Authors: Mônica Mesquita and Sal Restivo
Henceforth, my dear philosophers, let us be on guard against the dangerous old conceptual fiction that posited a “pure, will-less, painless, timeless knowing subject”; let us guard against the snares of such contradictory concepts as “pure reason,” absolute spirituality,” “knowledge in itself”: these always demand that we should think of an eye that is completely unthinkable, an eye turned in no particular direction, in which the active and interpreting forces, through which alone seeing becomes seeing something, are supposed to be lacking; these always demand of the eye an absurdity and a nonsense. There is only a perspective seeing, only a perspective “knowing”; and the more affects we allow to speak about one thing, the more eyes, different eyes, we can use to observe one thing, the more complete will our “concept” of this thing, our “objectivity,” be. But to eliminate the will altogether, to suspend each and every affect, supposing we were capable of this — what would that mean but to castrate the intelect?
From Nietzsche’s The Genealogy of Morals, s III.12
Our objective here is to discuss the encounter that occurred on São Paulo’s asphalt between the asphalt children and the asphalt academics. Our perspective is grounded in the sociological worldview and in the ethnomathematics posture; the integration of this worldview and this posture was achieved during the process of a Phd research project. The bringing together of marginal and central positions and voices results in and is an activist social practice. The aim of looking at this encounter is to fuel the end of verbalism, purism, and essentialism and the beginning of a situated knowledge that is engaged with our everyday lives, with our very being as researchers who marry acts of science to concerns for social justice and equity in everyday and professional lives.
During the Phd research project that is the basis for this paper, the freedom of knowledge was the main focus of our research and theory; the freedom of knowledge was exercised by giving voice to all the actors inserted in this script through a dialogical process.
“ … o diálogo é uma exigência existencial. E, se ele é o encontro em que se solidarizam o refletir e o agir de seus sujeitos endereçados ao mundo a ser transformado e humanizado, não pode reduzir-se a um ato de depositar idéias de um sujeito no outro.” (Freire, 1970: 79)
We recognize without fear of contradiction the presence of the innumerable academic works that could support many different ways to conduct this research, creating different scripts. The diversified context of the academic environment itself could propose directions, through any of its departments of knowledge, to work with our data or even with our own conduct during this project with the “children in street situation”, the children in locum (the asphalt children). In the end, this project was developed under the reality followed in its construction; it imbricates different contexts through different point of views (cf. Campbell’s  “fish scale model of science/omniscience”). The way through the complexity of human relations, walking by different systems where those relations penetrate, was supported to re-search the freedom of knowledge.
Some necessary parameters to develop this script in the format of an academic research project were followed with the intention of maintaining a dialogical process with the academics in our audience. In this script we are, have, and exercise many languages, perspectives, everyday cultures, and professional cultures to claim and re-claim the freedom of knowledge
The Sociological Worldview
The sociological worldview adopted is present in the format of the script, promoting to the actors the possibility to exist within it and to the readers an encounter with sociology in action. We searched the movement of the sociological worldview to provide the opportunity of placing lived experiences in asphalt conceptual places. We are obliged to express the complexities of social and cultural realities and to affirm the difficulties of a sociological understanding directly and with a view to recreating for our readers, our listeners, our interlocutors, our “subjects” the same sorts of challenges we face in the world as we go about trying to make sociological sense of our experience.
To make a sociological sense of lived mathematical experiences was the central goal during the “Children in street situation’s Culture and Concept of Space” Project; this movement had a deep influence during the whole development of this research. After the inclusion of mathematical knowledge in the jurisdiction of sociology, conquered by Durkheim and Spengler and recovered in recent times by David Bloor and Sal Restivo, the sociology of mathematics can argue the discontinuity of the human relations existent in the urban non-space in the ways our research and theory reveal.
The fact that the sociology of mathematics involves two academic environments (traditionally recognized as different and, before Durkheim, Spengler, Bloor, and Restivo as antagonists) itself, promotes a change in the position of an observer capable of exercising the observation with more sets of eyes. With this, it also promotes more freedom for the observed knowledges as well as for the involved knowledges in the action of observation.
An Ethnomathematics Posture
The ethnomathematics posture guaranteed the application of a study of the social life of mathematics founded in the cultural roots of urban cultural groups. What is the status of mathematics in the asphalt children’s world, and how does it compare to professional academic mathematics. If this posture was not accepted, the risk to have and to impose a predominant view over the mathematics knowledges in the urban cultural groups would prevail. In the case of mathematical knowledges, the actual predominance is in the academic knowledges and the children’ knowledges in question could be stifled and made invisible. This posture defines a claim about dignity:
It is widely recognized that all the issues affecting society nowadays are universal, and it is common to blame, not without cause, the technological, industrial, military, economic and political complexes as responsible for the growing crises threatening humanity. Survival with dignity is the most universal problem facing mankind. (D’Ambrosio, 2007, p25)
One movement could put us on the path of dignity – relationships viewed in terms of ethics and power. The representations of ourselves out of us and our representation to and in others are understood as a cultural model, a political representation, or a social artefact. Both cases in which the children in street situation developed their spatial construction in this Phd research project were embedded by their social construction, imbricated in all the complexities of their environment as well as in the multiplicity of the systems by which they are directly or indirectly surrounded.
If we did not know about the children in street situation’s social construction some cases could sound very aggressive or insignificant. However, knowing their social construction, it was possible to make a sociological analysis of their mathematical knowledges; looking to the intrinsic models, representation, and artefacts in their social life.
The Freedom of Knowledge and the Responsibility of Sapience: an exercise of equity between to know and the practices of knowledge
The possibility to be with both cultural groups, the Children in Street Situation and the Academy, allowed bringing different points of view to the same urban images and actions. From the confrontations of these differences appears the necessity of searching for material and intellectual artefacts to develop a symbiotic movement between them, to promote a dialogical process between them.
To observe that the space concept of the children in street situation’s culture was different from the space paradigm of the urban population was the first step toward trying to find ways to understand their concept better. A paradigm controls the logic of the discourse; it is a way to control the logic and the semantics at the same time. It is a relationship that includes and excludes persons, ideas, artefacts, and values (cf. Morin, 2002).
In some academic presentations, it was normal to hear the criticism that “it is a social problem, not an academic problem”. Some of those outcries redirected observations to the Social Assistant Department, denying them, in a strong way, as an observation stuffed with mathematical knowledges, or any knowledge deserving the attention of the academic environment.
The actual position of the academic environment has been rethought by some voices; many of them are present in this Phd research project. Ubiratan D’Ambrosio (1999), one of those, is explicit when assuming an opposite direction to the etymological significant of academy; the word academy means “distant of people”.
“… queremos ir na direção em que o povo está, nas praças, nas ruas, campos, construções, nos espaços abertos para o confronto, para a busca compartilhada do conhecimento.” (D’Ambrosio, 1999: 70).
Sal Restivo insists, in his works, to affirm that the hegemonic system, in which Occidental societies are engaged these days, has supported the development of self-aware mathematicians working in an academic autonomous system to maintain the “bourgeois mathematics”. In that sense, his academic voice has discussed the necessity to act in the changing of the material bases and social structure of mathematics based in the changing of the social, economic, and political conditions of our lives.
A radical change in the nature of our social relationships will be reflected in radical changes in how we organize to do mathematics – and these changes will in turn affect how we think about and the content of our mathematics (Restivo, 1983: 266).
There have in our time voices in the academy that spoke to, through, and in the voices of the Other, of the disenfranchised. From C. Wright Mills to Dorothy Smith and Richard Falk, there have been academics who resisted the academy’s exclusion of the Other’s knowledge. And yet it is not an exaggeration to say that for the most part academics have excluded the reasoning, the findings, the lives of non-academics. Why is asphalt science “science”?
We do not claim a positivist perspective aimed at destroying the value of science, as we explain in our book, Asphalt Children (2011). What we affirm is that to deny the others, to deny their knowledges, is the height of the unilateral and univocal rationalism that defines the core of the academy. Through our academic practices we were able to expose the children in street situation’s mathematical knowledges. And then we observed how intolerable it is for some academics to listen, to interact, or even to know about some knowledges. What good are knowledges not recognized by them as directly important in, for example, developing chemical or nuclear weapons, strategies that funnel human beings into labor that serves capitalism (more realistically, the industrial-technological society). What good are methods and theories and findings that do not water their own academic environment and nourish the power that maintain the academy as a closed system.
The movement of intolerance is a post-modern condition for human beings; it is not only in academic institutions. The existence of the urban non-space is an example of this intolerance and constitutes in part this movement. However, in a dialectical way, Slavoj Žižek (2006) affirms that tolerance is the hegemonic ideology of global capitalism. In that sense, he argued that the academy, as a structured social body where each part occupies its place, to recognize, validate and make compatible a part of the “partless” – the invisible ones – put in a deep conflict the functional order of the relations inside of academic environments. The recognizing, validating, and making compatible of the children in street situation’s mathematical knowledges with the academic mathematical knowledges, as part of academic society is an elementary gesture of “politization”. In an opposite way, to recognize, validate, and make compatible only the traditional academic knowledges characterizes the process of “depolitization”, feeding the marginalized conditions, increasing the urban non-spaces, and leaving the mathematical knowledges in a closed system.
The act of the asphalt academics claiming to open the academic system was exercised through the work with the children in street situation’s mathematical knowledges, with their contexts, and with the mixture of different voices around the same subjects under a certain intolerance by Dr. Mesquita as the on-site ethnographer. The intolerance came in the sense that she had to claim her own condition as an academic person (inserted in the bourgeois position), and the absurd silence around the knowledges of these children. The practices of living with this intolerance taught her not to be tolerant to any closed system but to be “smart”, according to Capoeirinha (2000), with the attitude that treats each local culture in a colonization process.
“Nunca ninguém quis sabe o que a gente sabe, como agente faz as coisas. Sempre vem gente pra sabe como a gente está, porquê a gente faz. Ah! E porquê a gente está na rua!… Essa coisa de saber como a gente faz, de compreendê como a gente faz e aprendê como você faz deixou agente ser mais irmão e mais esperto. Até hoje temo vontade de sabê mais e mais como a gente faz (a gente quem?)… Nós tudo…(Quem?)… Eu, você, a Irmã Ana Célia, o cara da esquina, minha mãe.” (Antonio, 2001)
Antonio (2001). Vozes do Projecto Cultura da Criança em Situação de Rua e Conceito de Espaço. In Mesquita, M., Restivo, S. & D’Ambrosio, U. (2011). Asphalt children and city streets: A Life, a City, and a Case Study of History, Culture, and Ethnomathematics in São Paulo, Sense Publishers, Rotterdam / Netherlands.
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Capoeirinha (2000). Vozes do Projecto Cultura da Criança em Situação de Rua e Conceito de Espaço. In Mesquita, M., Restivo, S. & D’Ambrosio, U. (2011). Asphalt children and city streets: A Life, a City, and a Case Study of History, Culture, and Ethnomathematics in São Paulo, Sense Publishers, Rotterdam / Netherlands.
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