Introduction
The main theme of my project for EMT 805 is to understand Piaget and his
sociological studies considering a well-known fact that he worked on the
aspects of learning of an individual child. I thought this was going to
be meaningful, in particular, when I considered the current criticism about
Piaget's work on an individual child's learning compared to so-called Vygotsky's
explanation about a child's learning in a sociocultural framework. The criticism
that I described before intrigued me to find out what Piaget might have
thought about the sociocultural influences in children's learning environment.
The starting question was that "did he never concern the sociocultural
sides of children's learning? " In addition to that, at the beginning
of the quarter, von Glasersfeld's recommendation to a book, "Sociological
Studies" (1995) by Piaget helped me lead into shaping this project.
My interpretation is that this social criticism of Piaget's position has
not been based on a correct analysis about his work. I was able to see that
what people criticize about Piaget's studies does not give sufficient attention
to Piaget's account to the social aspects of children's experience. Piaget's
many thoughts about sociocultural influences in children's learning will
be explained in this paper.
This paper consists of introduction, two major parts, discussion, and Appendix
1 and 2; Piaget's sociological studies, and question and Piaget's contribution
to the individual aspects of children's learning. In the first part of this
paper, I will elaborate on Piaget's understanding about sociological aspects
in children's learning. The book, "Sociological Studies"(1995)
which is translated by Brown et all is the main source of information. In
the second part of this paper, I will revisit to his contribution to the
individual aspects of children's learning which can never be separated from
his understanding about sociological aspects of children's learning. Then,
I will continue to explain my understanding of the importance of individual
aspects in children's learning. In addition to that, the issues of "egocentrism"
will be discussed in order to support the rationality of Piaget's studies.
In the Appendix, I will excerpt two dialogues from Chapter 7 of "Sociological
Studies", The development in the child of the idea of homeland
and of foreign relationships for readers' useful information. It will
be good to start reading the dialogues first before you get into the second
part of this paper.
Part 1: Piaget's Sociological Studies
Differently from general understanding, to Piaget, the social aspects of
children's experience was one of the most important assumptions in their
learning processes just as the individual aspects of children's experience
were. Piaget did have a clear understanding about how social practices occur
in children's acquisition of available knowledge and the creation of novel
knowledge. Leslie Smith, the editor of the "Sociological Studies",
says that Piaget claimed that 'the social need to share the thought of others
and to communicate our own and to convince is at the basis of our need for
verification. Proof is born through discussion' (p. 5). I think it is important
to highlight that Piaget's explicit claim is that the individual and society
per se are severally and jointly insufficient in the formation of rationality.
But, Piaget's aim is not to ignore the social basis of knowledge but rather
to focus on the acquisition of knowledge with due attention to its rational
legitimization. Let me take a specific question here in order to understand
Piaget's intention in a more practical way in mathematics education: "Who
are the actor in a learning situation of a mathematics class?"
"Who actually opens the door under the influx of social need
from outside of the mathematics classroom?" If I assume a mathematics
classroom in a school, then "what would the children in the classroom
be doing when the teacher introduces a new mathematical concept?"
I think Piaget will probably answer that it is the each individual child
who shows the different levels of understanding by his(or her) own operational
activities in learning. I believe that this is what Piaget's work makes
distinct from that of others.
I said in the introduction that I would present the two dialogues from
Piaget's empirical study concerning children's ideas about the homeland
and foreign relationships later in the Appendix 1 & 2. Now I want to
ask the following question. "What do this kind of empirical studies
by Piaget tell us? " Smith says the following: Science is an integral
part of culture and tracking the course of 'intellectual mutations' as they
occur in children's re-discovery of logic and scientific method is a legitimate
form of social investigation. Thus it could be said that all of the phenomena
investigated in Piaget's empirical studies are social phenomena, even if
the converse is not true (p. 8). Related to Smith's saying, I want to say
that Piaget's own position stated that social elements are indeed essential
to the formation of knowledge. I think it is because Piaget thought more
about what is the contribution of individual experiences to the initial
origins of knowledge when he considered children's learning, specially at
the early stages of intellectual development of the children. To him, the
concept of psychology of children must have been equivalent to that of sociology
of the children.
Let me approach the issue at a little bit different angle by thinking of
what "equilibration" might have meant to Piaget: Does
it only happen in the internal side of an individual child?
Fact is a form of equilibrium - or disequilibrium - whilst the ideal is
another equilibrium, as real in a sense as the first, but often sketches
rather than realized: the ideal is a limiting case, as the mathematicians
say, or even the full equilibrium towards which the false or unstable equilibria
of the actual world tend.... Ideal psychological equilibrium occurs
when whole and parts are in a state of harmony,
of reciprocal conservation. (Piaget, 1918, pp. 46, 178)
I had to interpret what Piaget wanted to mean by "whole and parts".
I think he wanted to say the social side of learning by "whole"
and the individual side of learning by "parts". Smith also explains
that Piaget's account of equilibration has a social component because the
search for coherence requires two types of matching, both within one mind
and between the minds of partners to a communicative exchange. Even though
the "equilibrium" can give us some flavor of self-regulation
from an individual mind he made it clear in the "Sociological Studies,"
that knowledge arises neither from the subject nor the object but from the
inter-dependent interaction between them, so as to advance from there in
the dual direction of an objectified exteriorization and a reflexive interiorization(p.
27) To Piaget, there was no series of three successive terms: biology ---
psychology --- sociology, but rather a simultaneous link from biology to
psychology and sociology together, these two disciplines having the same
object, but treating it from distinct and complementary viewpoints. Therefore,
psychology and sociology are comparable, in their interdependence(p. 33).
In the "Sociological Studies", Smith even suggests that
Piaget's account is an advance over that of Vygotsky with two reasons. First,
it is because Piaget's account does address the question as to when social
experience is successful. Second, Piaget was able to squarely address the
'learning paradox' . Since I think the second reason is not much
related to my theme of this paper I will just treat the first reason here.
Piaget thought that a central feature of social experience is human communication
leading to an exchange of thought. Yet not all communication is successful(p.
11). Isn't it true that the mathematical communication in a classroom is
not always successful? If we even refer to Davydov's activity theory (P.
Cobb, M. Perlwitz, & D. Underwood, 1996), then the ways of classroom
communications would be able to be characterized by the dominance of the
unilateral utterance from teacher to student. However, I think what should
happen in classroom communication is mutual respect and cooperation which
are aligned with what Piaget suggested. In consequence, Piaget thought that
criteria are necessary to identify the minimum conditions which must be
satisfied for attempted, or intended, communication actually to succeed.
But, from Smith's saying, Vygotsky does not offer a criterion as to when
an exchange of thought leads to successful internalization while Piaget
does state conditions which have to be satisfied for an exchange of thought
to occur.
Smith's explanation of the advance of Piaget over Vygotsky have triggered
me into thinking of individual differences in learning of mathematics. In
particular, the issue was standing out whenever I went to the Clarke High
School and observe a mathematics classroom during this quarter. It was striking
to me to see the different levels of understanding of the mathematical content
in the classroom. Shouldn't I say that it was the same sociocultural environment
for the students in the classroom? I have thought a lot about what ought
to be considered in answering why-and-how of the big individual differences
in students' learning mathematics. I believe what Steffe(1996) quotes from
Maturana(1978) helps make my point clear;
If the state a system adopts as a result of an interaction were specified
by the properties of the entity with which it interacts, then the interaction
would be an instructive interaction.... all instructable systems
would adopt the same state under the same perturbations
and would necessarily be indistinguishable to a
standard observer (p. 84)
Put it differently, if I just take the sociocultural theory of learning,
then how could the theory make me understand the individual differences
in the mathematics classroom in the real world? Rheta DeVries(1996) mentions
that "In Piaget's view, a life dominated by the rules of others through
a morality of obedience will never lead to the kind of reflection necessary
for commitment to internal or autonomous principles of moral judgment (p.
5)". She also awares that Piaget warned that coercion socializes only
the surface of behavior and actually reinforces the child's tendency to
rely on regulation by others. I think this is a critical point for us to
keep mind if we want the child to construct his(or her) own knowledge.
Apart from any judgment about the advance-related matter of Piaget and
Vygotsky, I want to suggest that the social criticism to Piaget's work over
Vygotskian perspective should be reconsidered in a new way. Since Piaget
views education as a two-termed relation which links, on the one hand, the
values (intellectual, moral, social) under the charge of an educator and,
on the other hand, the individual mind of the child or learner(p. 14). Any
evaluation about Piaget's work and Vygotsky's work should be able to happen
in a way that the comparative scrutiny of their specific positions can be
offered rather than just trying to give the global comparison of the two
perspectives. Finally, let us remember that Piaget accepts as a given that
human experience is, and has to be, both psychological and social (p. 3).
Part 2: Piaget's contribution to children's learning based on sociological
studies
If readers take my explanations about the social criticism about Piaget
as a plausible interpretation at this point, then they might be curious
about what made Piaget work mainly on the individual sides of children's
learning. I wondered this so much during this project. Piaget mentioned
August Comte in the "Sociological Studies" (p. 215);
August Comte stated correctly that the most important phenomenon of social
life was the mutual pressure each generation exerts on the others. Now,
one of the principal aims of child psychology is precisely the study of
this phenomenon. So, the observation of children is not such a bad method
when deciding the extent to which rationality is a matter of individual
development and to what extent it is something social.
I think Piaget gave an answer to the question by quoting Comte. Piaget
also said that it is pointless to hunt for whether the seat of the mechanism
of children's learning is biological, purely psychological, or social( p.
216). But, one thing that we should understand is that to him, it must have
been important to believe that one cannot deny that intellectual development,
from birth, is simultaneously the work of society and of the individual.
Piaget's general characterization of heteronomous processes of understanding
is that they are egocentric, when based within the individual's mind, and
sociocentric, when based in social interactions. Then, why is the individual's
mind more important? Piaget gives an answer. "A real exchange of thought
is liberating, permitting the individual to re-cast available knowledge
into valid forms of new knowledge which is manifest both in the continual
adaptation to new circumstances which are never identical and in the growth
of the human powers required in their coordination(p. 14)".
I think it's time for me to introduce Piaget's explanation about "individuality".
He understood "individuality" in two very distinct ways.
The first is the self, that is, the individual as centered on himself.
The second is the personality which is exactly the opposite to the
self in some sense. To me, self explains a lot about "egocentrism".
The self goes without saying that, to the extent that society penetrates
into the individual from the outside, he was not prepared to accept this
without further ado: there is no pre-established harmony between each one's
psycho-biological constitution and the set of intellectual and moral values
proposed by communal life... (p. 218). He continues. Just as a child of
2 or 3 is not able to conceive of the laws of the solar system simply by
looking at the stars and his immediate horizon, so this same child cannot
discover the various aspects of intellectual and moral reciprocity all at
once simply by being in contact with his family circle. In both cases, a
mental transformation is required that consists not just in a passive recording
of external facts, but in a structural elaboration of new relations. Consequently,
a set of active, intellectual, but non-socialized drives will obviously
exist in the individual, either because they have not yet been socialized,
or because they resist this socialization(p. 218). Let us keep in mind my
question raised above: "why did Piaget concentrate on the individual
aspects of children's learning?" The key to another answer, I think,
might be that his insight about the existence of unique ways of learning
from each individual child even though they are in a very similar social
setting. I think it is important to understand that society is either cooperation
or constraint in a child. In my opinion, this is the place where a child's
"egocentrism" starts working when society does provide
specially constraint to the child.
Piaget explains that childhood represents quite different character. Childhood
individuality is not only partially resistant to socialization, as is our
own: it is above all prior to it, to the exact extent to which society only
conquers the individual progressively and from the outside in. I think the
next explanation is critical :
Consequently, childhood egocentrism is unconscious of itself: it is a sort
of 'innocence ' not only 'of the eye' but of the whole mind,
such that the immediate sight of people and things seems to be the only
one possible and is not yet situated in relation to other points of view.
This being the case, the young child is largely centered upon himself, but
unknowingly, and so projects his subjectivity into things and into other
people: he only perceives people and objects other than himself, but he
sees them only through himself (p. 218).
iaget uses the word "egocentrism" to refer to the tendency
to see things from only one's own point of view. Therefore, this use should
not carry the usual negative connotation of willful "self-centeredness"(P.
55. 1978). It is natural since the child is not even aware that other viewpoints
or perspectives exist. This is why I agree that children's "egocentrism"
is innocent and how differently they think and learn a new knowledge
from how we, adults, do. The some parts of the dialogues from two children
in the next shows the typicality of children's "egocentrism"
and how it is changed into a more adult-like way of thinking when they overcome
the innocent "egocentrism":
(From Christian's Dialogue, pp. 268-269):
If I asked the same question to someone who is French, if I said:
Tell me, imagine that you were born without a country and that you could
now choose any country you wanted', what do you think this child would choose?
He want to be Swiss.
Why?
Because he want to be Swiss.
And if I asked him who were nicer, the Swiss or the French or if they
are both the same, what would he say?
He would say, the Swiss are nicer than the French.
Why would he say that?
Because... they know the Swiss are nicer.
(From Arlette R.'s Dialogue, p. 273):
If I asked a Frenchman to choose freely any nationality he wanted, which
one do you think he'd choose?
French.
Why?
Because he was born in France and it's his country..
......
Between the two of you, who would be right?
You can't tell. Everyone is right from her own point of view. Each
person has her own opinion.
Let's think of the following question now; "How do you think Vygotsky
understood the "innocence" of a child when he(or she) starts learning?"
I am sure that this question might lead us to a great deal of discussion.
There is a nice part that shows Piaget's insight about children's way of
learning:
The history of scientific ideas, as Koyre says 'shows us the human mind
at grips with reality; reveals its victories and its defeats; shows us what
superhuman effort has been the cost of each step on the road to understanding
of the real, an effect which leads, sometimes, to a veritable 'mutation'
of the human intellect: a transformation which allows ideas
which have been painfully 'invented' by the greatest
geniuses to become, not merely accessible, but even
easy and obvious, to schoolchildren'(p. 36).
The individual child is sure dual, oscillating endlessly between
the social and egocentrism. I think we need to reflect upon our way
of teaching children in school. If it is as similar as what is described
in the above, then we should start taking actions to the way that Piaget
showed us long ago.
This second part of the paper did never intend to show any superiority
of Piaget over any other sociocultural theory. The point is to understand
Piaget's position better. In his book, "Sociological Studies",
he is saying that there should be certainly an individual pole to the mind(p.
227) and I think this claim has been supported by the recognition of the
existence of "egocentrism" . We should not dissociate children's
intelligence by isolating the individual pole from its complementary social
pole. The study about Children's "egocentrism" was a deep
effort to epistemic issues.
Here, let me briefly explain the result of Piaget's study. I believe that
for readers who are not clear about what "egocentrism"
means the dialogues from the Piaget's empirical study must be a good source
even though they are not mathematical dialogues. What Piaget observed from
the dialogues in his study was the existence of "reciprocity"
in the child. He concluded that both the discovery of one's own homeland
and the understanding of other people develop in the child according to
a process characterized by the passage from "egocentrism"
to the establishment of reciprocal relationships (PP. 273-274). To Piaget,
the main problem is not to determine what one must or must not instill into
the child, but the reciprocity in thought and in real life. I think that
the acquisition of "reciprocity" will finally get a child
to obtaining of a knowledge in a sociocultural context than the time he
was only in the egocentric stage. I may be able to say that this is the
time for the child when the formal and institutionalized school learning
happens effectively.
Discussion
To a question that I posed in the middle of this paper: "How should
I understand all the various individual differences in children's learning
specially in the setting of sociocultural theories?" I think
I have found an answer to this question. Needless to say, understanding
about children's "egocentrism" was a key to getting to
the answer. I also could start seriously thinking about the characteristics
of Piaget's work, the differences from others, school learning, children's
learning of mathematics, what's count?, and so on. I am also glad that I
have started getting the second insight to the importance of "individuality"
through the project - represented by "self" in Piaget's
term. Finally, it was a surprising result to me that I started being skeptic
about the ways of teaching in school learning during the project. In particular,
I thought a lot about what I need to do considering the current situation
in schools where mathematics instruction is unilaterally given to the children.
It really lead me into a belief that there should be certainly an individual
pole when we think of children's learning. So I say that this project has
been meaningful to me in understanding Piaget and other sociocultural studies
in many different view points and thinking of the problems that our mathematics
community has to solve for our children. I believe that "Being critical
constructively to our way of teaching and learning of mathematics"
is an important matter to us.
APPENDIX 1
CHRISTIAN K., 6;5.
If you were born without a country, which one would you choose?
I'd want to be Swiss. (The child is Swiss.)
Why?
Because!
If you could choose between France and Switzerland, would you choose Switzerland?
Yes.
Why?
Because the French are nasty. The Swiss are nicer.
Why?
Because the Swiss didn't go to war.
If I asked the same question to someone who is French, if I said:
Tell me, imagine that you were born without a country and that you could
now choose any country you wanted', what do you think this child would choose?
He want to be Swiss.
Why?
Because he want to be Swiss.
And if I asked him who were nicer, the Swiss or the French or if they are
both the same, what would he say?
He would say, the Swiss are nicer than the French.
Why would he say that?
Because... they know the Swiss are nicer.
APPENDIX 2
ARLETTE R., 12;6 (Swiss).
If you didn't have a nationality and you had a free choice in nationality,
which one would you choose?
Swiss nationality.
Why?
Because I was born in Switzerland and I 'm from here.
Fair enough. Who do you think is nicer, the French or the Swiss, or do you
think they are the same?
Oh! In general, they are the same. Some Swiss are very nice and some French
are very nice, it doesn't depend on the country.
Who is more intelligent, a Swiss person or a French person?
They all have qualities. The Swiss sing quite well, the French have great
composer.
If I asked a Frenchman to choose freely any nationality he wanted, which
one do you think he'd choose?
French.
Why?
Because he was born in France and it's his country.
And for a Frenchwoman, who would seem nicer, a Frenchman or a man who is
Swiss?
I don't know. Maybe for her the French, but I 'm not sure.
Between the two of you, who would be right?
You can't tell. Everyone is right from her own point of view. Each person
has her own opinion.
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