"More than one? Less than two? How about one DIVIDED by TWO?"

[kellogg]

In order to answer this question, we first read pp. 441-517 in 생각과 말 (up to the end of 6-5). You will also HAVE to show:

a) You understand the distinction between “development” and “learning”

Hongkong starts her answer with the THEORY not with the data. There are big advantages to this (it gets easier as you go along instead of getting harder, and you can use a deductive rather than an inductive method to connect the theory with the data!).

There are some disadvantages too. It seems to me that the biggest disadvantage is that it will be hard to integrate the theory and the data.

In other words, this is really Kitty’s and Handyman’s strategy on the midterm. Kitty was good (well, she was LATE, actually, which wasn’t very good). But not perfect. She tended to treat the theory and the data SEPARATELY instead of trying to INTEGRATE them the way that (for example) Ha-ha and La Belle do in their answers.

Does it matter? Well, it WILL matter. You see, the really thing about grad school is not difficult classes (I hope that my class has been a difficult one for you, but of course you know that you will all pass with high grades no matter how difficult you find it.)

The tough part is the THESIS. And the toughest part of the thesis is making sure that the different parts cohere and hang together, that the theoretical background is INTEGRATED with the study..

발달은 자연법칙에 따라 성숙에 의해 일어나는 과정이다. 신체적 성장과 생리적 성숙과 유사한, 자연적인 과정이라 할 수 있다.

Remember that Vygotsky’s really NOT talking about physical development. (Although when he DOES talk about physical development, he considers that is a sociocultural process too: children, for example, have to learn to exercise and to control their weight in various ways, and this is not natural: if anything we are naturally lazy and fat and we will naturally die young).

Vygotsky is talking about MENTAL development; that is, the child’s ability to form concepts, control his attention, use his memory selectively, and so on.

Can we really say that these are “natural” processes, Hongkong? That they have NOTHING to do with the child’s cultural environment? It’s true, that some people DO believe that language acquisition (for example) is a natural, innate, inborn process, like puberty. But even those people do NOT consider second language acquisition to be natural, do they?

But let’s take reading and writing in the first language. Can you really say that this is a NATURAL process? Why do we have to go to school to learn it then?

학습은 사회 논리적 과정을 포함하고 주변 환경이나 교육에 의해 나타나는 것이다. 이에 대해 비고츠키는 게 자기 가능성을 이야기 한다. 교재 455p에 정리된 바에 의하면 발달과 학습을 별개로 보는 것 (학습이 발달에 따라 일어나며 상호 영향을 미치진 않음), 발달과 학습을 하나의 똑같은 과정으로 보는 것, 어떤 방식에선 같고 어떤 방식에선 다른 것으로 보는 것이 그것이다. 비고츠키는 이 중 세 번째 과정에서 학습과 발달의 상호 의존이 가능하다는 견해를 제시하고 학습과 발달의 상호 의존이 가능함을 통해 근접발달영역을 소개한다.

Yes. I think that if Vygotsky considered development to be completely natural and learning to be completely sociocultural then the zone of proximal development would not be possible for children. Actually, that is what we see in chimpanzees—we see mental development which is pretty much NATURAL (that is visual, perceptual) and we see learning that is almost entirely ARTIFICIAL (that is, training by humans). So it’s not surprising that chimpanzees do not have the same kind of MENTAL development that children do.

But this is Chapter Four, Hongkong! We’re not THAT far behind, are we?

b) You know what the “zone of proximal development” REALLY means.

근접발달영역은 미소발생적 차원, 개체발생적 차원을 모두 포함한다.

Hongkong says that the zone of proximal development includes ALL of microgenesis AND ontogenesis.

Wait a minute! We just saw that some learning is NOT developmental, right? For example, when chimpanzees are trained to do things, they do NOT learn language, and they do NOT have the same mental development as the child.

And we know that Vygotsky considers a LOT of things to be NOT developmental. Look: Take a look at the footnote on p. 491. Look at what he said in Section One about riding a bicycle, playing golf, learning to type.

6-4-30] 3. 연구의 세 번째 그룹은 쏜다이크가 형식도야 이론을 논박하기 위해 행한 자신의 실험에서 제시된 것과 유사한 문제를 밝히기 위해 시행되었다. 그러나 우리의 실험은 기초적인 정신기능이 아니라 고등 정신기능과 관련하여 수행되었다. 우리의 실험은 선분의 길이나 각의 크기를 구분하는 것이 아니라 학교의 교수학습을 다루었다. 간단히 말하면, 우리는 교수학습의 과목들과 그 안에서 역할을 수행하는 정신 기능들 사이의 유의미한 연결 (주6)을 기대할 수 있는 영역으로 실험을 옮긴 것이다.

미소발생적 차원- 단순히 혼자 할 수 있는 일과 도움을 받아 할 수 있는 일 사이의 거리

개체발생적 차원- 아동 발달의 성격상 객관적으로 결정되어 있는 다음 단계

비고츠키는 6-4-47에서 ‘학습은 오직 발달에 앞설 때에만 가치를 가진다.’ 고 말한다. 학습은 근접발달영역에서 규정된 기간 한에 나타날 때 더욱 많은 결실을 맺을 수 있다.

Good! Now, isn’t this GOOD place to start talking about the DATA?

c) You recognize that what children say in a foreign language is not the same as what they think.

모국어와 외국어의 학습과정은 정 반대이다. 모국어 학습은 bottom-up이고 외국어 학습은 top-down이다. 모국어 학습의 경우 어린이는 의식적 파악이나 의도 없이 모국어를 배우지만 외국어의 경우 의식적 파악과 의도를 가짐으로써 학습이 시작되며 외국어의 음성적 구조, 문법등을 먼저 학습한 후 자유로운 사용이 가능해진다. 또한 외국어와 모국어의 발달은 상호 의존적이어서 외국어를 배우며 모국어의 지식 체계를 다른 언어의 영역으로 전이시킬 수 있다. (6-5-33~36내용)

Straight from the book. It’s a good paraphrase, Hongkong. Now, let’s see if it helps answer the question!

a) POINTING: Pointing to three oranges. Counting by pointing. Number is a concrete group of objects.

b) NAMING: Saying “three oranges”. Counting by wording. Number is a concrete group of objects called by a name.

c) GENERALIZING: Learning that “three oranges” and “three apples” are both kinds of “three”. “Number” is a quality of a group of objects we call “quantity”.

d) ABSTRACTING: Thinking “three oranges” WITHOUT THE ORANGES, not as quantity but as a pure, abstract idea.

e) CONCEPTUALIZING: Thinking of “three” WITHOUT THE NUMBER, e.g. y = 3x, where neither side of the equation actually equals three, where three is simply a relationship between y and x and not an actual quantity at all.

Now, we imagine a teacher who brings two apples to school. She cuts one of them in half, and she puts an apple and a half on a plate. She then asks:

T: How many apples?

S1: One. (one whole apple)

S2: Two. (Two apple-objects)

What stage are the children at? Are they at the SAME stage, or not? How can we find out?

지난 시간에 이 과제에 관한 설명을 듣고 다시 교재를 읽었다. 교사가 학생들에게 지도하고자 하는 개념은 ‘half' 또는 ’one divided by two' 등의 분수의 영어적 개념의 이해일 것이다. 이 수업을 듣는 학생들은 이미 분수에 대한 모국어적 개념이 확립되어 있다.

Good. What can the teacher say to find out?

다만, 영어로 그 것을 어떻게 표현하는지 모르는 상태일 것이다. 즉 S1과 S2 모두 모국어 상으로는 abstracting 또는 conceptualizing단계에 이르러 잇지만, 외국어로 이를 표현하지 못하여 naming, generalizing상태로 보여질 수 있는 것이다. You recognize that what children say in a foreign language is not the same as what they think. 라는 c)의 문제에서처럼 말이다. 여기서 교사는 학생들의 모국어적 개념을 외국어로 표현해 낼 수 있도록 유도하여야 한다. 그 방안으로 everyday conceptd인 half 와 academic concept인 one divided by two 중 후자를 사용하는 것이 좋을 것이다. half라는 개념은 쉽긴 하지만 만약 교사가 사과를 세 조각으로 자른다면 학생은 자신이 아는 외국어인 half라는 단어로 그 1/3을 표현하기 더 어려워지기 때문이다.

Of course, using a foreign language IS a form of abstract thinking: you abstract away the native language, don’t you?

So the question is, what can the teacher say to find out if the kids can express this concept, learnt in their native language, through a FOREIGN language.

교수님이 제공해주신 MORE DATA를 보면 학생들이 fraction의 개념과 mixed number를 확인함을 알 수 있다. 이처럼 위의 상황에서 교사는 T: How many apples? S1: 0ne. (one whole apple) 의 대답에서 T: One? This one(pointing to an apple) or this one(pointing to a half of the apple)? 등의 질문을 통해 상황을 이어갈 수 있을 것이다. 만약 학생이 사과 하나를 one 이라고 말했다면 T: What about this(pointing to a half of the apple)? Can you say this in Korean? Can you write this in numbers? 라고 말하며 분수의 개념으로 이끌어 나가야 할 것이다.

Suppose the teacher wants to UPTAKE what S1 and S2 have said and PUT THEM TOGETHER in some way.

After all, we know that it is the NEXT developing function that really tells us about the children’s level of development.

Can the teacher TAKE UP what S1 and S2 say and put them together into some kind of NEW formulation?

I think that one of the DANGERS of leaving the data to the last is that you get tired. Sometimes it’s more useful to tackle the data FIRST, and to characterize the LEVEL of the children ON THE BASIS OF WHAT THE TEACHER CAN SAY NEXT. Then you can talk about the zone of proximal development, and the question of whether the children can say what they think, and even the question of whether learning and development are one and the same thing.

[kellogg]

Yes, I can SEE that Hongkong is right; she did answer BOTH parts of the question--separately. It's a good answer, Hongkong (although I think it might be more useful to use DIRECT questions or COMMANDS instead of "Can you tell me....?"). So now the problem is INTEGRATING this answer with your GOOD summary of Chapter Six. By the way, where's the answer to Number Two?