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第一段
1 .Listen to part of a lecture in a psychology class.
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第二段
1 .For some time now, psychologists have been aware of an ability we all share.
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2 .It's the ability to sort of judge or estimate the numbers or relative quantities of things.
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3 .It's called the Approximate Number Sense, or ANS.
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第三段
1 .ANS is a very basic, innate ability.
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2 .It's what enables you to decide at a glance whether there're more apples than oranges on a shelf.
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3 .And studies have shown that even six-month-old infants are able to use this sense to some extent.
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4 .And if you think about it, you'll realize that it's an ability that some animals have as well.
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第四段
1 .Animals have number...uh...approximate...?
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第五段
1 .Approximate Number Sense. Sure.
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2 .Just think: would a bird choose to feed in a bush filled with berries or in a bush with half as many berries?
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第六段
1 .Well, the bush filled with berries I guess.
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第七段
1 .And the bird certainly doesn't count the berries.
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2 .The bird uses ANS: Approximate Number Sense.
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第八段
1 .And that ability is innate, it's inborn.
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2 .Now I'm not saying that old people have an equal skill or that the skill can't be improved, but it's present...uh...as I saicL.
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3 .It's present in six-month-old babies.
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4 .It isn't learned.
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第九段
1 .On the other hand, the ability to do symbolic or formal mathematics is not really what you would call universal.
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2 .You need training in the symbols and in the manipulation of those symbols to work out mathematical problems.
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3 .Even something as basic as counting has to be taught.
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4 .Formal mathematics is not something that little children can do naturally.
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5 .And it wasn't even part of human culture until a few thousand years ago.
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第十段
1 .Well, it might be interesting to ask the question:
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2 .Are these two abilities linked somehow? Are people who are good at approximating numbers also proficient in formal mathematics?
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第十一段
1 .So to find out, researchers created an experiment designed to test ANS in 14-year-olds.
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2 .They had these teenagers sit in front of a computer screen.
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3 .They then flash a series of slides in front of them.
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第十二段
1 .Now, these slides had varying numbers of yellow and blue dots on them.
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2 .One slide might have more blue dots than yellow dots, let's say...six yellow dots and nine blue dots.
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3 .The next slide might have more yellow dots than blue dots.
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4 .The slide would flash just for a fraction of a second.
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5 .So you know, there was no time to count the dots.
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6 .And then the subjects would press a button to indicate whether they thought there were more blue dots or yellow dots.
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第十三段
1 .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.
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2 .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.
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3 .Others had problems even when differences were relatively large, like twelve to eight.
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第十四段
1 .Now, maybe you are asking whether some fourteen-year-olds are just faster, faster in general, not just in math.
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2 .It turns out: tha's not so.
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3 .We know this because the fourteen-year-olds had previously been tested in a few different areas.
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第十五段
1 .For example, as eight-year-olds, they had been given a test of rapid color naming.
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2 .That's a test to see how fast they could identify different colors.
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3 .But the result didn't show a relationship with the results of the ANS test.
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4 .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.
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5 .And there was no relationship between ANS ability and skills like reading and word knowledge.
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第十六段
1 .But among all the abilities tested over those years, there was one that correlated with the ANS results: math, symbolic math achievement.
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2 .And this answered the researchers' question.
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3 .They were able to correlate learned mathematical ability with ANS.
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第十七段
1 .But it doesn't really tell us which came first.
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第十八段
1 .Go on, Laura.
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第一十九段
1 .I mean, if someone's born with good approximate number sense, um, does that cause them to be good at math?
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2 .Or the other way around:
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3 .If a person develops math ability, you know, and really studies formal mathematics, does ANS somehow improve?
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第二十段
1 .Those are very good questions, and I don't think they were answered in these experiments.
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第二十一段
1 .But...wait. ANS can improve?
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2 .Oh, that's right, you said that before.
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3 .Even though it's innate, it can improve.
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4 .So wouldn't it be important for teachers in grade schools to...
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第二十二段
1 .Teach ANS?
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2 .But shouldn't the questions Laura just posed be answered first?
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3 .Before we make teaching decisions based on the idea that having a good approximate number sense helps you learn formal mathematics.
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