Good Definitions and Baggy Underwear: An Indispensable PREVIEW of Chapter SIX

[kellogg]

On class last Tuesday night Ha-ha Smile asked me if I was going to tackle Data One. I WAS going to try some of the data this week, but  I was busy blogging on Wednesday and then Koala beat me to it.

I’m glad I didn’t give it a try, because my answers tend to be too long and complicated (and they are in English too). Here, Ha-ha gives an EXEMPLARY answer: I think it’s a much BETTER example to follow for classmates than anything I could have done!

KT: Look at this map here. This is a world map.

S1: 세계지도다.

Let’s see…first of all, where is SUNNY? Sunny, notice the use of self-directed speech!  

Is it FORMALLY self-directed or FUNCTIONALLY self-directed?

KT: Yes.

KT: And here, we can see large lands in different parts. Do you know what they are called?

S1: con...(inaudible)

S2, S3: Continents.

a) The level of thinking

여기서는 두 경우의 생각 ․ 사고 단계를 엿볼 수 있다.

첫 번째로, S1가 continent라고 답을 하려고 했거나 S2, S3가 정확하게 답을 말한 것은 pseudoconcept(의사개념)의 단계라고 볼 수 있다. 어린이의 생각에서 형성되는 이러한 일반화는 외형상 어른이 지적 활동에서 사용하는 ‘개념’을 떠올리게 하지만, 본질에 있어서 그 심리적 특성상 진정한 개념과는 완전히 다르다.

Ha-ha Smile “uptakes” the data: she says that first of all S1 tries to answer and that S2, and S3 answer correctly, but the answer may be “seen” to be the pseudoconceptual stage. She also gives a very skillful DEFINITION of the pseudoconcept.

The child uses the same word as the adult. So it’s STRUCTURALLY the same, at least on the outside. Worse, the child uses the word for the same functions that the adult uses for “concept”. So it’s FUNCTIONALLY the same too.

For example, a child uses the words “uri nara” just like the adult. The child means the same country as the adult (Korea).

But the child thinks visually or graphically, as a flag or a football team or a big family of people. The child does NOT think of Korea in terms of citizenship, and that is why we have to teach the child these concepts.

Now, if that’s true, what would be EVIDENCE that the child’s use of the word is not conceptual but pseudoconceptual?

We can’t expect it look structurally different on the outside. And we can’t expect it to look functionally different in interaction either (though we might notice that the child is much more VISUAL and much less LOGICAL when we ask the child to DEFINE the concept!)

어린이의 생각은 그 외형과 결과, 최종 산물에 있어 개념과 일치함에도 불구하고 어른의 생각과는 생각의 양식과 지적 작용의 유형에 있어 결코 일치하지 않는다는 것이다.

Right! Although the PRODUCT looks the same, the PROCESS is different. Now that means that the pseudoconcept may be STRUCTURALLY the same (externally) and FUNCTIONALLY the same (in practice), it’s not GENETICALLY the same.

Sociogenetically, we know that “대륙” is a Chinese word. It comes from “big land mass”, and in fact that’s the word that the teacher uses later in English. Like “대륙”, “continent” is from a foreign language: Latin. The original Latin word means something like "contain"; so itt means a land mass that is self-contained, “continguous” or a “continuous” piece of land (as opposed to an island or a country).

But the main difference to notice here is not sociogenetic but MICROGENETIC. The children use “continent” without a plural or an article. They are really using a Korean, or a Chinese, word meaning. It looks like an English concept, but it isn’t.

It is a pseudoconcept, exactly as Ha-Ha Smile says. It has a Korean, everyday, empirical meaning and it has a structure that suggests a Korean word and not an English one.

어린이는 성인들로부터 이미 정교화한 말의 의미들을 획득하지만 이들을 구체적 대상과 복합체로 표현할 수 밖에 없다고 보았다. .그러므로 여기서도 어린이는 어른들의 사고를 자기 것으로 흡수하여 추상적 개념으로 일반화했다기보다는 단지 어른들의 산출물과 비슷한 결과물을 습득한 것으로 생각된다. (5-9-2, 5-10-4-5, 5-10-14) -4~5, 5-10-14 참고)

Yes, a very good summary. We can see that Ha-ha Smile has done the reading carefully, perceptively, and with a very solid understanding. Now, let’s see if it is useful. Let’s see how it relates to the data!

두 번째로, 만약 아이들이 아시아가(또는 남아메리카, 북아메리카 등 대륙의 종류 어떤 것이든) 대륙이라고 알고 있었는데 여러 개의 큰 땅(large lands)을 보니 그 예시 중에 아시아가 포함되어 있었다고 가정해 보자. 여러 개의 큰 땅이 비슷한 특징(similarity)을 가지고 있기에 자신이 알고 있는 아시아(대륙의 종류 중 하나)와 묶어 생각했다면, 이것은 associative complexe(연합적 복합체)단계의 사고를 했다고 볼 수 있다.

Here Ha-ha gives an almost PERFECT microgenetic description of complex formation; it’s almost like watching Paula’s eight-year-old!

Ha-ha says we may assume that there are some children who are aware that Asia and South America, North America, or some other continent) are continents. They can then BUNDLE the various features of the examples, the way we did when we blogged Section Ten and talked about how to teach circles to second graders. The result is a complex!

Of course, that is not the ONLY way to get a complex!

A continent is a very large area of land, such as Africa or Asia, that consists of several countries. (Wikipedia 백과)

Notice that this definition does not really apply to Antarctica (which does not contain several countries) or Oceania (which is not a large area of land). There are only seven continents, and it does not apply to TWO of them.

Is it a concept or a complex?

Wikipedia is often a good source of complexive thinking, for three reasons. First of all, the articles are DESCRIPTIONS and not definitions. We know that visual-graphic descriptions are quite typical of complexive thinking.

Secondly, the articles are meant for very GENERAL readership, including children. This means that they are often not written as part of a system of scientific knowledge. For example, the article on “continents” does not have to relate to the article on geotectonic plates.

Thirdly, the articles are often WRITTEN by different people. Anyone can upload and anyone can edit! This means that many Wikipedia artlcles are chain-like in their construction.

위의 정의를 토대로 보았을 때, continent는 크게 두 가지 특징을 지닌다.

1) very large area of land

2) consists of several countries

large lands(factual and concrete thing!)는 어느 정도 objective한 성격을 가진다.

Right. Remember we said that a good definition (according to Aristotle, anyway) consists of two parts: a GENUS and a SPECIES, a GENERAL part and a SPECIFIC part.

An apple is a fruit             which grows on the tree malus pumila.

            GENERAL        SPECIFIC            

            “genus”          “species”

Even the word “malus pumila” (the scientific word for the apple tree) has a “genus” and “species”.

GENUS      SPECIES

Malus       pumila

Homo       sapiens  (= “human”)

Canis        domesticus (= “dog”)

Another way to put this is that every concept belongs to a SYSTEM: it has a SUPERconcept and a SUBconcept—some concept that is BIGGER and MORE GENERAL and some specific provision which specifies and indicates which of the many objects included in the superconcept corresponds to the concept defined.

In other words, every good definition contains BOTH generalization (the genus) AND abstraction (the species): both “adding on” and “taking away”.

Now, here, the key provision is really that a continent consists of several COUNTRIES. Now, in some ways, this is not a good place for the teacher to begin, because it confuses two different categories (sociopolitical and geotectonic).

SOCIOPOLITICAL          GEOTECTONIC

United Nations            Earth

European Union           Eurasian continental plate

Europe                   European subcontinent

United Kingdom          British Isles

England               Britain

But there are three advantages:

a)    It does correspond to what the kids know: they know about countries like Russia and Greenland, and that is where they begin when they start guessing.

b)    It is analytic: just as “land mass” is a way of stating the SUPER-concept, “country” is a way of stating the SUB-concept.

c)    There are contradictions that will help the children understand. For example, Russia and Greenland are BOTH politically part of Europe but geographically part of other continents. And “Europe” is in some ways not a continent and yet not a country. It does have a capital city (Brussels) and it is not surrounded by water.

기준이 되는 특징이 주관적인 활동이나 상상이 아니라 대상 자체에 속해있는 점이 혼합적 더미와 는 구별된다. 하지만 대륙의 특징 중 일부만을 생각하며 연결 지어 같은 것이라고 보고 있다. 이는 비록 같은 아이들(S1, S2, S3)의 답은 아니지만, data 6에서 large lands의 특징만을 생각하여 아이들이(S6, S9) Russia나 Greenland를 continent라고 생각한 것을 보면 알 수 있다. (러시아나 그린랜드도 넓은 육지이다! 하지만 대륙은 아니다!) 이렇듯, 노란 삼각형을 보며 파란 삼각형 또는 노란 사각형을 연결지어 생각하는 유형의 associative complexe(연합적 복합체) 사고 단계 또한 엿볼 수 있다.

Ha-ha points out that complexes always have an objective character. The feature that puts the object into the complex is not a subjective activity by the child but some quality that the child notices, which belongs to the object itself.

Good definitions are like good underwear; they fit perfectly. That is they include ALL examples of the concept, and NO examples that do not belong to the concept. Every instance of the concept and NO instances of the non-concept.

That, however, is NOT true of a complex. An associative complex is big and baggy, and of course a diffuse complex is infinite. Even a pseudoconcept is cut by OTHER PEOPLE and so it will fit the child’s way of thinking badly, as when the child wears adult clothes.

As Ha-ha points out—this “continent” does not fit the child’s thinking. The child thinks of Greenland and of Russia: both are big land masses! 

Ha-ha compares this to one of the complexes in the Sakharov-Vygotsky experiment: a yellow triangle, a blue triangle or yellow rectangle associated with a type of associative complex. She’s RIGHT.  

Russia is a big land mass. But…it isn’t surrounded by WATER.

Greenland is surrounded by water. BUT…it doesn’t contain more than one country.

KT: Yes, Continents! Does everyone know what 'continent' is in Korean?

Ss: 대륙!

b) How to raise the level of thinking

continent를 새로 가르치면서 continent가 몇 개이고 어떤 것들이 있는지를 알고 외우는 것은 구체적 나열일 뿐, 추상적 개념으로 이어지지 않는다.

앞 부분에서 Do you know what they are called? 라는 질문과 마지막 부분에 Does everyone know what 'continent' is in Korean?

WHY do teachers ask questions like “Do you know what they are called?”

We can see that they LOOK like existence questions. But they are not, functionally, existence questions: they function as essence questions. What is the point of using such an indirect, confusing, complex and misleading construction on children who have not yet mastered either existence questions or essence questions?

I really think it is not a good thing for teachers or for children. It’s bad for teachers because it’s difficult, and leads to mistakes, and even when it is done correctly, it looks wrong:

T: Do you know what this is?

S: You mean, “Do you know what is this?????”

It’s bad for children because questions like “Do you know what they are called?” instead of “What’s this?” help to create a  gap between the language that the child hears and the language the child uses. We have a DIS-integration of functions, because the functions of listening are completely different from the functions of speaking.

It seems to me that it is only good for professors. It is good for professors because it means there will always be work for people like me. Some of us are unlucky and our job is to correct train teachers and teach them to talk in this ridiculous and pointless way.

Some of us (like me) are a little luckier, and our job is to teach the theories of “comprehensible input” that really underlies this idea. Thanks to Krashen, we all imagine that because the language is functionally understood that somehow the structure will be “automatically” acquired.

I know the “comprehensible input” theory. But I have never seen ANY real evidence that this particular version is true. I have never seen ANY real evidence that elaborate classroom teacher talk in English that is functionally understood by children will lead to productive acquisition of structure by the children.

And I must admit I find it very hard to believe. To me, it really looks like one of those theories that professors dream up with which cause so much trouble for teachers and so much damage in the classroom: language laboratories, English Villages, electronic whiteboards, specialist EFL teachers.

Of course, part of the problem is that children do not ask questions very much (and this is why I was encouraging Koala to teach the game of “Ask and Answer” in class). But when they DO ask questions, they do not say “Does anyone know what they are called?” or “Does everyone know what this is called in Korean?”. They tend to say “What?” or “What this?”.

Doesn’t this suggest that if we want to integrate the functions of speaking and listening we should NOT use indirect questions and passive constructions? 

대륙이 한국말로 무엇인지를 묻는 질문은 Essence question 에 해당된다. 하지만 이 또한 단지 한국말로 대륙을 뭐라고 하는지 단답형으로 묻는 것이 아닌 대륙의 의미를 아느냐고 묻는 질문(What is 'continent'?)에 비하면 한층 더 단순한 질문이다.

좀더 아이들의 사고를 높은 개념적 단계로 이끌어주려면, 단순 지식을 묻는 질문(Existence question, Essence question)보다는 개념을 생각하게끔 하는 질문(Explanation question)을 던져주어야 한다. 이를 위해서는

1) 처음에 world map을 보여준 후, 7개의 large lands를 지시하며 공통성, 유사성을 아이들 스스로 찾아보도록 한다.

2) 그 다음 Russia 나 Greenland 등 아이들이 오개념을 가질 수 있는 lands 를 가리키며 앞의 7개의 large lands와의 차이점을 찾아보도록 한다.

  -Why aren't they(Russia or Greenland) called 'Continent' ?

3) 그리고 난 후, continent 라는 단어를 도입 및 학습한다.

I think that Ha-ha Smile demonstrates here that, like a good teacher, she has a PERFECT functional understanding of the data.

She also has a PERFECT grasp of Vygotsky’s explanation of pseudoconceptual reasoning. She says RIGHT AWAY that the children are reasoning pseudonconceptually, and she gives a good reason why: the kids are going from one quality (e.g. big landmass) to another (I think the kids are thinking of the WATER around Greenland, but I’m not sure).

Her comparison with the Sakharov-Vygotsky experiment is perfect too.

Some questions:

a)    The link between “daeryuk” and “continent” seems to be an ASSOCIATIVE link—it’s just relabeling a Korean meaning with an English sound. Associative links are not strong logical links. They are not even very strong psychological links, because the mind tends to keep the Korean meaning and just throw away the difficult English sound. Can we build some SYSTEM of concepts that provides stronger links BETWEEN English words instead of between English words and Korean ones? (e.g. the “~a” ending that we find at the end of many continent names).

b)    Ha-ha points out VERY CORRECTLY that “upgrading” the level of thinking often has to do with asking “Why?” But notice that her “Why?” question has to do with why a country like Russia is CALLED a country and why Greenland is CALLED a country. This is a little like asking why Jinho is called Jinho. Can you think of an explanation that has something to do with ESSENCE? For example, WHY are the continents separated by oceans? Why are there earthquakes? Do continents move? Where are they going? Why?

c)    “Country” and “continent” are both concepts, but they belong to different conceptual systems. One obvious difference is, as we said, that continents are connected to geotectonic and to seismic facts in a way that countries are not. But another difference is that countries are connected to political and cultural facts in a way that continents are not. The data looks at countries that are not continents. What about continents that are not countries? (e.g. “What is the capital of Russia?” “Now, what is the capital of ASIA?”