Official 43 Set 3

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Approximate Number Sense

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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

显示答案 正确答案: B

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    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:[Questioning] 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 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 for just 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 ina 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? [remembering] 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:[interrupting]...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.

  • 旁白:请听心理学课上的部分内容。

    教授:迄今为止,心理学家已经意识到我们都有的一种能力。它是一种判断或估算数字或事物的相关数量的能力。它被叫做近似数字感,或者ANS。

    ANS是一个非常基础的、与生俱来的能力。正是这项能力让你看一眼就能决定架子上的苹果是不是比橘子多。研究表明,甚至6个月大的婴儿在某种程度上都能使用这种感觉。如果你细细想一想就会发现,一些动物也有这种能力。

    学生:动物有......数字.......?类似于这样的...

    教授:近似数字感,没错。你想啊,一只鸟会选择在一个满是浆果的树丛中进食,还是在一个只有一半浆果的树丛中进食?

    学生:我猜是满是浆果的那个树丛吧。

    教授:而且鸟肯定不会数浆果的数量。鸟使用了ANS:近似数字感。这种能力是与生俱来的,天生的。我不是说所有人都有同等的能力或者这种能力不能提高,但是它显现在......就像我说的,它显现在六个月大的婴孩身上。它不是习得的。另一方面,做符号数学或形式数学的能力并不是你们会认为普遍的能力。你需要对这些符号以及运用这些符号解开数学难题进行训练。即使简单如数数这样的事情都必须被教授。形式数学不是小孩子天生就能做的事情。直到几千年前,它甚至都不是人类文化中的一部分。提出下面这个问题也许很有趣:这两种能力在某种程度上有联系吗?擅长近似数字的人也会精通形式数学吗?

    于是为了弄清真相,研究人员创造了一个设计用来测试14岁孩子的ANS的实验。他们让这些青少年坐在一个电脑屏幕前,然后在他们面前快速放映了一系列图片。这些图片上有不同数量的黄色和蓝色圆点。一张图片上的蓝点也许比黄点多,比如有6个黄点,9个蓝点。下一张图片上也许黄点比蓝点多。这些图片会在零点几秒内闪过。所以没有时间可以数这些圆点,然后这些实验对象会按一个按钮表明他们认为图片上的蓝点更多还是黄点更多。

    研究人员在看实验结果时注意到的第一件事是,人与人之间存在着巨大的ANS熟练度差异。一些实验对象能不断辨认出哪一组的圆点更多,即使只有很小的差距,即使数量几乎相等,比如10个和9个。其他人即使在差异相对较大的情况下也很难辨别出来,比如12个和8个。

    你也许要问一些14岁的孩子是不是总体上都反应都更快一些,不仅只是在数学上,结果显示不是这样的。我们知道这一点是因为这些14岁的孩子之前已经在好几种不同的领域被测试过了。比如说,在8岁时,他们接受了一个快速说出颜色的测试。那是个看看他们能多快辨认出不同颜色的测试。但是结果并没有显示和ANS测试的结果有关系,那些8岁时能非常快速地说出颜色的名字的人,14岁时在ANS测试中表现不一定好。而且ANS能力和像阅读与文字知识这样的能力也没有关系。但是那些年测试过的所有能力中,有一个和ANS结果有关联,那就是数学,符号数学成就。而这就解答了研究人员的疑问。他们可以把习得的数学能力和ANS联系起来。

    学生:但是它并没有告诉我们哪一种能力是先形成的。

    教授:Laura,继续说。

    学生:我是说,如果一个人天生有良好的近似数字感,那会不会导致他们擅长数学呢?或者反过来?如果一个人发展出了数学能力,并且好好学习了形式数学,那他的ANS多多少少会有所提高吗?

    教授:那些问题非常好,而且我认为这些实验并没有解答这些问题。

    学生:但是......等一下,ANS能提高?哦,没错,你之前说过......虽然它是与生俱来的,但是能提高。那这是不是很重要?让老师在小学......?

    教授:教ANS?但是不是应该先回答Laura刚才提出的问题呢?在我们根据有一个良好的近似数字感能帮助你学习形式数学这个想法做出教学决定之前......

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    题型分类:主旨题 

    原文定位:Well, it might be interesting to ask the question, are these two abilities linked somehow? 

    选项分析:教授自问自答,提出lecture的重点是两者的关系,对应选项B

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