[00:00.00]NARRATOR: Listen to part of a lecture in a psychology class.
[00:04.47]FEMALE PROFESSOR: For some time now, psychologists have been aware of an ability we all share. [00:09.76]It's the ability to sort of… judge or estimate the numbers or relative quantities of things. [00:16.07]It's called the approximate number sense or ANS.
[00:22.43]ANS is a very basic, innate ability. [00:26.36]It's what enables you to decide at a glance whether there are more apples than oranges on a shelf. [00:31.80]And studies have shown that even six-month-old infants are able to use this sense to some extent. [00:38.17]And if you think about it, you'll realize that it's an ability that some animals have as well.
[00:46.08]MALE STUDENT: Animals have number…uh approximate…
[00:49.03]FEMALE PROFESSOR: Approximate number sense. Sure. [00:51.96]Just think: would a bird choose to feed in a bush filled with berries, or in a bush with half as many berries?
[00:59.30]MALE STUDENT: Well, the bush filled with berries, I guess.
[01:01.57]FEMALE PROFESSOR: And the bird certainly doesn't count the berries. [01:04.55]The bird uses ANS—approximate number sense. [01:09.86]And that ability is innate…it's inborn… [01:13.88]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. [01:25.66]It isn't learned.
[01:28.55]On the other hand, the ability to do symbolic or formal mathematics is not really what you'd call universal. [01:36.76]You'd need training in the symbols and in the manipulation of those symbols to work out mathematical problems. [01:43.73]Even something as basic as counting has to be taught. [01:48.14]Formal mathematics is not something that little children can do naturally, [01:52.65]an-and it wasn't even part of human culture until a few thousand years ago.
[01:57.77]Well, it might be interesting to ask the question, are these two abilities linked somehow? [02:06.56]Are people who are good at approximating numbers also proficient in formal mathematics? [02:13.97]So, to find out, researchers created an experiment designed to test ANS in fourteen year olds. [02:22.50]They had these teenagers sit in front of a computer screen. [02:25.82]They then flashed a series of slides in front of them. [02:29.52]Now these slides had varying numbers of yellow and blue dots on them. [02:34.18]One slide might have more blue dots than yellow dots—let's say six yellow dots and nine blue dots; [02:41.07]the next slide might have more yellow dots than blue dots. [02:45.11]The slide would flash just for a fraction of a second, [02:49.06]so you know, there was no time to count the dots,[02:52.30] and then the subjects would press a button to indicate whether they thought there were more blue dots or yellow dots.
[02:59.04]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. [03:11.17]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. [03:22.78]Others had problems even when differences were relatively large—like twelve to eight.
[03:29.30]Now, maybe you're asking whether some fourteen year olds are just faster. Faster in general, not just in math. [03:36.92]It turns out that's not so. [03:40.17]We know this because the fourteen year olds had previously been tested in a few different areas.
[03:45.86]For example, as eight year olds they'd been given a test of rapid color naming. [03:51.65]That's a test to see how fast they could identify different colors. [03:55.85]But the results didn't show a relationship with the results of the ANS test: [04:01.58]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. [04:10.82]And there was no relationship between ANS ability and skills like reading and word knowledge.…
[04:17.61]But among all the abilities tested over those years, there was one that correlated with the ANS results. Math, symbolic math achievement. [04:29.77]And this answered the researchers' question. [04:32.76]They were able to correlate learned mathematical ability with ANS.
[04:40.18]FEMALE STUDENT: But it doesn't really tell us which came first.
[04:43.73]FEMALE PROFESSOR: Go on, Laura.
[04:44.78]FEMALE STUDENT: I mean, if someone's born with good approximate number sense um, does that cause them to be good at math?[04:51.91]Or the other way around, if a person develops math ability, you know, and really studies formal mathematics, does ANS somehow improve?
[05:01.74]FEMALE PROFESSOR: Those are very good questions. And I don't think they were answered in these experiments.
[05:08.79]MALE STUDENT: But wait. [05:09.59]ANS can improve? [05:11.45]Oh, that's right. You said that before. Even though it's innate it can improve. [05:16.58]So wouldn't it be important for teachers in grade schools to...
[05:20.03]FEMALE PROFESSOR: …Teach ANS? [05:21.65]But shouldn't the questions Laura just posed be answered first? [05:25.57]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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