CHI LDREN , SPACE, AN D TH E URBAN STREET:
AN ETHN OM ATH EM ATI CS POSTURE
Dissert at ion present ed for t he PhD Degree in Educat ion Science – Cur ricular Theory and Science Teaching, by Univer sidade Nova de Lisboa, Faculdade de Ciências e Tecnologia. The present dissert at ion was prepared under t he auspices of t he I I I Quadro Com unit ário de Apoio, exist ing bet ween European Social Fund and t he nat ional fund of MCTES, in t he Fundação para a Ciência e a Tecnologia.
LI SBON
2008
Children, Spa ce, and t he Urban St reet :
An Et hnom a t hem at ics Post ure
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Môn ica M ar ia Borg es Mesqu it a Universidade Nova de Lisboa / Pt
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. Sa l Rest ivo – Advisor Rensselaer Polyt echnic I nst it ut e / USA
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. Ubirat an D’Am brosio – Advisor Universidade de São Paulo / Br
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. João Filipe Mat os Co- Advisor – Universidade de Lisboa / Pt
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. Vit or Du a rt e Teodo ro I nst it ut ional Link – Univer sidade Nova de Lisboa / Pt
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. Pet e r Gat es I nst it ut ional Link – Not t ingham Universit y / UK
Some exercises observed during my life in Portugal…
The promotion of social interactions focusing the study of
complexity that involves all life coexistent on Earth.
The listening of the voices that claim the emergent position of
diversity, focusing the recognition and validation
of different knowledges.
The struggle to have a space, being a woman
in the current Western society.
The unconditional friendship.
The presence overcoming the physical absence.
Being Teresa Ambrósio.
“ … na exigência sempre actual de dignificação e defesa do humano, nehum plano de
acção de aprendizagem ao longo da vida, poderá prescindir, qualquer que seja a sua
uegência, da indispensabilidade de investigação e de avaliação continua, crítica,
reflexiva tendo como referência maxima o Homem na sua globalidade – fim e sujeito
de toda a aprendizagem. Creio que o diálogo entre a comunidade de investigação, os
técnicos, os poltícos e os administradores dos sitemas é hoje mais que nunca
imprescindível. Os quadros da preparação das políticas educativas em que nos
baseávamos nos anos 60, 70 e 80, já não são adequados ao conhecimento
compreensivo que temos hoje desta actividade social, que é a acção educativa e de
aprendizagem ao longo da vida.” (Ambrósio, 2001 p169)
ACKN OW LEDGEM EN TS
Professor Dr. Sal Rest ivo… a m ovem ent from t he m ind t o t he heart , uncondit ional and integral presence in t he developm ent of t his work, in t he developm ent of m y hum an condit ion, in the developm ent of m y int ellect ual process. My deep recognit ion and grat it ude for all t he effort and energy t hat you have spent along t his t rack. The coherence bet ween your writing and your pract ice is in m y m ent al em ot ion.
Professor Dr. Ubirat an D ’Am brosio… a m ovem ent from t he heart t o t he m ind, coraj oso encoraj ador, libert o libert ador, pacífico
pacificador, fort aleza da em oção e sensível fort ificador. My gratit ude
will be in m y t ranscendence; m y spirit is st ronger and m y st eps can reach further. The coherence between your writ ing and your
pract ice is in m y em ot ional m ind.
My grat it ude t o Professor Dr. João Filipe Mat os, a hum an being who opens spaces, list ening t o different voices and working wit h new ideas in favor of dignit y, equit y, and love. I t has been a
pleasure t o work with you and witness your at t itudes in face of t he violent discrim inations that pursue those who m arch against the im perialism present in the world.
My grat it ude t o Professor Dr. Vit or Duart e Teodoro, a hum an being who opened m y spaces in different m om ent s and let m e wit ness t he legality st ill exist ent in the world. I learned a lot wit h you!
Universit y, and t o Professor Dr. Tony Cot t on, a hum an being who opened m y spaces abroad and m ade m e feel at hom e in t he cit y of Not t ingham .
Const ant pleasure and learning spaces … Lia, Renan and Lucas! My deep grat it ude for t ransform ing an egoist ic PhD process int o a com m unit arian process… t o live this was wonderful!
Margarida, Terezinha and Sergio… you are m e and I am you! Thank you so m uch for all t he support , all the prayers, and all the love.
Osw aldo, Benedict a, Vict or, H elena, H ilda, Ana, H eit or, D irceu, and Teda… st rong act ors of m y life. An anarchist fam ily, what m ore could I ask for? Moni… m ade in t his fam ily.
Professor Dr. Enrique de La Torre, a person t hat has list ened t o m e and has given m e courage t o jum p in t his process – an
Educat or, in Paulo Freire’s sense. My deep grat it ude, dear friend!
Professor Drª Rhet t a Moran and Professor Drª Fiona W alls: Here is m y grat itude for all t he pat ience as m y English reviewers of chapt ers 2 and 3. A hard t ask that linked us m ore as soul sist ers.
To Fundação para a Ciências e Tecnologia – FCT, I present m y
respect as one who was part of a liberating inst itut ion where t he st udent s lead, in all t he direct ions of their processes and are uncondit ionally support ed in their decisions.
Leo H aupt and Ant ónio Raposo, m y soul brot hers who gave m e em ot ional support t o be alive and showed m e t hat I was not alone in m y m usical delirium s.
W om en… Maria do Carm o Dom ite, Wenda Bauschpies, Madalena Sant os, Fiona Walls, Gracinda Caet ano, Ana Viana, Mart a Tabares, Adelaide Paredes, Josefa Alves ( Leda) , Margarida Belchior e Maria João… a fem inine influence present in t his process t hrough m y
voice, m aking it alm ost im possible t o ident ify each one of you inside m e separat ely. My appreciat ion t o you is in what I am now… a lit t le bit of you!
My recognit ion for and in a space of freedom nam ed Mat hem at ics Educat ion and Society - MES; an unusual int ernat ional conference t hat nourishes free int ellect ual spaces for ideas in m at hem at ical educat ion and prom ot es com m unal social int eract ion am ong the part icipant s. This is a com m unity t hat loves m athem at ics but opposes t he inequalit ies, t he physical and m ent al abuses, t he recklessness, t he excess of power and the lack of et hics that
m at hem at ics as a social inst itut ion, a profession, and a bureaucracy has fost ered t hroughout hum an hist ory.
My grat it ude t o t he colleagues of Grupo de Estudo e Pesquisa em Et nom atem át ica – GEPEm h t t p:/ / paj e.fe.u sp.br/ ~ et n om at /, from São Paulo
– Brazil, and of Grupos de I nvest igação At elier 3 4
h t t p:/ / at e lie r 3 4 .u ied.f ct .u n l.pt / in dex.h t m, and ATMS h t t p:/ / p roj e ct os.crie.f c.u l. pt /,
Lia… t he world was given a gift when you arrived, and I was chosen t o walk with you as your apprent ice. You helped m e const ruct m y English and m y soul, and shared in t he developm ent of t his thesis, and here as in m y life m ore generally you have been a basic
elem ent of what I am , where I am , and where I am going. You are m y daught er, a light that shines on m y pat h.
Children, children of t he world, and especially t he 1 4 of you: Priscila
Ant onio Capoeirinha
Cam ila Geni
Pinguinha Pablo
Am arelinho N úbia
Laulau D avid
W aldem ir
Elizet e Toninho
… m y num ber of “ luck” and “ t he num ber” t hat t aught m e how life is social and how t he collect ive st ruggles in local com m unit ies could be
t he key t o the open syst em s.
2005 – Supposed year of Capoeirinha’s deat h, who was killed in São Paulo´ st reet s aft er a conflic wit h t he police ; he disappeared from his st reet brot hers and sist ers and m e.
2006 – Laulau died t hree years aft er he was exposed t o a clandest ine ( illegal) kidney operat ion : t he fam ous and silent robbery of t he hum an beings’ organs, very frenquent in children in t he st reet sit uat t ion around t he world.
SUM ÁRI O
Est e t rabalho explora as experiências urbanas das vidas sociais m arginais at ravés dos regim es epistém icos da m at em ática no cent ro das suas est ratégias de
sobrevivência. Concent ra- se, em particular, nos regim es epist ém icos da m at em ática da crianças em situação de rua e visa reconhecer, com preender e validar form as de m at em ática const ruídas e ut ilizadas fora das instituições de produção m at em ática estabelecidas. Este t rabalho assenta na fundam ent ação d’A I m aginação Mat em ática’, que reúne const rucionism o social ( com o é desenvolvido na sociologia da m at em ática de Sal Rest ivo) e a concepção da Etnom at em át ica de Ubiratan D'Am brosio. Aqui, estas duas idéias cent rais cont ribuem para o obj ectivo de ligar a produção da m at em ática form al e a práxis da m at em ática inform al, que é a m at em ática produzida nas m argens onde sobrevivência é m ais im portant e do que refletir e reproduzir culturas profissionais. O fact o é que a m at em ática
institucionalizada profissional no âm bito do m odo cont em porâneo de produção dom esticou obj ectos m at em áticos. A m at em ática inform al surge e é difundida em posições e vozes nas m argens da sociedade e da m atem át ica. O encont ro das posições e vozes m arginais e não m arginais resulta e é um a prática social act ivista. Esta prática representa o fim do verbalism o e o início de um a
conhecim ento sit uado que está envolvido com o nosso quotidiano, com a nossa exist ência. Só at ravés desta form a de prática, um a prát ica que une o form al e o inform al, podem os perceber o com pleto poder do conhecim ento m atem át ico com o um a coisa social ( no sentido de Durkheim ) , um produto da consciência colect iva que expressa realidades colectivas e um a cat egoria de conhecim ent o exist ente em qualquer cult ura. I sto é tão verdade para a m atem át ica nas
m argens com o para a m at em át ica profissional. O foco dest e t rabalho é contribuir para um m anifesto polít ico em ergent e do m arginal que dem onst ra as realidades sociais e o poder social da sua m at em át ica. I sto faz- se possível por m eio da aplicação de t eoria social, e das prát icas da etnografia e história. Estas
ABSTRACT
This work explores the urban experiences of m arginal social lives through the m athem at ical epistem ic regim es at the core of t heir survival st rat egies. I t focuses in particular on the m at hem atical epist em ic regim es of children in a st reet
situat ion and seeks to recognize, understand, and validat e form s of m at hem atics const ruct ed and used outside of t he established institutions of m athem atical product ion. This w ork rest s on t he foundat ion of "The Mathem atical I m aginat ion", which draw s t ogether social const ruct ionism ( as it is developed in Sal Restivo's sociology of m athem atics) and Ubiratan D'Am brosio's concept ion of
et hnom at hem at ics. These t wo cent ral ideas cont ribut e to t he obj ective here of connecting t he production of form al m at hem at ics and the praxis of inform al m athem at ics, t he m athem at ics produced at the m argins where survival is m ore im portant t han reflect ing and reproducing professional cultures. The fact is that professional institutionalized m athem atics wit hin the contem porary m ode of product ion has dom esticat ed m athem atical obj ect s. I nform al m athem atics arises and is broadcast in the positions and voices at t he m argins of societ y and
m athem at ics. The bringing together of m arginal and non- m arginal positions and voices results in and is an act ivist social practice. This pract ice represents t he end of verbalism and the beginning of a situated knowledge that is engaged with our everyday lives, with our very being. Only through t his form of practice, a pract ice that links the form al and the inform al, can w e realize the full pow er of
m athem at ical knowledge as a social thing ( in Durkheim 's sense) , a product of the collective consciousness that expresses collect ive realit ies and a cat egory of know ledge present in every cult ure. This is as t rue for m at hem at ics at t he m argins as it is for professional m at hem atics. The point of this work is to
cont ribut e to an em erging polit ical m anifesto of the m arginal that dem onst rates the social realit ies and social power of their m at hem at ics. This is m ade possible through the applicat ion of social t heory, and t he practices of ethnography
TABLE OF FI GURES
Chapt er 1
1.1 Non- Spaces and I nvisible Beings 05
1.2 Scenarios and Narrat ives 19
Chapt er 2
2.1 Thinking and Seeing 29
2.2 Durkheim : a Social Being 30
2.3 Basic Concept s 62
2.4 First Cont act 80
Chapt er 3
3.1 Kaleidoscope 92
3.2 Mat hem atics and Space 98
3.3 Et hnom at hem at ics 113
Chapt er 4
4.1 Geographical and Hist orical Cont ext s 123
4.2 Bar I I At o 124
4.3 Chuvas no Glicério 124
4.4 São Paulo in t he world 125
4.5 The Cit y 126
4.6 Green Areas 127
4.7 Favelas and Cort iços 128
4.8 Tiet ê and Pinheiros 130
4.9 Prim eira Missa 137
4.10 The Wheel of Exposed 145
4.11 Baianas no Bexiga 146
4.13 Oliver and Gravoche 150
4.14 I t alian Hist ory 152
4.15 Past and Present 155
4.16 Social and Cult ural Cont ext s 165
4.17 Moni 1971 166
4.18 Moni 1966 167
4.19 Praça da República 168
4.20 I m plosion 170
4.21 Copan Lineas 172
4.22 Copan – Avesso do Avesso 174
4.23 Moni 1968 175
4.24 Moni 1969 175
4.25 Rua Maria Ant onia 176
4.26 The ram ps in Block B 177
4.27 Block B 177
4.28 Fam ily, Windows, and St airs 178
Chapt er 5
5.1 I piranga X São João 184
5.2 I rm ã Dulce and The Cult ural Painel in YMCA 189 5.3 Minhocão – a sym bolism of t he non- space 190 5.4 Pont ifícia Universidade Cat ólica de São Paulo
Cam pus Marquês de Paranaguá 192
5.5 Sit ucionalidade 198
5.6 FI PE’s Table 205
5.7 The World by St reet Signs 211
5.8 Casa Art e e Vida 217
5.9 Rua 218
5.10 Capa 219
5.11 Space, Social St ruct ure, and St reet 222
5.12 Social Cont ext 227
5.14 Spat ial Context 228 5.15 The Pyt hagorean Exercise – Act 1 229 5.16 The Pyt hagorean Exercise – Act 2 230 5.17 The Pyt hagorean Exercise – Act 3 231
5.18 A Point of View 234
5.19 The Robbery and Mathem at ics Knowledge – 1 235 5.20 The Roberry and Mat hem atics Knowledge – 2 235
5.21 Being 238
5.22 Making Bread 242
Chapt er 6
6.1 Asphalt Academ ic 249
TABLE OF CON TEN TS
PART I
I N TROD UCTI ON , BACKGROUN D , METH ODS AN D CON CEPTS
Chapt er 1 : Som e et hnographic “im ages & act ions” 0 1
I nt roduct ion: Problem s and Perspectives 05
Diving int o Urban Space: The Urban Non- Space and t he I nvisible Beings 05
What is m y quest ion? 08
Why is t his im port ant ? 12
The Social Relat ions of m y Track 17
Scenarios and Narrat ives 19
An Ethnographic I m aginat ion 19
Chapt er 2 : Som e sociological “im ages & act ions” 2 8
Thinking and Seeing – Durkheim 29
The Theoret ical Search for a Sociological Vision of t he Children in t he Cult ure of a
Durkheim – a social being 30
Durkheim , Rousseau, and social t hings 36
Durkheim , Rousseau, and social being 38
Durkheim and t he social self 41
Durkheim and t he division of labour 43
Durkheim and social solidarit y 46
Durkheim and t he social fact 49
Durkheim and sociological m ethod 52
Durkheim and logic 55
The Realit y of Societ y 60
Basic Concept s: How and Where are t hey? 62
Cultural I dent ity and Self- Governing 64
Corporificat ion and I dentification 71
Multicultural Racism 75
Chapt er 3 : Som e m at hem at ical “im a ges & act ions” 8 8
The Sociology of Mathem at ics 92
Mat hem at ics and Space 97
A Concept ion of Mathem at ics 97
A Concept ion of Space 103
Space in t he m at erial subst rat um of
societ ies 105
Levels of space 106
Et hnom athem atics 112
Part I I
TH E STRUCTURE AN D D YN AMI CS OF LEARN I N G: MULTI PLE,
SYSTEMI C, AN D COMPLEX I N TERD EPEN D EN CI ES
Chapt er 4 : São Paulo 1 1 8
The Geographical and Hist orical Cont ext s 122
The Social and Cult ural Cont ext s 163
São Paulo in Moni 163
Copan in Moni 171
Cit y Cent re in Moni 178
The Love Cont ext 182
Sam pa 182
Chapt er 5 : Children in Street Sit uat ion 1 9 3
Who are They? 196
We are… 196
Their Situcionalidade 197
The Term 198
Ages and Genders 200
Policies 205
How do They Live? 209
The Social St ruct ure of the Urban St reet 209
How Do Children Manage in t heir Given Space? 211
Our Proj ect 214
How do the Children Creat e and Define t heir
Space? 220
The Pyt hagorean Theorem in Survival 223
The Cart esian Coordinat e System in
Act ion 234
Being 235
Making Bread 239
Chapt er 6 : The Freedom of Know ledge 2 4 3
Asphalt Academ ics and Asphalt Children 247
Next St eps: This is not the End 253
References: Som e Bibliogr aphical “im ages & act ions” 2 5 8
CH APTER 1
SOM E ETH N OGRAPHI C
To begin wit h ethnography is t o begin in synchronism wit h t he act ions and im ages of this research.
“ You learn et hnography t hrough practices, and perhaps a lit tle bit of apprent iceship. There are guidelines but few rules. More or less anyt hing goes.” ( Buraway, 2000, p25)
I grew up in an urban area, in the cit y cent re of São Paulo – a m egalopolis of Brazil, exchanging energy wit h cert ain m odes of life – urban m odes. The people t hat live in the st reet have t heir own m ode of life and t his m ode im pact ed m y own m ode of life in m any powerful ways. I n t he life of t he st reet , a newspaper becom es a blanket , a but t on is changed int o a weapon, or a piece of cardboard becom es a wall. These are som e of the act ions and im ages t hat showed m e t he connect ion bet ween the product ion of knowledge and t he rupt ure of t he am orphous veil that covered t he city of São Paulo at t he end of 60s. The exercise of et hnography com es as a t ool t o know and describe knowledges exist ent in t his m ode of life, int rinsic t o t he urban space.
The urban space increasingly becom es a space m anaged by policies of beautification and cont rolled socializat ion; enclosed and wat ched spaces. Neoliberal is an exam ple of t he policy of beaut ification and cont rolled socializat ion, an exam ple of the policy of “ unique
t hought ” , and the new world order aft er t he 70s. I n a count ry like Brazil, t orm ent ed by a hist ory of colonizat ion and m ilit ary
dict at orship, t he new world order has creat ed gaps separat ing cult ural groups wit hin t he urban population and m aking som e of t hem invisible.
et hnography was not a choice; it was t he real m ovem ent around t his research, which allowed the voices of all participant s t o appear const ruct ing t his research. This research began as part of a proj ect of life and was “ walking” as part of proj ect s of lives. The social phenom ena described in this research will always be linked with the m at hem at ical knowledge of t hese children, m ore specifically, t heir concept of space. However, t hese knowledges, em bedded in
et hnographical im ages and actions, will be approached t hrough t he syst em s in which they are int rinsically linked, focusing on som e of t he cont ext s perm eat ed by t hem .
The voices present here are in const ant int eract ion with m y voice, in a dialogical process, const ructing a work in which I underst and t hat every voice has the sam e energy, has the sam e right s, has t he sam e values. These voices draw at t ent ion t o the m yt h of the
visibilit y t hat the large society has given t o every “t hing” that is in a m arginal position. The m yt h is part of the neoliberal m ovem ent and it keeps even progressive governm ent s from act ing t o unveil t he m yt h and act ing on behalf of the m arginal groups and classes The large societ y, arrogant in it s m at erial and int ellect ual
predom inance, fails t o act legally or ot herwise on behalf of m arginal peoples. The welfare st at e is designed t o m aint ain t he new world order, wat ering t he hegem onic syst em in which we are living, and keeping t he m arginal peoples invisible – unreal, inactive, docile, and as poor hum an beings. The t ools of t he new et hnography and t he older t radit ion of act ion anthropology reveal t hat t he urban
populat ion is also m arginalized, acting and react ing in t he process of urban social const ruct ion.
t o dive int o t he urban space, t hrough t wo t erm s that provoke and inspire m e t o be in the urban space: t he urban non- space and t he invisible beings. I developed t he t erm urban non- space faced with t he necessit y of ident ifying the space of urban social relat ions m arked by t he visual int ersect ion am ong m arginalized and non-m arginalized groups and st rongly denied by bot h groups. The t ernon-m invisible beings is present in m any academ ic works from different areas but here, it is present and developed t hrough t he voices of children in st reet sit uat ion.
St ill in t his first part , I share m y research question as well as t he process of t he quest ion before and during t he research. I begin focusing on a large question – a quest ion of t he act of t he hum an being as a social fact . This is followed by the quest ion of non-dialogue in int ersectional urban spaces. This encom passes t he silence of cert ain m at hem atical knowledges possessed by m arginalized urban groups, t he m athem at ical knowledges of
children in st reet sit uat ion. These questions and problem s converge on t he space concept of t he children in st reet sit uation. The
im port ance of t his quest ion as well as t he social relat ions of m y t rack will be m ade clear as m y work unfolds.
I n a second m om ent of Chapter 1, I share scenarios and narrat ives t hat I proposed during t his j ourney discussing “t he why’s” and “ the how’s” of t his t rack in t he script t hat I present .
I ntroduction: Proble m s
a nd Pe rspe ctive s
D I VI N G I N TO URBAN SPACE: TH E URBAN N ON - SPACE AN D TH E I N VI SI BLE BEI N GS
Before present ing the prim ary st eps of this research, I would like t o dive int o t he urban space t hrough a discussion around t he urban non- space and of the invisible being as well. I t is necessary for m e t o share this diving process with the reader in order t o convey t he st rengt h of the background present in m y ethnographical eyes. While working wit h people in st reet sit uat ion, and not only wit h children, in t he city cent re of São Paulo, I could realize the
I n t he case of this research, t he urban populat ion is const it uted by people t hat are in a st reet situat ion and people t hat are not in a st reet sit uation. I could realize t hat t o be invisible is t o be in t he m arginal space of the m aj or societ y, is to survive without being direct ly included in the et hical and power relat ions of t he m aj or societ y, developing “invisible” ethical and power relat ions. This way of life dem onst rat es t hat life is m ore t han capit al and m ore t han t he specific knowledges t hat ground and sust ain t his capit al. Žižek ( 1994; 2005) works with the idea of hum an beings that are I N ( hum an beings included in t he legally regulat ed societ y of well-being and hum an right s) , and that are OUT ( from t he hom eless of our urban cities t o hungry Asians, Am ericans, and Africans) . I t is necessary t o add t hat being I N is having m at erial and intellect ual visibilit y in the neoliberal form s of life and in t he hegem ony of t he urban spaces. Being OUT is not having m at erial and int ellectual visibilit y; t o be OUT is t o be invisible in the m ost profound hum an senses. Through m y observations of t he social relat ions bet ween invisible and visible, I saw t hat t he denied space where these
relat ions happen could be categorized, as it gradually increased and ent ered m y awareness as som eone who was engaged in t hese
social relat ionships. I call it urban non- space and it s m ain charact erist ic is the presence of t he cultural groups which are
m at erially and int ellect ually m arginalized in t he urban cent ral areas. During t he I ndust rial Age, t he urban m arginal groups were usually locat ed on the out skirt s or t he periphery of the cit y or cont rolled by put t ing t hem m et aphorically and lit erally in chains ( in prisons,
inabilit y t o adapt t o life in t he urban cent ral areas. I n the next st ep, t hey becam e invisible.
The m ovem ent of the m arginal cultural groups int o t he urban cent ral area appeared as a t opological answer t o the conurbat ion m ovem ent during the I ndust rial Age. This m ovem ent has developed t he non- space ( i.e., unident ified and unident ifiable physical space) organized around ent ropy and anom ie. I t is here t hat we find a space for a cert ain kind of invisible set of social relat ions. I n the urban non- space, t he social relat ions happen in a process of nat ural capit al osm osis. However, the fear of t he invisible ot her becom es t he consequence of a wall it self in t he eyes of t he visible one. A wall of anguish, const it uted, am ong other things, by the clogging of bodies in t he urban spaces, by the m anipulat ion of the appearance of a const ant t hreat posed by the invisible ot her. The legal and et hical cont rol over bodies is broken by t he creativit y and different values com ing from the invisible ot her.
The phenom ena of non- space is not cent red in cit ies. I t can be observed in a zoom - out m ovem ent focusing on st at es, count ries, and t he whole world, as well as t he conurbat ion phenom ena at issue in this proj ect .
I t is relevant t o rem em ber t hat m any urbanologist s in different academ ic areas, develop their works around urban spaces. Som e of t hem , such as William Whyt e ( 1980) , Henri Lefebvre ( 1991) , Marc Augé ( 1992; 2005) , Boavent ura de Souza Sant os ( 2000) , Michel de Cert eau ( 2001) , Sheepers ( 2004) , and Rhom berg ( 2004)
This gave rise t o the necessit y of claim ing for m yself the idea of t he urban non- space.
Marc Augé ( 1992; 2005) , an anthropologist who explores the non-places, alludes t o t he undefined, inexistent , or anonym ous spaces where the past is confused with the fut ure, approaching t he solit ude of t he individual of what he designat es as superm odernity. Som e exam ples of non- places are the I nt ernet, a hot el, or a st reet . This work was very significant in m y effort t o identify what I experienced in m y urban life, m y urban experim ent s. However, t his work has it s cent ral focus, t hrough anthropological eyes, in the et hnology of solit ude in t he post - m odern world. The focus of t he urban non-space is it s exist ence, it s m at erial invisibilit y and relational visibilit y, it s intersect ional and non- individual characterist ics,
charact erist ics t hat I present and discuss t hroughout m y research.
WH AT I S M Y QUESTI ON?
I do not know if I can call m y quest ion “m y” quest ion. I n t his research, I discuss a large quest ion t hat I underst and as being about coherence bet ween t o be and t o be in – t he question of t he act . To be alive and t o survive m eans t o be wit h… with the others of t he sam e species, wit h others of t he different species, wit h t he inanim at e ot hers, and with the others inside us. These “ ot hers” could be seen as const itut ive beings of social ecology – system ic and com plex net s exist ent am ong all living organism s and fed by social act s.
t his research and idealizer of a work where t his research is insert ed, and is founded in different m odes of urban life and it s social
relat ions in urban non- space.
I am a hum an being, I am a social being, I am a product of t he social and I produce t he social, m y m ind and m y actions are social and t herefore a reflection of m y social ecology in t he syst em ic and com plex net s exist ent where I am .
Where am I in t his research? I can say that m y social ecology was at t he m iddle of an urban area. I was born in São Paulo, t he third largest city of Eart h – a m egalopolis. To be born in an urban area, at t he period that I was born – 1965, where the m igrat ion t o t his m egalopolis was reaching it s m axim um , is t o be born and raised wit h t he question of povert y as one of the foundat ions of the urban social const ruct ion.
I n t he occident al m ent ality, that act ually left it s geographical
posit ion and could be found all around the world, hum an beings are recognized by their propert ies. The propert ies range from m at erial t hings t o int ellect ual things. The quant ity of propert ies has a great value; the act ual values are in what we have and not in what we are, or I can say t hat we are what we have. The quant ity of propert ies is support ed by t he recognit ion and the validation of cert ain knowledges or by capit al. I t is these knowledges and capit al t hat sust ain the hegem onic syst em s t hat we know as urban areas. Knowledge and capit al appear int rinsically linked by t he value of int ellectual and m at erial propert ies.
The recognition and validat ion of cert ain knowledges, defined as correct and necessary, is determ ined by t he necessit y of
m aint aining the hegem ony of t he current system in urban areas occident ally organized. However, t o recognize different
populat ion, is a norm al pract ice of t he m aj or societ y, fort ifying the m yt h of “ partners” as m uch in m aterial as in intellect ual propert ies. To know t he knowledge of t he “ ot hers” is a t ool of t he post - m odern m ovem ent t o prom ot e corporificat ion, let t ing t he “ ot hers” becom e and be invisibles. These ot hers are not responsible for their act s, t heir st rat egies are unusable, and they are “ accept ed” in a process of m ult icult ural racism1. The real validat ion of these different
recognized knowledges has not been pract iced; it has only been a m at t er of m erchandizing hum an knowledges.
The cent ral point in t his research is t o quest ion why the
m at hem at ical knowledge of t he children in st reet sit uat ion’s cult ure is not recognized and validated by t he urban populat ion? From t his quest ion, we are led t o realize t hat t he recognit ion and the
validat ion of t he children in st reet sit uation’s knowledge could be a st ep t oward elim inat ing t he idea t hat they are victim s. We can com e t o see t hem as a real cult ural group, as act ive hum an beings, and not as fragile, docile, or aggressive children.
The urban m arginal space, like all m arginal spaces and everything t hat t hey represent , is act ually t reat ed as “ good” obj ect and “ bad” obj ect . On t he one hand, t he “ good” obj ect of t he m arginal space represent s a charact er of being passive, suffering, being a poor obj ect . On t he ot her hand, the “ bad” obj ect of t he m arginal space represent s a charact er of being aggressive, being selfish in it s ethics and power relat ions. Both sides of the urban m arginal space
prom ot e t he surplus value of t he urban populat ion; t hey are ways of m anipulat ing capit al t hrough t he appropriat e knowledge of each
1 Slavoj
Žižek1 ident ifies m ult icult ur al racism , as a post - m oder nist m ovem ent . I will discuss t his in t he
side, as for exam ple, assist ance proj ect s or put t ing people in chains, respectively.
I t is norm al t o link t he urban m arginal space wit h the “t hird world” … and all m y experience com es from t he “t hird world” , from South Am erica – Brazil. However, t he urban m arginal space has no fixed place; it can be found at any place of t he world, t he single existence of a different m ode of life t hat opposes “societ y” defines this space. To be act ive inside an invisible cult ural group ( t hat is in t he m argin) is a risk t o the norm alized, the dom est icat ed, societ y. This risk is based on t he obedience of pleasure. Meanwhile, t o be act ive inside a visible cult ural group is an illusion, an illusion based on t he
pleasure of being obedient . To be act ive is a condit ion of living in open syst em s, exchanging energies wit h all syst em s that t he act ivist is part of, prom ot ing t he act of dialogical int eract ion, not wat ching as an out side audience but acting as an inside act or. The role of this research is t o share, t o recognize, and t o validat e, m aking som e m at hem at ical knowledges of the Children in st reet sit uat ion ( an urban m arginal cult ural group) com pat ible with t he m at hem at ics of the Academ y ( a urban non- m arginal cultural
group) . I effect t his et hnographically, arguing around som e not ions of t he space concept of Children in st reet situat ion’s cult ure.
I n t hat sense, I considered the quest ion previously m ent ioned as t he m ain academ ic focus of this research in it s first st eps. However, during t he research process it self, the cult ural legacy of t he children in st reet sit uation’s generat ion m ade it im possible t o rest rict the research t o one point , t o one quest ion. The com plex and syst em ic approach, in which this quest ion is involved, was analyzed,
allows t he recognition and validat ion of m at hem at ical knowledges of t hese children by different urban cultural groups.
WH Y I S TH I S I M PORTAN T?
While working in t wo different urban cult ural groups, it is necessary t o consider why the prim ary quest ion of “ space” , and all resonant effect s that exist around it , is im port ant t o bot h groups and in t he wider societ y.
Through the voices of t he m ain act ors of t his research, we can list en t o an invisible culture:
“ Saca só Mônica, se tu canta pros hom e que nós sabem o o m esm o que eles, m as de out ro j eito, eles pode enxerga agent e e dexá agent e sê o que som os, num é?” ( Priscila, 2000)
“ Sei não Priscila…. Eles pode sum i cu’agent e pra eles sê os bom !” ( Capoeirinha, 2000)
“ Tu acha brother, que eles vão fica preocupado cu’nóis? Tá noiado! ” ( Cam ila, 2001)
“ Dô a m aió força pra tu, Mônica. Quem sabe nós ganham os cor… quem sabe eles com eçam querer saber o que querem os invéz de fazê agent e querer o que eles querem !” ( Antonio, 2001)
As t he children in st reet sit uation argued above, one point of t his research is t o work at t he int ersect ion of t he urban spaces t hat exist bet ween different urban cultures – t he non- space. My research is about arguing, sharing, validat ing, and knowing well t heir
work has as it s basic focus t he knowledge, and not t he rhet orical assist ance, which penet rat es and feeds t he urban non- space. However, the process of arguing, sharing, validat ing, and knowing well som e m at hem at ical knowledges, found in different dialogues, can be a “ knife with t wo cutt ing edges” . As t his research was being developed in an ethnographical way, other knowledges appeared. To be in open syst em s – as the et hnography claim s t o be – is t o be in a fragile posit ion, is t o be act ing, is t o be a script writ er where t he real voices of t he script would have no m at erial or int ellect ual hierarchies except in a dialogical process.
I n t hat sense, it is very im port ant t o pay at tention t o t he pluralit y of ways in which t his kind of research could have unfolded. As
Capoeirinha point ed out in the second voice of the previous page, it is necessary t o be “ sm art ” so t hat the wider societ y cannot use all t his inform ation t o exterm inat e t he children in st reet situat ion’s cult ure. Or so that t he wider societ y, including t he voices of this researcher, does not m ake t hese knowledges even m ore invisible t hrough not validat ing t hem or m aking them com patible. One m ust be alert t o punishing behaviours in which t hey express t heir
knowledges or continuing wit h t he assist ance eyes over them .
“ Tam os ai Mônica, sem m edo de ser feliz. Leva isso pra eles e quem sabe! Trabalham o m uit o e acho que t em o que m ost rar... é o ato que tu fala, não? Tem o que faze esse ato de dividir.” ( Antonio, 2001)
“ Medo… que noia! !! Num vai dá em nada… eles num vão saca nóis nunquinha! I sso foi legal pra nóis… som o diferent e agora. … Ah! Som o m ais int endido de nois m esm o, do que rola aqui nas nossa cabeça, das nossa história, som o m ais brot her e sabem o que querem o m em o fica j unto.” ( Cam ila, 2001)
“ Ainda acho que vai sobra prá nóis, sem pre sobra! Mas não m ando sozinho não… nessa som o o conj unt o todo, fom o at é agora e serem o at é o fim . E tam bém é bom que eles… ( eles quem Capinha?) … os hom e claro! … eles saca que som o bom m esm o no que fazem o! Será que eles sabe o que faz? … ( Acho que sim ! Mas o que tá rolando na sua cabeça pra pensa isso?) . Tô pensanso se eles conhece o espaço deles, se eles ficam j unto conversando o que nois som pra eles igual tam o fazendo aqui. ( silêncio) .” ( Capoeirinha, 2001)
I ii… tá noiado Bro? Claro que não! Nois, se som o algum a coisa, som o m esm o é fantasm a… dos m al, dos fudido! ” ( Cam ila 2001)
I n t he voices of t he t eam , even being fragile beings in an open space, arguing, sharing, validat ing, and knowing well t heir different knowledges relat ionship t o t he “ large societ y” , it is necessary t o exchange energy, t o give life t o t his research, t o let the voices com e and be.
I have list ened t o the voices of t hese children in st reet sit uat ion, and t his has led m e t o the concept of space question, and it s echo: t he value of t heir product . The social act ivit ies developed by the children in st reet sit uat ion during t his research could be observed and discussed by the children them selves, from t heir hist orical urban posit ion t o t heir urban social act s.
From t he academ ic point of view t he quest ion of t he concept of space is approached in a large field of work in different areas. The relevance of t his question in this research, looking t hrough t he academ ic lenses, is locat ed in t wo fact s: t o bring new knowledge, t o Mat hem atics Educat ion, Sociology of Mat hem at ics, and
Et hnom at hem at ics; and t o explore t he root s of t hese very sam e academ ic knowledges.
groups. For exam ple, Sonia Claret o ( 1993) , from Brazil, discusses space am ong the “ Caiçara2” com m unity and St at hopoulou Charoula
( 2007) , from Greece, analyzes t he way a Rom any ( Gypsy)
com m unit y perceives ideas about space. I n ot her cases, researchers explore ot her quest ions focused on children in st reet situat ions. For exam ple, Ricardo Lucchini ( 1988, 1993, 1994, 1996) , analyzes the life st yles of “ st reet children” around t he world t hrough t he eyes of a sociologist ; and Lewis Apt ekar ( 1988) , has carried out an
et hnography about Colom bian “ st reet children.” Renuka Vit hal in 1998, at t he first int ernat ional conference on Mathem atics
Educat ion and Society’s at Not tingham Universit y, organized a Discussion Group (DG) on Working wit h St reet Children. I t was t he first , and a unique, m ovem ent t o int egrat e the Mathem at ics
Educat ion and Children in St reet Situat ion’ cult ures. The prom ot ion of t his DG was accent ed in her experience in a shelt er of “ st reet children,” or m ore specifically, girls in street situat ion, called Tennyson House in Durban, South Africa. The experience in t his house consisted of a tut orial program m e in which student t eachers t ake responsibility for t he m athem atical growt h and developm ent ( schooling in m at hem at ics) of a learner who lives at Tennyson House. Renuka act ed in t his program m e as a m at hem at ics t eacher educat or in cooperat ion with an educational psychologist , Cheryl Sm it h who, according t o her, works extensively with st reet children. This program m e was designed t o achieve m ult iple goals based on t he principle of reciprocit y and, from m y point of view, had it s m ain focus on t he st udent t eachers and not properly on t he children in st reet sit uation’s m athem atical knowledges.
“ As a t eacher educat or, it gave m e new insight s in understanding what it m eans to becom e a t eacher. I t was clear t hat know ledge and skills in t eaching
m athem at ics were developed but the program m e offered an opportunit y for student t eachers t o learn to be ‘caring’ towards learners in their m athem atics teaching and to show com m it m ent and dedicat ion. They w ere learning to t each m athem at ics in a cont ext in which it m at t ered if the learners learned because the consequences of t eaching and learning or failing to t each and learn w ere authentic and tangible. I t was a chance t o m ake a real difference in t he life of a young person whom societ y had alm ost given up on.” ( Vit hal; 1998, online)
My research, by cont rast wit h t hese earlier effort s, proposes t o work wit h t he children in st reet sit uat ion’s space concept , focusing on using t he m athem atical knowledge t o ret hink and discuss, in a dialogical process, t he general question of t he space concept in cult ure. The t ransposition of t he knowledges will be explored, discussing our knowledges in a large cont ext , observing where, how, and why our knowledges are int rinsically linked wit h our act s and with our visibility t o t he large society. The value of knowledge is approached. To know t he knowledge is t aken as a value, as an
exchange value, as a posit ional value, and as a survival value in the
TH E SOCI AL RELATI ON S OF MY TRACK
The basic approach of this research cam e from the social relations developed through m y t rack; t o be in the boundaries m ixed with different urban cult ural groups.
The possibilit y t o be with bot h cult ural groups, t he Children in St reet Situat ion and t he Academ y, allowed m e t o bring different point s of view t o the sam e urban im ages and actions. From the confront at ions of these differences appears t he necessit y of searching for m at erial and intellect ual art efact s t o develop a sym biosis m ovem ent bet ween them , t o prom ot e a dialogical process bet ween t hem .
To observe t hat the space concept of the children in st reet sit uat ion’s culture was different from the space paradigm of t he urban populat ion was the first st ep t oward t rying t o find ways t o underst and t heir concept bet t er. A paradigm cont rols the logic of t he discourse; it is a way t o cont rol t he logic and t he sem antics at t he sam e t im e. I t is a relationship t hat includes and excludes persons, ideas, art ifact s, and values ( cf. Morin, 2002.
To be in the boundaries and t o realize that the paradigm atical act nourishes t his sit uat ion was one of the social t hings that t he cont act wit h t he children in st reet sit uat ion’s cult ure t aught m e. The
according t o Morin ( 1977) , a system is a global unit y of int errelations bet ween elem ent s, act ions, and hum an beings.
Sce na rios a nd N a rra tive s
AN ETH N OGRAPH I C I MAGI N ATI ON
This et hnography can be underst ood as a play where t he voices are t he voices of act ors t hat , from different approaches, were involved in const ruct ing it dialogically wit h t he sam e int ensit ies.
The suggest ed play has a background scenery – the asphalt scenery, as you can see in that previous pict ure and can realize during t he descript ion of t he research. The asphalt scenery was t he urban st reet of São Paulo, m ore specifically t he urban st reet s in t he cit y cent re. However, t o share t he voices t hat were in t he
background scenery in a dialogical process it was necessary t o overlap anot her specific scenery – t he academ ic scenery. I t
happened in accordance wit h t he audience of the Academ y, so t hat t he cont ent of t he script would be present ed in t hat cont ext and argued dialogically.
The form of t his elect ion was cent red in t he int erlocut or of bot h sceneries, the scenery where t he things happened and t he scenery where the t hings will be described. The int erlocut or has t he role of t he script writ er of t his play; I am t he script writ er. I n a first
m om ent , it could sound as a self- decision based only in m y desires as a hum an being living in bot h scenarios – perhaps t hat is t he case. To describe how m athem atical knowledge is active in the children in st reet sit uat ion’s cult ure, being a crucial t ool in t he const ruct ion of t heir cult ure, t o t he int eract ive t arget public – the academ ic one, sounds like a st rong reason t o be selfish.
This supposed selfish m ovem ent , locked in m y desires, involves ot her desires existent in bot h of m y scenarios. I n the academ ic scenery, I could realize som e voices having m y desire as their desires – t he desire of underst anding t he ethical and power relat ions in social life, the desire of claim ing act ion. These voices are represent ed in t his spect acle by t he int eract ion t hat I invit ed t hem t o in som e synopses present during t he first part of t his play, t radit ionally called the “t heoret ical fram ework.”
about societ y are linked wit h quest ions about hum an pot ent iality, about hum an lim it ations, and about the hum an condition of social hum an beings. Societ y, he says, is an im m ense cooperat ion that ext ends not only t hrough space but also t hrough t im e and can be considered as being not sim ply a set of inst itut ions but a collect ive way of being em ergent from diverse form s of hum an relat ions. Durkheim t oday would be in t he cam p of the st rong social
const ruct ionist s. He em phasized t he necessit y of t aking full account of t he int errelat ions bet ween religion, educat ion, politics, fam ily, cult ure, geographical, and hist orical locat ion. These fact ors alt oget her shape the com plex realities of hum an social life. Durkheim ’s voice is t he prim ary foundation t hat support s the academ ic voice in this research.
Som e academ ic voices are invited t o discuss concept s which I could realize only in locum. A vast lit erature was st udied for t he
const ruct ion of t his part , which discusses som e new concept s as well as som e concept s previously cit ed in different ways. These voices of t he script com e from academ ic voices exist ent in the background scenario, in t he asphalt . They are voices born not from a cont em plat ion m ovem ent , but from observed or, som et im es, from lived act ions in t he asphalt .
As t he focus light of a scenario, Slavoj Žižek’s voice appears
recursively shaping all script s wit h his cent ral idea about t he hum an being. According t o Žižek ( 2000: 109) , the hum an being cannot be reduced int o sym bolic codifications of "ot herness" which offer
rem ind us of t he hum an focus claim ed by Marx, Durkheim , Rest ivo, and D’Am brosio; he locat es t he origins of social life in hum an
capacit ies and pot entialit ies, which are able t o develop through our social const ruct ion, our int eract ion with t he others of any species. St ill in t he academ ic scenery, but in all part s of t he script as design cost um es t o com pose a scene, the constant and deep int eraction wit h Sal Rest ivo and Ubirat an D’Am brosio and t heir works
cont ribut ed t o t he overlapping of t his scenery t hrough our com m it m ent with the sam e desires – t he desire of knowing,
recognizing, validat ing, m aking com pat ible t he knowledges of the hum an beings, t he desire t o be in t he boundaries, exchanging energy. Sal Rest ivo and Ubirat an D’Am brosio’s voices are t he academ ic support that bring int o m y script m athem atical language wit hout m yst icism , as a product of hum an being, socially
const ruct ed by different cult ures in different tim es and spaces. The t radit ional and Plat onic paradigm of m athem atics is broken through t heir social speech about m at hem atics, m aking visible t he
m at hem at ical knowledge of t he children in st reet sit uat ion’s cult ure. I nt ensive desires can be found in t he asphalt scenery t hrough
different voices. Many voices are in t his scenery, including the voices of t he children in st reet sit uation. However, t he urban st reet is an open urban place where t he pluralit y of t hese voices, excludes t he voices of t hese children, sharing a “single t hought ” – t he
children in st reet sit uat ion are vict im s and t hey need help; dist ant help, as I will discuss during t his research. However, it is necessary t o not e t hat in t he actual polit ical m om ent in Brazil, the necessit y of let t ing the children in st reet situat ion be defined as victim s is a socio- polit ical focus.
I n t he m iddle of these voices sit uated in t he asphalt scenery,
t hese children resist . For a first inst ance, t he resist ance is prom ot ed by t he large societ y as a necessit y t o m aint ain the m ode of
product ion insert ed in t he urban cities. This cont ribut es t o
m aint aining the hegem ony of t he system . I t is, act ually, part of t he urban social const ruct ion. For a second one, t he children in st reet sit uat ion resist under t heir voices claim ing by “ colour” , as Ant onio previously said.
The second part of t his play is shared am ong st reet voices. At the beginning hist orical, geographical, social, cultural and love cont ext s of children in st reet sit uation in São Paulo are brought int o our light , let t ing our m inds fly int o their scenario in locum – t he urban st reet s of t his city. Their voices appear through m y voice and t hrough t he voices present in m y social relat ions in this locum. My experience arises in t hese context s; som e hist ories of life are present ed, som e im ages are shared, and som e observed act ions are described and, som et im es, analyzed by t he academ ic voices.
The im port ance of t his part is revealed in t he general context , where knowing of these five context s t hat I present is having a universal view over t he m arginalized group in quest ion. I do not feel any need t o describe the cont ext s of t he ot her group because as a non- m arginalized group it s knowledges are m uch m ore expansive, and m uch bett er known in t he larger societ y.
I n t he m iddle of the second part , t he script “ frees t he voices” of t wo children in st reet sit uat ion’s subgroups from São Paulo. We see who t hey are, how t hey underst and t he st reet s, t heir posit ion within t heir culture and wit hin t heir ecological syst em ; and we encount er som e aspect s of t heir space concept . During t his process, I invite t he guest s from the academ y t o m aint ain a dialogue wit h t he children in st reet sit uat ion’s voice. However, t his invit at ion is
dat a of m y children in st reet situat ion’s represent at ion. This is a process t hat evidences the dialogue between bot h m y ident it ies, which is m ediat ed by t he knowledges of bot h these urban cult ural groups t hat I inhabit .
To finalize t he script , but not t he research, it unfolded around final st eps t hat are dedicat ed t o t he social relat ions of asphalt , a unique scenario where t he play goes on in m ult icult ural voices. The
asphalt , the cent ral lim it where hum an relat ions are developed in our t im e, is approached t o claim at t ent ion t o our st reet act s. The com plexity of t he st reet syst em is port rayed in this script . The script links the quiet st reet voices of t he visible cult ural groups, norm ally cat egorized as quiet act s of reading, t o the voices of t he children in st reet sit uat ion. These asphalt children feel the silent st reet noises echoing in their act ions, in t he react ions t o their act ions, and in t heir m inds.
Searching t o live a dialogical int eract ion, I developed a script where all the voices from bot h cultural groups t hat I was working wit h, and all the voices and im ages that perm eat e t heir social relat ions, could appear and exist . The act of surviving t o prepare t his script like t hat is st rongly linked wit h the act of surviving of the children in st reet sit uat ion as a cult ural group; we bot h seek respect and visibility in t he larger societ y. To respect t he m ult ilinguist ic aspect of this script , it is necessary t o m aint ain t he original language of each act or present in it . To have int ellectual visibilit y in the larger societ y, the script needs t o be in a language where t he knowledge of t he st reet children could be divulged.
English language was hard but necessary t o m aint ain t he coherence wit h t he developed t rack by the script writ er. Why t he English
language?
When Ubirat an D’Am brosio learned about m y assist ance work wit h t he children in st reet situat ion of São Paulo and about som e
quest ions around t he space concept that I exposed him t o, he suggest ed that , am ong ot her t hings, I m ake cont act wit h Sal Rest ivo’s work, which he said was in English. At t hat t im e, during m y Masters Course in Mathem atics Educat ion at t he Pont ifícia
Universidade Cat ólica de São Paulo, I had read m any t ext s in
French and som e in English. English was not com fort able for m e, cult urally speaking. A st rong “ bom bing” against everyt hing that was Am erican, including t he English language, was the landm ark of t he t im e that I was born.
The m ovem ent against t he English language developed during t he 60s in São Paulo had t wo result s. By one hand, t here were people t hat t ook advant age of t his t o learn t his new language in t he great cent ers of Brazil. By the other hand, t here were people who t ried t o react against t he learning of this language, t hus react ing t o the abrupt polit ical ent rance of t he U.S.A. in Brazil; m y fam ily assum ed t he second post ure.
I went t o Montechoro; Crist ina Maranhão, m y Mast er Course advisor and I prepared a paper, a dialogical exercise, which was accepted. I t was the first paper of m y life; it was a litt le bit far from t he cent ral point of t his congress and it was sent out of dat e t o the Scient ific Com m itt ee. However, I did know t hat it was an im port ant st ep t o underst and, t hrough academ ic lenses, t he nat ure of the concept of space of the children in st reet situat ion’s cult ure. I n t his m eet ing, I found t heoret ical support t o dive deeply int o t he
academ ic cult ure.
The process of t his academ ic search was developed wit h t he
children in st reet sit uat ion with whom I was in daily cont act . On the previous days of the m eeting, I was engaged in t he new t asks
Ubirat an D’Am brosio had suggest ed t hat I prepare m y present at ion in English. Like a robot , repeat ing word aft er word what I knew by heart from t he preparat ion phase, I present ed m y paper on the first day, not about t he quest ion of space and children in st reet
sit uat ion, but a quest ion linked wit h m y Mast ers t hesis. Aft er t hat , during dinnert im e, I began t o share m y st reet experiences wit h Henrique de la Torre and his wife Lula. He list ened t o m e and invit ed ot her colleagues of t he conference t o list en t o m y st reet experiences. I t ried t o survive wit h m y not so im proved English and, from t his necessity, I could realize t hat learning English was
im port ant t o give visibilit y t o the knowledge of the children in st reet sit uat ion. English was the necessary language t o let m y experiences be underst ood around the world, m ainly by it s m ain arguer Sal Rest ivo and all st reet voices in the academ y. This was t he way t o give visibility t o t he knowledge of t he children, of t heir aut onom y wit hin the division of labor, of t heir context s of life, of t heir
st rat egies of survival, of t heir life in t he m argins.
pat ience and respect , t o hear m e, t o go in through m y st reet experience, and t o share discussions which have been, wit hout doubt s, t he great est guides of this script.
CH APTER 2
SOM E SOCI OLOGI CAL
Think ing a nd Se e ing:
Durk he im
TH E TH EORETI CAL SEARCH FOR A SOCI OLOGI CAL VI SI ON OF TH E ASPH ALT CH I LD REN .
Two approaches have predom inat ed in the study of children in
st reet sit uation. The first concerns t he reasons t hat drive children t o t he st reet s and the condit ions in which they endure t heir exist ence, wit h particular reference t o the st rat egies t hey use t o guarant ee survival. Observat ion and ethnographic m et hods are t ypically used in this form of research. The second is focused on the policies
designed t o care for st reet children offered by a range of public and privat e organizat ions, and the evaluat ion of t hese policies using various t ypes of im pact assessm ent . I n t his research, I use a
t heoret ical m odel of social class t o st udy t he childrens’ concept ions of space according t o t hree dim ensions of t heir lives:
• t heir aut onom y within the division of labor;
• t he cultural cont ext in which they develop t heir processes of ident it y const ruct ion;
I argue that for t he children in st reet situat ions, the concept ion of space is linked wit h other social pract ices. My approach is t o sound out and writ e about social ways of t alking about m at hem at ics and space, using t erm s such as social class, self- governing, cult ure, racism , values and social power and ethics.
This approach gives a m ore com prehensive view of t he children in st reet sit uation’s life experiences. I t illum inates issues about self-governing, cult ural ident ity, and social relat ions. I t em phasizes t he role of children as social agent s who are act ively engaged in t he const ruct ion and exploit at ion of social capit al.
I base m y work on Durkheim ’s theories, especially som e of t he point s that he developed about t he realit y of society: social t hings, social being, social self, division of labor, solidarit y, social fact s, sociological m et hod, and logic.
DURKH EI M – A SOCI AL BEI N G
To explore som e point s from Durkheim ’s t heoret ical fram ework I decided t o write a brief description of his life and his social
environm ent , in sum his social const ruction as a social being. This descript ion was developed during fifteen days in 2005 t hat I spent at Èpinal, sit uat ed in t he Vosges’ Region of Lorraine, located in the nort heast region of France. The dat a for t his t opic cam e from a search in t he Bibliothèque Municipale d’Epinal (Bibliothèque
int ercom m unale d’Èpinal- Golbey) and in Archives Départ em ent ales
David Em ile Durkheim was born on April 15t h, 1858 at Épinal, in Lorraine. His m ot her was a m erchant 's daught er and his father was t he Rabbi of Épinal and was also Chief Rabbi of the Vosges and Haut e- Marne that are regions of Lorraine in nort h-east France. Durkheim spent part of his early school years in a rabbinical school; his fat her, grandfat her and great grandfat her, had been rabbis. Surrounded by an environm ent organized around Jewish cult ure he st udied Hebrew, the Old Test am ent , and t he Talm ud, while at t he sam e tim e following the regular courses at the Collège d’Épinal
where he had a short -lived m yst ical experience t hat led t o an
int erest in Catholicism . At the age of t hirt een, he had his t radit ional Jewish bar m it zvah.
Durkheim lived in an im perialist situat ion in France unt il 1870, Sept em ber 1st. France was not j ust a m onarchy but , like Brazil, it
was an em pire. The Em peror was Napoleon I I I , nephew of Napoleon I . Napoleon I I I was aut om atically proclaim ed em peror one year aft er he was elected president in 1850 and he was in power unt il t he Germ ans j ailed him at t he Sedan Bat t le. Before this chaot ic sit uat ion, t wo parallel polit ical m ovem ent s were born: The Paris Com m une in 1871, concent rat ed in t he capit al and with it s
foundat ion in Marxist ideas and, in t he sam e year, t he m arch on the Versailles Governm ent , concent rat ed in t he Palais du Louis XI V and defending the m onarchy and conservative ideas. During that period, t he Second Prussian Republic and Third French Republic were born in France – t he first prolet ariat revolution, according t o Marx3.
3
Marx and Engels discussed it in t he int roduct ion t o The Com m unist Manifest o…
“ I n view of t he gigant ic st rides of Modern I ndust ry since 1848, and of t he accom panying im proved
Durkheim always rem ained the com bined product of an ort hodox Jewish fam ily, his experiences in Cat holic school, and of t hat long-est ablished Jewish com m unit y of Alsace- Lorraine t hat , having been occupied by Prussian t roops in 1870, suffered from t he consequent nat ionalism and anti- Sem it ism of t he French cit izens. Durkheim viewed t he Paris Com m une of 1871 as senseless dest ruct ion and evidence of t he alienat ion of t he working classes from bourgeois societ y. The resurgence of nationalism and anti- Sem it ism convinced Durkheim t hat progress was not , as m ost posit ivist s of the tim e had assum ed, the necessary consequence of t he developm ent of science and t echnology, but on t he cont rary, an out com e of t he growt h of t echnology and m echanisat ion t hat underm ined societ y's et hical st ruct ures.
At t hat t im e, he was subm erged in a social environm ent t hat was m ade up of a chaot ic polit ical scene and in his religiosity. Soon aft erwards, he t urned away from all religious involvem ent , t hough em phat ically not for lack of int erest in religious phenom ena. Rat her, he becam e a freethinker, a non-believer, and an agnost ic.
“ Mais elle est avant t out , un syst èm e de not ions au m oyen desquelles les individus se représent ent la sociét é dont ils sont m em bres, et les rapports, obscurs m ais intim es, qu'ils sout iennent avec elle.” ( Durkheim , 1912; 2002_2 / 1989 / 1995, p109, p281, p227)
I n 1874 Durkheim obt ained his Baccalauréat in Lett ers and in 1875 he obt ained his Baccalauréat in Science at Collège d’Épinal. He was a great st udent and was awarded with a variety of honours and prizes. Because of t his achievem ent , he was t ransferred t o one of
t he French high schools, the Lycée Louis le Grand in Paris and t his m ovem ent from Épinal t o Paris changed Durkheim ’s percept ions about religion and t he fam ily, and indeed im pact ed his worldview. I n his first t hree years in Paris, Durkheim prepared him self for the exam inat ions t hat would open the doors t o t he prest igious École
Norm ale Supérieure, the t radit ional t raining ground for t he
int ellectual elite of France. However, his fat her’s illness affected his st udies and, after t wo unsuccessful at tem pt s t o pass t he rigorous ent rance exam inations, he was finally adm it t ed in 1879.
Durkheim 's generat ion at the École was a part icularly im port ant one in the intellect ual life of France. Here, the socialist Jean Jaure
becam e a life- long friend, along wit h t he philosophers Henri Bergson, Gust ave Belot , Edm ond Goblot, Felix Rauh, and Maurice Blondel, t he psychologist Pierre Janet , the linguist Ferdinand Brunot , t he hist orians Henri Berr and Cam ille Jullian, and t he geographer Lucien Gallois. I n t his social environm ent , Durkheim becam e an act ive part icipant in t he high- m inded polit ical and
philosophical debates that charact erized t he École. Léon Gam bet t a and Jules Ferry, whose ant i- clerical educat ional reform s would soon lead t o the nat ional syst em of free, com pulsory, secular educat ion of t he Third Republic, were figures who had som e influence in his const ant reconst ruct ion of his worldview.
His life inside the École Norm ale was m arked by dissat isfaction. Som e of his charact erist ics ( for exam ple, he was int ensely st udious and dedicat ed) creat ed a new ident it y for him am ong his peers: the m et aphysician. I n t his scenario, Durkheim was excluded by
no m ore t han t o be alm ost at t he bot t om of t he list of successful aggregat ion candidat es when he graduat ed in 1882.
Far great er t han his professors, who irked and annoyed him , one of t he influences upon Durkheim during t hese t hree years at t he École
Norm ale, involved the use of crit ical and rigorous m et hods in
hist orical research as advanced by t he hist orian Fust el de
Coulanges4. Durkheim ’s approach t o t he philosophy of science, which st ressed the basic discont inuit ies bet ween different levels of phenom ena and em phasized t he novel aspect s t hat em erged as one m oved from one level of analysis t o anot her, cam e from philosopher Em ile Bout roux5. Coulanges and Bout roux were t he m ain writ ers whose ideas would lat er show up as influences in Durkheim 's landm ark sociological st udies.
I n 1887, Durkheim was given responsibilit y for the course of Social Science and Pedagogy at Bordeaux. Not everyone was pleased by his appointm ent because he was a social scient ist and t he Facult y of Let t ers at Bordeaux was predom inat ely st affed by hum anist s.
At about the t im e of his academ ic appoint m ent t o Bordeaux,
Durkheim m arried Louise Dreyfus and they had t wo children, Marie and Andre. Not m uch is known about his fam ily life. She followed t he t radit ional Jewish fam ily pat t ern of taking care of fam ily affairs and helping him in proofreading and secret arial duties; he devot ed all his act ivity t o his int ellect ual pursuit s.
At t hat period, t he value of sociology and of education was
em phasized by Durkheim in his academ ic life. Subj ect s like kinship, crim e, law, religion, incest and socialism were his m aj or focus as a social science t eacher in Bordeaux.
4 Durkheim ’s Lat in t hesis was dedicat ed t o t he m em ory of Fust el de Coulanges.
