense托福听力问题：

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托福听力答案：

A1:正确答案：B

A2:正确答案：A

A3:正确答案：B

A4:正确答案：D

A5:正确答案：A

A6:正确答案：C

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