 So let's talk about an important method of teaching how to count, known as saying ten. And this is based on some international comparisons. By the age of three, children in China and the U.S. have learned the names of the first ten numbers. By the age of four, children in China can generally count to one hundred, meanwhile children in the U.S. are still struggling to learn to count to twenty. And after two months of kindergarten, children in China can solve about three times as many basic arithmetic problems as children in the United States. Now, does this mean there's some ancient Chinese secret to mathematics, or maybe some genetic predisposition to numeracy among those of Asian descent? Because the same things, or very similar things, are also true of children in Japan, children in South Korea, and children in a number of other Asian countries. Most people who study this actually attribute the difference to the language, to the number words that are used in Chinese, versus the number words that are used in English. And so for that, let's take a look at what those number words are. And imagine that you're learning the language, which children are. And if you knew the first couple of number words, could you predict what the next number words are? What pattern is beneath the naming of the numbers? So in English, I have one, two, three is my first number words. And in Chinese, I have Yi, Air, Sun. And on the basis of knowing that the first three words are Yi, Air, Sun, can you predict what the next number word is going to be? Probably not. The next few number words are going to be Xi, U, and again, if I know the first few numbers words are one, two, three, four, five, can I predict what the next number word is going to be on the basis of these are what the first few are? And the answer is no, you really can't. There is no relationship between these words. Each must be learned as its own object. And this places a particular burden of memory on the child learning the number words. So again, I, after many, many decades of practice, know what these words are in English. And after quite a bit of practice in Chinese, I have a vague recollection of what they are in Chinese as well. Now what happens after 10, which the Chinese would call Xi? Well, the first number after 10 is known as Xi Yi. And if you translate that, that's 10-1. And the number after that is Xi-er, 10-2. And on the basis of these numbers after 10, immediately after 10, Xi Yi, then Xi-er, can you guess what the number after Xi-er is going to be? Well, if you guessed it with Xi-san, you're correct. And in fact, the numbers after that Xi, Xi, Xi-u, Xi-li, Xi-chi, Xi-ba, Xi-chi. And I'm not going to burden you anymore with my garbled Mandarin pronunciation. But the important thing here is that if you know how to count from 1 through 10 in Chinese, you also know how to count from the number after 10 to 10-9, and to a number you might call 10-10. So you know the next set of number words. And after we get to a number we might call Xi-xi, but let's try to be systematic about this. If I were to actually count in Chinese the number of Xi here, I would count Yi-1-er-2. There's er-xi present. And this is in fact the name of the number after 10-9. It's actually called er-xi, two tens. Now try the same thing in English. After 10 the number is 11-12. And on the basis of these two, can you predict what the number after 12 is going to be? And unlike in Chinese, there's no way to predict that the number after 12 is going to be called 13. But even if you knew that, you couldn't predict the number after that. In English, the numbers after 10, which are called the t-numbers, follow no regular pattern. Now you might say, well, wait a minute, don't we have the number 16-17-18? Isn't this a nice regular pattern? Well it is, except it's a nice regular pattern that emerges after a very irregular pattern. So we have to make the mental switch from words like 11, 12, 13, alright, so 14. So now we start to add the t-n to the numbers. But then at some point we switch over to using our old number words. So there's a bunch of irregularities that lead up to this somewhat regular pattern here. And then once we get there, there's a problem. Because we've run into what are called the decade names. So in Chinese, the number after 10-9 is 2-10s. And this is what we call 20 in English. And the 10s in English and in other languages are their own set of number words that we call the decade name. Now how do we count after this? Well after 2-10s, we have air-xi-i, 2-10s-1, 2-10s-2, 2-10s-3, and so on. All the way up to 2-10s-9. And then after that, as with the number following 10-9, we might call it 2-10s-10, but that's just san-xi, 3-10s. And so we begin our decade names, 2-10s, 3-10s, 4-10s, and so on all the way up to 10-9-10s. Now let's see what happens. So in English, the number after 19, again what we might say, that's an analogous to 10-9, well again I could think about that as 10-10, which becomes 2-10s. Well I don't call it 10-10 of course, but I call it 20. And I introduce a completely new naming convention at this point. So now I have 20, and then my remaining decade numbers are 30, 40, 50, and so on up to 90. And again there's not any regular pattern. Well again what we actually have is something that's even worse than no regular pattern. We have a pattern that exists but that is irregularly applied. And even worse, a couple of features that happen here, let's consider how I write the digits for the numbers 16. If I write 16, then the 6, which is the first thing I say, is the second digit that I write. On the other hand, for 60, the first thing that I say is the first thing that I write. So here we have another irregular pattern that's applied on top of the irregularity of the number words. Even worse. Suppose I take a number named like 67. Well if I listen to what I'm saying here, it sounds like I should be writing that as 67. And this type of mistake is so common, it has its own name. It's called a concatenation error. There's a small consolation for us. English is, for once, not the most irregular of languages. There are some languages that are even more irregular in their naming convention than English is. Well, what can we do about this? Well, one thing we might do is we might teach kids to count in Chinese. Probably a valuable skill, certainly learning another language is always useful, but in this case it's probably impractical to do so. The other thing we can do is to try to count the same way, but this time using standard English. And this leads to what's called the saying ten method of counting. And so how are we going to count? Well, we'll start off as we do in Chinese. We'll have our number words for the numbers from one through ten. After ten, the number after that is going to be called ten, one. Now more naturally, logically and sensibly, we might call this ten and one, but this is deemed grammatically incorrect. The English teachers tell us that we don't use the word and when describing whole numbers. So rather than saying ten and one, which is what all of us want to say, we're going to drop the and and call it ten, one. And then after that, we'll have ten, two, ten, three, ten, four, and so on up to ten, nine, then two tens. And again, the non grammatical form ten and ten would lead very naturally to two tens. Not considered grammatically correct. But then after that, two tens, one, two tens, two and so on up to three tens, four tens, five tens, and so on up to nine tens, at which point we introduce our next number word, the hundreds. At that point, our naming convention becomes a lot more regular.