Space conception in a
specific culture:
Children in the street
situation
Mônica Mesquita
Pontifícia Universidade Católica de São Paulo, Brazil
Abstract
This paper explores aspects of the conception of space
among the ‘street children’ from a project called the “Art and Life House”, in
São Paulo city, Brazil. As we know, the human being and its actions manifest
themselves in their natural, social, cultural and emotional environment. In the
“Art and Life House” I used the conception of space to investigate the
children’s reality, motivating them to learn more about the reality around
them, finding and describing meaning in their environment.
The beginning
I work with “children in the street situation” since
1993. “Children
in the street situation” are children who spend their days living with other
children in the streets of the city and their nights in shelters—or in another
place. The complexity of thought and the internal
beauty of these children and their culture fascinate me. The path I went
through—Mathematics, Mathematics Education and Ethnomathematics, and Sociology
of Mathematics, helped me to wrapped up the perspective of these
children in the context of the question that I will present here: the analysis
of the “space conception—orientation”—, i.e., how children’s conception of
space allows them to interact with their day-to-day world. For this analysis, I
made a transition from an anthropological position (Geertz, 1989;
Pinxten, van Dooren, & Harley, 1983) to a sociological position (Restivo, 1993). My position also draws on the work within
ethnomathematics by Ubiratan D’Ambrósio and on Alan Bishop’s work within
mathematics education.
In
a anthropological discussion, Geertz (1989) argues that the cognitive
aspects of a specific culture describe an individual’s “view of the world”. The
view of the world of a specific people is a picture this group draws of the
things, as they perceive them in a “simple reality”.
From
my observations, readings, and reflections I could perceive the necessity of
working with children in street situation to develop their world vision. To do
this, I looked for a ‘natural’ form of education, supported by my vision of the
individual human beings as a whole, integrated in the cosmos. For me, it is
important to reflect upon the way we human beings have understood ourselves
throughout our history..
Accordingly to
D’Ambrósio (1999), the distortions in the way we human beings
have understood ourselves lead to power, presumptuousness, greediness, envy,
avarice, arrogance, and indifference. I work with his hypothesis that peace
violations is a result of these distortions, that is, violation of the human
dignity and the elimination of the individual, and the inevitability of an
equitable society and an excessive aggression against nature. Like D’Ambrósio (1999), I consider that it is important for us to
reflect on the shape of the beliefs of humanity throughout their history.
Restivo (1993) helped me in this reflection when he says that
a “social construction” perspective shows how deeply politics, education, and
other social factors are implicated in mathematical work and mathematical
knowledge. He also suggests that as a social institution, modern mathematics is
itself a social problem in a modern society. Restivo points out that this perspective
focus on transforming both ways of living, our social relationships, and the
values evident in society at large.
The “Art and Life House”
The project I describe here deals with the concept of space among
‘street children’, sleeping overnight in a hostel called “Art and Life House”
in São Paulo city, Brazil. The aim of the house, in its social and political
context, is to promote and practice the vision of peace in its many dimensions:
inner peace, social peace and environmental peace. In this paper, the children
I describe are both children and teenagers aged from 3 to 16..
São
Paulo has an enormous number of ‘street children’. The overall number of these
children is highly transient, since they are in and out of their homes,
institutions and the street. We can easily find hundreds of children in the
street. Only on one year, 2000, the “Art and Life House” received 185 different
children.
The
goal of this paper is to analyze the space concept, i.e., the every day
geometric sense of these children. I believe it is possible to establish a
global view of the worldview among these children, a global view of their views
of the reality of the world as it impacts on their everyday lives. My intention
is to use their points of view as a starting point to encourage them in their
desire to understand the reality that surrounds them. I suggest that this can
be done in terms of a sociological approach to the every day mathematics
(especially the mathematics of space), which expands on a purely social
conception of mathematics.
In
this particular moment of world and cultural history, it is our priority to
establish a moral pattern and the highest ethical guarantee, always working
with the three qualities that, according to D’Ambrósio (D'Ambrósio, 1999), comprise a higher ethic: respect
for the other, solidarity with the other, and co-operation with
the other. To develop and apply these ideas in a way that a child can grasp the
true value of their individuality, and that s/he may have the opportunity to
practice this individuality in order to be valued for what s/he is, and not by
how s/he is. This is our real intention.
How
My starting point is Bishop’s (Bishop, 1999) presupposition that spatial structure has been
key in the development of the mathematics as an epistemic work—calling this the
activity of “locating” (that is, location as a form of the universal quest—to
localize an idea in our personal understanding, to localize ourselves within
our contexts). This activity is essential for the beginning of the search for
our place within the universe. The humans need to know its own grounds, looking
for food, exploring sea and land, and self-study are needs so basic that we can
understand why “location” is a priority. Bishop (Bishop, 1999) even suggests that “location” comes prior to
the activity of counting.
All
societies developed methods, more or less sophisticated, to codify and
symbolize spatial structure. The location activity has received less attention
than the counting activity, and, as a consequence, location is less well
documented in the cultural studies of mathematical ideas (Bishop, 1999).
Pinxten
et al. (Pinxten et al., 1983) examined in detail how
particular cultures established space concepts. They consider three levels of
space: physical space, social-geographic space, and cosmological space. The
spatial world has multiple perspectives, not only through geometric notions but
also through ideas of directional space (internal and external), positional
space (intra- and inter-personal), and unlimited space (global vision), notions
all of which are closely related to our own image. From these multiple
perspectives, I focused on orientation
to work with the children. My hypothesis was that orientation was closely
connected with the social integration of these children, as individuals. This
choice is, also, a first step towards the respect of the other, that is,
towards inner peace.
Since
May 2000 I worked on this project with these children twice a week – until
September 2001. In the “Art and Life House” there is room to lodge 30 children
overnight. The data used in this paper refer to 14 settled children, which
participated in all sessions. I worked with
28 children—but it was not possible to have reliable data from the other 14,
since their presence in the “Art and Life House” was very variable.
It
was not necessary to perform any socialization session between the children and
me since I had already worked with them for three years as a volunteer. All the
sessions were documented: by description of the one observe as well as
tape-recorded. The institution has two teams of educators, rotating every day,
to create and perform activities with these children. These educators work for
the São Paulo City Hall and took an active part on this project. I had open
interviews with them, as well as with all other employees. From the analysis of
these interviews, I’ve collected precious data to base the activities as well
as some information about how these children arrive at the “Art and Life
House”.
Only
a small fraction of the sessions referring to the “orientation theme” — are
reported here. The sessions allowed me to realize “immediately” that these
children have a different conception about space, and work with this conception
could helpful me to clarify some of their behaviors, and possibly learn
something from them.
In
the first session, the group sat in a circle and through an open and collective
interview, I observed what
represented for each child the orientation conception. There were 20 children
in this session. In the discussion, I then asked the children a question which,
at the time, did not seem that important to me, but which their answers
revealed to be the critical issue:
"What
do you do when you are lost?".
All the children answered:
"I
go back home.".
After discussing this response, I concluded that these children didn’t
have the “being-lost” concept.
How? – I asked
I always know to do it! I always go back home
when I want. – One of them answered.
I
agree with Lewis (Lewis, 1976) about the human capacity to
find a route and orientate oneself in space. His hypothesis is that children
have a kind of “inner compass”. For me, this “inner compass” is developed
through social interactions.
In
this session, I observed that the most difficult issue for the children were to
understand what is “to be lost”. The word “lost” was used in some previously
activities, using games. In the beginning, I repeated a lot of times for each
child the same question: “What do you do when you are lost?” Children did not
answer my question — for them it was very difficult to understand the
expression “you are lost”.
A typical reaction was:
Am I lost? How? – The child said.
When you are lost! – I said.
How can I be lost? – The child said.
For the next sessions
I developed an activity about making bread — in this activity children worked
in pairs on maquettes of bread. They used the bread to represent how to find
their route. I chose it because of the necessity to bake bread for breakfast.
Using the maquettes of bread, I wanted to observe the children’s intellectual
organization regarding their “inner compass”. This would help me to understand
the orientation concept within their culture. These children showed a deep
knowledge of the urban topography. They built the bread dough maquettes on
boards with ideas of orientation, showing significative knowledge of prepositions
such as behind, in front of, above, below, near, far. As they orientated
themselves with their maquettes, they illustrated their knowledge about the
sun, the stars and the wind. Each pair built a maquette about the theme “which
is the way back home?”.
At last
Encouraging each child to achieve his/her
creative potential showed me that these children in the street situation have
ideas of orientation, which are more dynamic than static. They can distinguish
objects and consider the relation among them; “everything moves” seems to be an
important property objects have, according to them. It is impressive to see how
easy is for them to find their route, their way, evidenced through the
activities.
The
observation of the activities also supports the idea that there is a process of
knowledge transmission from one generation to another, within the group. Older
people — always older youngsters that assume a “street parents” role — teach
children in the street situation not only to orientate themselves by means of
watching static objects, like buildings, train stations, street signs, and
streets, but also through observation of natural objects such as the sun, moon,
stars, and the wind..
The
activities have brought this group of children to co-operate in the
preservation of common property, because while these children orientated
themselves by means of their maquettes, they give meaning to the objects on
their route, on their way. Through the activities, children could observe more
about what is around them… and probably could observe it because they discussed
it in the group… in their group. They seem to have a complex and peculiar
spatial system that can be used as subsumer to learn more formal concepts such
as distance, part/whole, internal/external, and central/peripheral.
To
work, study, learn, and live with these children showed me how human values and
life can significatively nourish the construction of knowledge in the context
of their specific culture: “All cultures have theirs own specific ways to represent
the world” (Pinxten et al., 1983).
I
would like to thank Ron Eglash for your many helpful comments and discussions
regarding this paper from my MES3 paper.
References
Bishop, A. J. (1999). Enculturación matemática, la educación matemática desde una perspectiva cultural. Barcelona: Paidós.
D'Ambrósio, U. (1999). Educação para uma sociedade em transição. São Paulo: Papirus.
Geertz, C. (1989). A interpretação das culturas. São Paulo: Papirus.
Lewis, D. (1976). Observations on
route-finding and spatial orientation among the aboriginal peoples of the
Western Desert of Central Australia. Oceânia
Newspaper, XLVI.
Pinxten, R., van Dooren, I., &
Harley, F. (1983). The anthropology of
space. Pennsylvania: University of Pennsylvania Press.
Restivo, S. (1993). Math worlds, philosophical and social
studies of Mathematics and Mathematics Education. Albany: State of
University of NY.