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

旁白：请听一段心理学的讲座。

Professor: For some time now, psychologists have been aware of an ability we all share.

教授：在一段时间里，心理学家已经意识到我们都有一种能力。

It's the ability to sort of judge or estimate the numbers or relative quantities of things.

这种能力就是判断或估计数字或事物的相对数量的能力。

It's called the Approximate Number Sense, or ANS.

我们把她称为预估数感，即ANS。

ANS is a very basic, innate ability.

ANS是一种基础的、与生俱来的能力。

It's what enables you to decide at a glance whether there're more apples than oranges on a shelf.

它使你一眼就能看到柜子上的苹果是否比橘子要多。

And studies have shown that even six-month-old infants are able to use this sense to some extent.

研究表明，甚至6个月大的婴儿在某种程度上也能够利用这种预估数感。

And if you think about it, you'll realize that it's an ability that some animals have as well.

如果你思考一下这个问题，你会发现动物也有这种能力。

Student:Animals have number... uh... approximate...?

学生：动物也有数字……额……预估……？

Professor: Approximate Number Sense. Sure.

教授：数字预估能力。有的。

Just think: would a bird choose to feed in a bush filled with berries or in a bush with half as many berries?

思考一下：鸟类会选择浆果较多的灌木采食呢？还是会选择浆果只有一半的灌木里采食呢？

Student: Well, the bush filled with berries I guess.

学生：我猜会在浆果多的灌木里采摘。

Professor: And the bird certainly doesn't count the berries.

教授：鸟肯定是不会数这些浆果的。

The bird uses ANS: Approximate Number Sense.

它用的就是ANS数字预估能力。

And that ability is innate, it's inborn.

这种能力是天生的。

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's present in six-month-old babies.

我并不是在说每个人拥有同等的这种能力或者这种能力不可以被提升。正如我所说，6个月的孩子就有这种能力。

It isn't learned.

这不是学习获得的。

On the other hand, the ability to do symbolic or formal mathematics is not really what you would call universal.

另一方面，这种处理符号或形式数学的能力并不是真的普遍。

You need training in the symbols and in the manipulation of those symbols to work out mathematical problems.

你需要训练和处理这些符号从而计算出数学问题。

Even something as basic as counting has to be taught.

即使是像数数这样基础的事情也必须被教。

Formal mathematics is not something that little children can do naturally.

形式数学问题并不是小孩子天生就会做的。

And it wasn't even part of human culture until a few thousand years ago.

甚至直到几千年前，它才是文化中的一部分。

Well, it might be interesting to ask the question: Are these two abilities linked somehow?

有一个有趣的问题：这两种能力之间有联系吗？

Are people who are good at approximating numbers also proficient in formal mathematics?

一个估算能力很好的人形式数学就一定会好吗？

So to find out, researchers created an experiment designed to test ANS in fourteen-year-olds.

为了找到结果，研究者们设计了一个实验来测试14岁的孩子们的ANS的能力。

They had these teenagers sit in front of a computer screen.

他们让这些青少年坐在电脑屏幕前。

They then flash a series of slides in front of them.

电脑屏幕上有一系列的幻灯片闪过。

Now, these slides had varying numbers of yellow and blue dots on them.

这些幻灯片有各种黄色、蓝色的点在上面。

One slide might have more blue dots than yellow dots, let's say... six yellow dots and nine blue dots.

一张幻灯片上蓝色的点可能比黄色的点要多。假设有6个黄色的点，9个蓝色的点。

The next slide might have more yellow dots than blue dots.

下一张幻灯片可能黄色的点比蓝色更多。

The slide would flash just for a fraction of a second.

这些幻灯片一闪而过。

So you know, there was no time to count the dots.

你知道的，根本就没有时间数上面的点。

And then the subjects would press a button to indicate whether they thought there were more blue dots or yellow dots.

这些参与者将会按下按钮来表明他们是觉得黄色的或蓝色的更多。

So the first thing that jumped out at the researchers when they looked at the result of the experiment was that between individuals, there were big differences in ANS proficiency.

当研究者们检查实验结果时，第一件吸引研究者注意的事是，不同个体在ANS熟练度上，差异很大。

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.

一些参与者一直可以确定哪组点更多，即使差异比例很小，数字很接近，比如10比9。

Others had problems even when differences were relatively large, like twelve to eight.

其他人可能即使在实验的差别相对更大的时候，例如12比8，判断就有问题了。

Now, maybe you are asking whether some fourteen-year-olds are just faster, faster in general, not just in math.

现在你可能会问是否一些14岁的孩子速度会快一些，总体上快一些，并不仅仅是在数学方面。

It turns out: that's not so.

结果表明：并非如此。

We know this because the fourteen-year-olds had previously been tested in a few different areas.

我们知道这一点是因为14岁的孩子已经在其他领域测试过了。

For example, as eight-year-olds, they had been given a test of rapid color naming.

比如，给8岁的孩子进行一个快速颜色命名测试。

That's a test to see how fast they could identify different colors.

这个测试是看孩子辨认这些颜色有多快。

But the result didn't show a relationship with the results of the ANS test.

但是结果并没有表明和ANS测试结果有关系。

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.

那些在8岁能够快速辨认颜色的人并没有在14岁的时候很擅长ANS的测试。

And there was no relationship between ANS ability and skills like reading and word knowledge.

在ANS能力和阅读能力以及词汇知识等技能之间并没有关系。

But among all the abilities tested over those years, there was one that correlated with the ANS results: math, symbolic math achievement.

但是在这些年测试的所有能力中，有一个和ANS测试结果有关系：数学，符号数学成就。

And this answered the researchers' question.

这个回答了研究者的疑问。

They were able to correlate learned mathematical ability with ANS.

他们能把数学能力和ANS能力形成关联。

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

学生：但是，它确实没有告诉我们哪个首先出现。

Professor: Go on, Laura.

教授：继续，Laura.

Student: I mean, if someone's born with good approximate number sense, um, does that cause them to be good at math?

学生：我的意思是如果一个人天生数字估计能力较强，是不是意味着那会导致他们也很擅长数学呢？

Or the other way around: If a person develops math ability, you know, and really studies formal mathematics, does ANS somehow improve?

或者另一方面：如果一个人提升了数学能力，也确实学习了形式数学，那ANS能力是不是也会提升呢？

Professor: Those are very good questions, and I don't think they were answered in these experiments.

教授：这些问题很好，我认为在这个实验中并没有给出这个答案。

Student: But... wait.

学生：但是……。等一下，

ANS can improve?

ANS能力会提升？

Oh, that's right, you said that before... even though it's innate, it can improve.

是的，你之前说过，尽管它是天生的，但它可以提升。

So wouldn't it be important for teachers in grade schools to...

所以学校里的老师来……是不是很重要？

Professor: Teach ANS?

教授：教ANS?

But shouldn't the questions Laura just posed be answered first?

不过不是应该先回答Laura提出的问题吗？

Before we make teaching decisions based on the idea that having a good approximate number sense helps you learn formal mathematics.

在我们根据良好的ANS能力可以帮助你学习正规数学的想法做出教学决定之前。