We often have rather silly, ROMANTIC ideas about the differences between native language learning and foreign language learning. We imagine, for example, that native language learning was "painless", simply because it was unconscious.
The idea is that children do not feel pain, embarassment, frustration and humiliation in native language learning. If we look at La Belle's data, and Ha-ha Smile's data, we can see immediately that this is not true.
A few years ago there was an interesting book by Frances Christie about Classroom Discourse. The argument Christie made was that the "Morning News" activity, where children bring an object to school to "Show and Tell", is not challenging enough for linguistic development.
But her own data shows something quite different: the children find it EASY to show and tell about a toy they have just acquired, or a souvenir from a trip, or a snack they have brought for lunch. But they find it very DIFFICULT to talk about the circumstances in which the object was acquired or the potential uses it has, because this requires the use of complex tenses and/or hypothetical statements, and the child is still learning how to use these in his NATIVE language.
From this book I really learned that native language learning is NOT painless. Of course children are not conscious of first language learning. Since, as Vygotsky teaches us in Chapter Seven, the child's very consciousness is MADE of language, they must necessarily be unconscious of learning a first language. That is why we cannot remember it. But that doesn't mean it is painless.
So what ARE the differences between first and second language learning. Vygotsky remarks that one of the key differences between learning a native language and learning a foreign language learning has to do with the deliberate control of PHONEMES.
In Russian, the child can say "Moscow". But the child cannot say the /sk/ sound by itself! This ability to control individual phonemes comes with learning to read and write, and above all with being able to speak foreign languages. Before the child can read and write, and before the child knows a foreign language, the idea that letters have their own sounds, and that these sounds do not by themselves have meaning, is...well, foreign.
Now, one of the interesting things about our SECOND final exam question is that there is, hidden in the question, a related question. It has to do with the distinction between a NUMBER and a NUMERAL. As Sunny shows us, below, there are an infinite number of numbers. Not only that, but each number has an infinite number of names. So that is an infinite number of infinitely-named quantities.
The truly amazing thing about the decimal system, though, is that this infinite number of infinitely named quantities comes from a VERY small set of signs: only nine numerals, plus zero. This is a very surprising, and very useful, fact: it tells the child not only a good deal about big numbers, but also a lot about the way conceptual systems (including reading and writing) work.
A finite number of signs work to create infinite names for infinite things, using a linear grammar, where the position of a particular sign is meaningful. This is, I think, a different lesson from the idea that every number has an infinite number of names. The latter lesson is closer to our BOOK (because Vygotsky refers to it in 6-6-22), but the former, the idea that a finite number of signs can create an infinite number of names for an infinite number of things, is rather closer to the data.
Let's see how close Sunny can get to this idea:
Let's imagine that the children understand that one and a half apples is more than one and less than two.
T: Look at this.(Writes "3/2" on the white board) "Three halves." Is it ONE number or TWO numbers?
S1: One.
T: Now, look at this. (Writes "1 1/2" on the white board) "One and a half". Is it ONE number or TWO numbers?
S2: Two.
T: But...aren't they the SAME number? (Writes "=" on the white board)
Ss: !!!!!
How does this CONTINUE? How can the teacher show the children that every number has INFINITE NAMES, and can be accessed (quite literally) through ANY OTHER NUMBER?
..............................................................................................................................................................................................................................
T: Look. (온전한 사과 한개와 반쪽 짜리 사과를 가리키며) Tell me. How many apples?
S: One and a half.
T: Right. (온전한 사과를 반으로 쪼개어 반쪽 짜리 사과 3개를 각각 떼어 놓는다)
How about this?
How many halves here?
S: Three.
T: That's right. Three halves. (3/2=1/2+1/2+1/2를 칠판에 쓰며) 3/2 is three halves.
(1 1/2와 3/2 를 가리키며) Are they different or (the) same?
S: Same.
T: Good. They are (the) same. But they can have different names.
Sunny’s solution is simply to teach the children that numbers can have many names. Now, you can see that this is a possible solution, and that it fits the child’s COMPLEXIVE thinking very well.
숫자는 많은 방법으로 표현될 수 있다. 이는 숫자가 무한히 많기 때문이기도 하고 또한 수체계에서 각 숫자의 개념과 더불어 다른 숫자와의 관계가 주어지기 때문이다. 예를 들어, 숫자 1은 연속하는 두 수 사이의 차이로, 무수히 많은 다른 방식으로 정의될 수 있다. 100-99, 99-98 등등...
It’s a good paraphrase, Sunny. Refer this to the book; look at para 6-6-22. Remember that you are supposed to have one eye on the data and one eye on the book.
학생들은 개념의 등가성, 즉, 모든 개념은 무한히 많은 방식으로 다른 개념들을 통해 표현될 수 있다는 것을 잘 모르는 것 같다. 어린 어린이는 자신이 배운 의미의 문자적 표현에만 의존하는 경향이 있다. 그러나 어떤 개념을 이해한다는 것은 그 개념이 가진 일반성까지 이해할 때 가능하다. 학령기 어린이는 자신이 배운 문자적 의미로부터 상당히 독립된 복잡한 의미 내용을 전달 할 수 있고, 일반성의 관계가 발달함에 따라 개념이 낱말에 대해 갖는 독립성과, 의미가 표현에 대해 갖는 독립성이 덧붙여져서 의미에 대한 생각 작용은 그 언어적 표현으로부터 최대의 자유를 맞이하게 된다. 즉, 어떤 개념을 정확히 가지고 있다면 표현이 다르더라도 이해하고 사용할 수 있을 것이다.
Vygotsky says:
5-5-18] 어린이 발달의 이 단계에 있어서 어린이들에게 말은 더 이상 각자의 이름을 갖고 있는 개별 사물들을 지칭하는 수단으로 기능하지 않는다. 말은 성(姓)이 되었다. 따라서 어린이 발달의 이 시점에서 어린이가 말을 하면, 그는 상호 간에 가장 다양한 친척관계로 얽혀 있는 사물의 가족을 가리키는 것이다. 특정 사물을 그에 해당하는 명칭을 이용해 지칭하는 것은 어린이에게, 그것을 그에 연관된 특정 복합체와 연결하는 것을 뜻한다. 이 단계의 어린이에게 사물의 이름을 말하는 것은 그에 가족의 이름(姓)을 부여하는 것이다.
But in the data, the children DO recognize the distinction between number and NUMERAL. And it must be kept in mind that a numeral is not really a name for a number—it’s a PART of a sign for a number, whose value depends on the “grammar” of the decimal system. Shouldn’t the teacher be using this?