Writing that begins and moves through the micropolitics of life and desire

The aim of this article is to provide an invitation to desire in favor of a trajectory of teaching in and for life in deaf education. We understand the educational context as a web of macro and micro-political forces that incessantly affect and produce subjectivities, in the face of historical and still ongoing attempts to colonize life and desire. There is an urgent need for a different kind of pedagogical thinking and acting that can re-exist

[...] to multiply dissonant voices and insurgencies in the contemporary capitalist colonial world in order to escape the agencying of modern scientism that solidify thinking around societies, collectivities, individualities, subjectivities, political, social and cultural times and spaces. Creating, inside and outside these strata, forces and flows such as other lines and ways of thinking (re)existences, other possible worlds in this present world, is the challenge under construction (^{Voss, 2020}, p. 222).

In this context, we believe it is necessary to think about the relationships between teaching and educating deaf people in order to resist the presence of deaf life in common schools, distancing ourselves from the "[...rational subject, [from] single and universal causes, [from] metanarratives, [from] historical linearity, [from] the notion of progress, [from] the realist view of knowledge [...]" (^{Meyer & Paraíso, 2012}, p. 26), understanding it as a cultural subject constantly produced in the midst of social and educational subjection. In this vein, we intend to transgress the universalisms and essentialisms of teaching deaf people in ordinary schools, embracing the post-structuralist perspective as an epistemological and methodological force for doing research, through these lenses

[...] has constantly reminded us that we can break out of our imprisonment, out of fixity, out of methodological essentialism, and has mobilized us to search for and find new ways of doing research in education. It is now possible to be suspicious of established practices and knowledge and of the meanings produced by fixed and stable concepts; it is now possible to denaturalize what is presented as natural and absolute and to find strange what is presented as familiar and normal (^{Tedeschi & Pavan, 2017}, p. 13).

From a post-structuralist perspective, with the contributions of philosophers Foucault, Deleuze and Guattari, along with other authors who intercede with their thoughts, we set out to find a research itinerary in which we could problematize teaching with deaf people in common schools, building a path that would allow us to resist and re-exist against "[....] educational experiences of fundamentalist cloisters that circumscribe human subjectivity to the limits of truths that aim to reflect and reproduce the same" (^{Carvalho, 2010}, p. 139).

We were instigated to embrace the post-structuralist perspective because of the possibility of subverting and transgressing modern and structuralist logic, with its discourses and truths, and because of the "[...] potential of this epistemological and methodological perspective for research in education [...]" (^{Tedeschi & Pavan, 2017}, p. 13), providing, through research, other problematizations, always multiplying, deviant, rhizomatic.

In this sense, we chose "[...] thought as a strategy [...]" (^{Deleuze, 1992}, p. 119-120) "[...] to give life, to free life where it is imprisoned, to trace lines of escape" (^{Deleuze, 1992}, p. 176), welcoming trajectivity as the itinerary of a life-research. We operate with trajectivity (^{Virilio, 1993}) because it mobilizes the middle, the in-between, and it is a power because the "[...] possibility not only of paths, but of new transits between what you have - the objective - and what you can extract from what you have - the subjective" (^{Carvalho, 2021}, p. 49). We explored trajectivity as a theoretical-methodological possibility so that the teacher-researcher³ could think about what she experienced in the processes of schooling deaf people in ordinary schools, based on her experiences, which will be exemplified throughout this article, as an opportunity to produce another through the encounter, in the present moment and in the production of research, with these events and their problematizations.

The teacher-researcher, based on trajectivity, composed a life-research between the objective and the subjective, the past and the present, between herself and with other-united⁴ in education, distancing herself from imprisonment and binary relationships in order to mobilize the insurgence of life in and through coexistence. In this sense, the central objective of this article is to present the notion of trajectivity as a theoretical-methodological operator, aligned with a post-structuralist perspective, as a power in the composition of a writing-life-research that is concerned with thinking about the modes of production of another teaching and education with deaf people in common schools.

We found interesting clues in trajectivity to think of it as a possibility of liberation from the already established and legitimized paths of thinking, researching and being in education. We see trajectivity as a strategic force for problematizing the "[...] naturalized consolidation of the paths [...] by which we come to live, to feel, to want, [...] paths by which we accept things as if they weren't historical inventions and as if they couldn't be different from what they are" (^{Carvalho, 2016}, p. 4).

We want to research in and through the post-structuralist perspective because of the freedom it allows for other methodological compositions and bricolages, and because of the attempt to deconstruct epistemologies that aim to fix and homogenize knowledge and subjects. After all, according to ^{Corazza (2007}), in post-structuralist theorizing:

[...] there are no criteria that authorize anyone to select this or that research methodology. Precisely because one doesn't choose this or that method, but rather a research practice that 'takes us over' in the sense that it is meaningful to us. And how does it take us? Each research practice is a language, a discourse, a discursive practice, which is always assimilated by the historical formation in which it was constituted. This historical formation marks the discursive place from which we emerge; from where we speak and think; also from where we are spoken to and thought about; from where we describe and classify reality(ies) (^{Corazza, 2007}, p. 120-121, emphasis added).

Accepting trajectivity as a life-research practice, we set out to present, in the next section of this article - 'Trajectivity: what can this theoretical-methodological movement do?' - its ethical and aesthetic strength through the trajectivity of the self, with others and with education and the school. In the second section, 'Essay writing: the (de)formation of the trajective self', we highlight the importance of essay writing operating in this movement. And finally, we share an invitation to keep thinking, because of the power we find in trajectivity, in the composition of an unpredictable and incessant writing-life-research.

Trajectivity: what can this theoretical-methodological movement do?

Research in education is produced by choosing between various epistemological, theoretical and methodological perspectives. In this choice, we outlined our research itinerary by deciding to operate with trajectivity as a theoretical-methodological movement, based on ^{Virilio's (1993}) studies, explaining that

[...] between the subjective and the objective, there seems to be no place for the dispositive, this being of the movement from here to there, from one to the other, without which we will never have access to a profound understanding of the various regimes of perception of the world (^{Virilio, 1993}, p. 107).

In this respect, it is worth pointing out that research anchored in the post-structuralist perspective allowed us to choose trajectivity as a research itinerary that welcomed and spoke to the teacher-researcher's experience as empirical material.

To compose living-researching as a "[...] path that opens to the time in which one walks [...]" (^{Larrosa, 2003}, p. 112) is to open up the possibility of being on the lookout for what one is in order to welcome what one is becoming, recognizing the unpredictable in education and in life through encounters. Thus, by choosing the theoretical-methodological movement that operates through trajectivity, the researcher allows himself to live-research through the in-between:

[...] between things does not designate a locatable correlation that goes from one to the other and reciprocally, but a perpendicular direction, a transversal movement that carries them from one to the other, a stream without beginning or end, that gnaws at its two banks and acquires speed in the middle (^{Deleuze & Guattari, 2014}, p. 49).

In this atmosphere, the problematization of research "[...] would be less of a solution and more of a horizon of machination [...]", that is, the possibility of "[...] machining a problem, opening it up in its forces, multiplying the possibilities of connections, of contagions between these forces" (^{Ribeiro, 2020}, p. 177). In this way, we also welcome other readings, other understandings, other new concerns in and through research, distancing ourselves from the production of universal truths for thinking about educational problems.

The machining of the research problem becomes "[...] not an adjustment of representations, but a work of thought [...]" (^{Foucault, 2014}, p. 227) that enables the researcher to be and be productive, creative, inventive in and through the research process. A way of researching that makes you vigilant of the methodological paths that have already been established and also critical of the knowledge that you produce and that produces you. It also encourages them to be deviant, since it forces them to think in and through the empiricality of the events of their research, not indicating

[...] where the researcher and the research should go, much less in what way, but the desire to put themselves and perceive themselves in a research movement, as soon as possible, is sharpened. Putting themselves in motion, as a condition for the possibility of exhausting a desire for research, which overflows with what is left in potency (^{Araujo & Corazza, 2017}, p. 237).

With this in mind, we followed the investigative paths in our Master's research with the following research problem: how can teachers function as educators with the presence of deaf people in common schools? After all, according to ^{Corazza (2007}, p. 119), the research problem arises from "[...] acts of rebellion and insubmission, from small revolts against what is established and accepted, from restlessness in the face of the truths that are plotted, and where they plot us".

Through trajectivity, the researcher produces and is produced by what happens in the middle, in between an existence-doctrine. He/she becomes the subject of the experience, "[...] this subject that we have already characterized as open, vulnerable, sensitive and ex/post" (^{Larrosa, 2011}, p. 18). The subjective teacher-researcher has allowed herself to think about the educational practices she has experienced, the positions she has occupied and still occupies in the educational scenario, and the ways in which she schools the subjects involved.

The choice of studying the trajectivity also came about because of the teacher-researcher's reading-encounter with the Brazilian literary work Grande Sertão: Veredas, by Guimarães Rosa. Through the narrative, it is possible to put oneself through a journey of the self, since this is the movement that the main character - Riobaldo - experiences in order to think about what he has lived, as he talks to an interlocutor who does not openly and explicitly express himself. A conversation not about "[...] the life of a sertanejo, even if he is a jagunço, but [about] the subject matter [...]" (^{Rosa, 2019}, p. 77), because Riobaldo revisits the events of the past, not in order to understand them, but to produce himself with these events, through the possibility of new encounters, affections and meanings. This movement makes possible to interact with the flowing material for other possible selves, in a subjectivity that is permanently on the move.

We believe that "[...] between oneself and oneself, the distance of a work of life to be realized opens up" (^{Gros, 2006}, p. 135). Thus, research into trajectivity takes on an ethical and aesthetic movement that works as an attempt to always put oneself in experimentation and, consequently, in the subjective encounter with the invention of other possible selves, as an affirmation of a life's work to be continually carried out. Trajectivity with the other also favors the encounter as a power for new relationships and the affirmation of their singularizations and multiplicities, which move through the collective. By means of this exercise in trajectivity of the self and with the other, coined in the context of teaching, we have chosen experiences as the materiality of trajectivity. By articulating the notions of 'experiences' and 'marks', by the authors Jorge ^{Larrosa (2016}) and Sueli ^{Rolnik (1993}), respectively, we were able to operate an enunciative force capable of transforming empirical findings into discursive monuments. In this sense, the experiences of teaching in the field of deaf education, the events that took place in the daily life of the classroom, the relationship between the teacher, the Brazilian Sign Language interpreter (Libras) and the students (deaf and hearing) became the discursive materialities of the research.

In the context of this study, the notion of experience coined by ^{Larrosa (2016}, p. 28) is presented as "[...] that which 'passes us by', or touches us, or happens to us, and, in passing us by, forms and transforms us [...] the subject of experience is open to their own transformation [...]", being understood as a path of passage, therefore singular, provisional, changing through the movement of exteriorization with oneself and with others and/or with other things.

The concept of marks, for ^{Rolnik (1993}), are unprecedented states produced in our existence through the compositions we live. For her, "[...] each of these states constitutes a difference that opens up an opening for the creation of a new body, which means that marks are always the genesis of a becoming" (^{Rolnik, 1993}, p. 242). Therefore, we understand marks as affections in/by the power of experience, which establish the opening of a becoming.

We chose to make up the experiences-marks as a way of thinking about what was lived through some events of teaching in the ordinary school, understanding that "[...] a lived event is finite, or at least closed in the sphere of the lived, while the remembered event is limitless, because it is only a key to everything that came before and after" (^{Benjamin, 1986}, p. 37). Questioning was the path chosen as a trigger to create the experiences-marks. To this end, some problematizations of events in the teacher-researcher's teaching experience with deaf people in ordinary schools were chosen in order to think about and problematize what was experienced.

To illustrate the modus operandi through which we moved in the context of the research, we highlight one of the experiences-marks:

[...] ‘a new deaf student: what a joy!!! My God, how can he not know LIBRAS? What now?’ Joy. Astonishment. Can the ordinary school be the only deaf reference point in this existence? Yes, it can! The experience with the deaf student showed me this and brought me a new challenge: literacy in LIBRAS. It also gave me the opportunity to see this student as a unique life, which didn't happen straight away. I think about what happened in this experience-mark, recognizing the process of subjection and the conduct of this deaf life that I produced. From the moment this new student arrived, I made comparisons with the deaf student because of her relationship with sign language and her relationship with other deaf people. Still constituted by discursive production, I plastered him with a deaf identity, understanding that every deaf person should know LIBRAS and belong culturally to the deaf community. According to Lunardi (2003, p. 1), when the deaf subject is ‘described, measured and compared to others and to themselves in their own individuality, they can be classified, trained, recovered and normalized’ and, I would add, colonized. Thus, I highlight LIBRAS as a machinic device that produces governance and normalizes deaf bodies. The way I was captured by this discursive production shows the ‘shock’ I felt when I learned that the new deaf student didn't know LIBRAS. It was by getting to know him better, not through an anamnesis, but through my relationships with him in everyday school life, in the exercise of his literacy in sign language, that I came to understand him as a life, and therefore unique. I relive this experience-mark, perceiving all the subjectivities in the ordinary school as 'living and mutating raw material from which it is possible to experiment and invent different ways of perceiving the world and acting in it' (Mansano, 2009, p. 112). From what I have already been able to share, I would like to point out that deaf subjectivities in ordinary schools can be more easily exposed to subjectification and its different forms of production. This experience-mark also triggered me to question how to be on the lookout for pedagogical strategies of normalization. How can we produce other possibilities in deaf education that break with the logic of classification and normalization? How to identify, problematize, transgress when it is so naturalized? (^{Dell' Osbel, 2022}, p. 46-47, emphasis added).

In this fragment of the experience-mark, we can see that the teacher-researcher is thinking about what she experienced, understanding the plots and productions of knowledge-power-truth in which she was and is involved, in a movement of problematization which, according to ^{Foucault (2003}, p. 390), "[...] is always a class of creation". In this way, the materiality of the experiences-marks made it possible to look at oneself, the other and the relationships that happened/occurred in the school for other possibilities through the insurgence of what was problematized. According to ^{Carvalho and Gallo (2022}), it is necessary and urgent that we

[...] back to the fundamental practice of philosophy: asking questions. We begin to renounce the poverty of our subjective condition when we inquire into the connections that have brought us this far, being what we are, thinking what we think, wanting what we want, doing what we do. We don't want to silence the power of inquiry (^{Carvalho & Gallo, 2022}, p. 162).

The post-structuralist perspective, in addition to everything already mentioned, reinforces the power of inquiry, an element that enabled the subjective teacher-researcher to find ways to "[...] exercise suspicion about the very historical formation that constituted and still constitutes us, and to question whether everything we say is everything that can be said, as well as whether what we see is everything that can be seen" (^{Corazza, 2007}, p. 119). The milestone experiences mobilized a problematizing encounter as a starting point for other understandings of teaching and educational relationships, for the constitution of other knowledge about education with the deaf and between other-united in education.

In this way, research happens, with the possibility of being able to return and think again, to feel again, not as a way of updating a form; but as a way of modifying another mode, including itself; a becoming that is recurrently possible at every moment; variables in a continuous variation in an alternation of states, in which each scribble can trace the difference it can invent. Investment in a careful look at the research and the researcher, in the sense of approaching how they become what they are at each instance of the relationship; and how and why a difference happens (^{Araujo & Corazza, 2017}, p. 244).

Thus, it was possible to problematize and produce other meanings through the in-between, through the flows of an existence-doctrine that was trajective, "[...] because the trajective presupposes escape, flight, sliding" (^{Carvalho, 2018}, p. 124). Understanding that trajectivity is made through the in-between, the experiences-marks were operated between thoughts, without marking frames and/or an analytical beginning and end, but showing the overflow through the in-between, which was also made possible by essayistic writing.

Through the machining of experiences-marks, the teacher-researcher was involved in the movement of hypercriticism that made it possible to "[...] cut into our own flesh, pull up the rug that is under our own feet" (^{Lopes & Veiga-Neto, 2010}, p. 160). In this movement, the past gained vital force, "[...] not because of the years that have passed, but because of the cunning of certain past things - of rocking, of moving from place to place" (^{Rosa, 2019}, p. 136).

By engaging in essayistic writing "[...] to give life, to free life where it is imprisoned, to draw lines of escape [...]" (^{Deleuze, 1992}, p. 176) for herself and for the other, the researcher-teacher problematized the presence-life of deaf students through the experiences-marks of her teaching. In the experience-mark shared in this study, it is possible to recognize the effects of discursive production and hearing coloniality in pedagogical practice with deaf people in common schools.

In the exercise of thinking about what happened, we see in this experience-mark the constitution of a powerful discursive network that produced and still produces in her teaching a regime of truth about deaf schooling. As an effect, we have 'Libras' with its strong linguistic accent on bilingual education, which is often seen as the only guarantee of quality in schooling processes for the deaf. We reiterate that it needs to be present, and alive, in relationships and in their multilearning, but in addition to sign language, other crossings take place in this collective, singular, multiple, alive, cultural crossings that also need to be considered in teaching and learning processes with deaf people. Through discursive gearing, 'Libras' often comes to function as a machinic device that governs deaf bodies by placing itself as an unquestionable truth.

Furthermore, we realize that the deaf and their unique experience with language and culture are no longer recognized in order to plaster them in an 'ideal' identity and cultural subject; they no longer venture into the encounter with this singularity and with other-united in education in order to trace a path that is already desired, instituted and predictable, destroying the power of multiplicity and creation. To this end, we have the challenge of "[...] making it possible for another education, or transformations, to enter the scene, leaving the discursive sameness that we have theorized about deaf education for so long" (^{Martins, 2016}, p. 720). We realize that recognizing the deaf student as a singularity and as other-united in education, from the perspective of the philosophy of difference, is an attempt to liberate the flows of forces and truths that produce the normalization and exclusion of the deaf in education with colonial and governing practices, annihilating their distinct forms of life.

Hearing coloniality, shaped by the universal and essentialized project of the modern subject, aims to place and hierarchize existences, languages and knowledge. For this reason, we understand that the common school can be a space-time in which

[...] the subjection and normalization of the deaf can [...] gain strength from the discursive constitution of hearing coloniality, since it maintains its dominant power structures, its hegemonic modes of knowledge production and its strategies for conducting deaf life (^{Dell' Osbel, 2022}, p. 40-41),

like the disciplining and normalization that puts into operation.

[...] when we operate in our research with a deconstructive reading of the categories that have been fixed, naturalized and universalized - as is the case with truth, discourse, the subject, power, identities and differences - we open up possibilities to produce, in encouraging difference, the invention of other meanings and/or other images of thought. We open up possibilities for making visible what has been made invisible by hegemonic discourse. Deconstruction, in this case, acts within hegemonic educational discourses, which, to a certain extent, still support modern Western thinking, as a way of questioning them, destabilizing them and, consequently, expanding their limits, expanding the possibilities of thinking about educational processes (^{Tedeschi & Pavan, 2017}, p. 5).

Thinking about the problematization of these effects in the discursive production on which the school-colonized education of the deaf is based and the need to present the operationalization of trajectivity, in the Master's research it was possible to understand how the teacher can function in the role of educator with the presence of the deaf in the common school, based on trajectivities. The educator-function, an intercessory notion of Foucault's author-function, is defended by ^{Carvalho (2010}) as a teaching exercise that, in its posture and practice, is open, exposed, alterable, contributing as a strategic force of liberation (action) to break with pedagogical continuities, with the truths told about the ways of doing teaching and education, in favor of a more active subjectivation of oneself and also of the other.

We understand that the educator function operates with trajectivity and has the possibility of

[...] to hold what escapes, so that passages of air permeate a body that experiences teaching, messing up the roles and models that the word teaching agglutinates around itself, [...] so that one can say, write, think, invent other, singular teaching (^{Garlet, 2018}, p. 13),

In other words, as a possibility to create a form of teaching in the midst of the relations of knowledge-power-truth in which we are produced and which we also produce.

Therefore, we understand trajectivity as an aspect (^{Rosa, 2019}) to "[...] de-automatize perceptions, gestures, ways of doing things. To de-automatize dominant pedagogies. Escape the automatisms that combat creation, variation [...]" (^{Tóffoli & Kasper, 2018}, p. 91), in order to invent singular teaching in and through the movement of trajectory with others-united in education.

We understand that trajectivity produces three major movements in an existence-doctrine, which are not recognized as separable, but co-functioning: the trajectivity of the self, the trajectivity with others and the trajectivity with things. We see, in trajectivity and its movements, important indications for rehearsing the invitation that ^{Deleuze urges us to make (1992}, p. 124): "[...] do we have ways of constituting [...], as Nietzsche would say, a sufficiently artist way, beyond knowledge and power?".

The trajectivity of the self involves "[...] operations of the self on the self [...]" (^{Foucault, 2004}, p. 199) as a possibility of thinking, inquiring, deforming and transforming one's existence in a movement of constant subjectivation of the self. By valuing the experiences of her teaching career and venturing into essayistic writing among them, the researcher mobilized her subjective processes in a movement of becoming.

Trajectivity with others mobilizes relationships with others. Thus, in the context of the research, we sought to think about relationships with students, with fellow teachers and also with the interpreter in education in the midst of (dis)encounters. Trajectivity with others allows us to affect and be affected "[...] by our interest in each other, by hearing each other's voices, by recognizing each other's presence" (^{Hooks, 2017}, p. 17). It also makes it possible to break with the "[...] types of links established between power, truth, discourse and everyday life as it takes into account all the types of relationship that are at stake in the constitution of subjectivities [...]" (^{Carvalho, 2010}, p. 103), valuing singular, provisional, pulsating life.

Trajectivity in relation to things, in turn, is walking through the process in relation to relationships and knowledge. In the context of research into education with deaf people in ordinary schools, it was possible to think about trajectivity between different languages and cultures and the relations of knowledge-power-truth. Trajectivity in relation to things also values the living event of the classroom, allowing the educator and their group to be trajectives in everyday life, seen as a multiple, hybrid and borderline universe. This trajectivity gains strength in affections and desires, valuing the life-presence of each person involved in the process, mobilizing:

[...] their subjects to think differently, to want to relate through the flows of sensitive affections that are closer to human singularities and multiplicities, to question knowledge outside the axis of merely applied and profitable truths, and, not least, to produce conditions so that life can be affirmed through desire (^{Carvalho & Gallo, 2022}, p. 638).

In this sense, we think of trajectivity in the plural, due to the power of productions that its movements imply, as other ways of researching, thinking and being in education. The trajective exercise between her experiences and the investigative experimentation in which the teacher-researcher was involved produced other ways of researching, contributing to the production of "[...] a singularity of its own in the existence of things, thoughts and sensibilities [....]" (^{Guattari & Rolnik, 2005}, p. 213) about her teaching and education with the deaf, distancing herself from the imposed, customary and accepted educational methodological paths, to venture into new (com)positions of researching and, consequently, being and being in education.

In this research movement, the mobilization of thought also takes place, which is why we understand other ways of thinking as a possibility,

[...] first of all, [to] see and [to] speak, but on the condition that the eye does not remain in things but rises to visibilities, and that language does not remain in words or phrases but rises to enunciations [...].Furthermore, thinking is power, that is, extending relations of force, with the condition of understanding that relations of force [...] constitute actions on actions, that is, such as inciting, inducing, diverting, facilitating or hindering, amplifying or limiting, making more or less probable [...] (^{Deleuze, 1992}, p. 119-120).

Through her experiences, the teacher-researcher also announced her ‘trajectivity’ as another way of being in education, since her teaching, through the strength of the encounter of others-united in education, enabled the formation of a collective. A collective that, in its multiplicities, has been involved in ethical and aesthetic relationships with itself and with the other and in favor of difference in education and can awaken other knowledge and relationships, distancing itself from the ways of seeing, thinking, being, living and coexisting present in the modern/colonial matrix in which we were produced.

In this way, we understand that trajectivity mobilizes escape, slippage and co-creation by the forces of the environment for new relationships and other productions of life and education. After all, "[...] to resist is to re-exist, to exist again, to affirm the powers of life [...]" (^{Gallo, 2017}, p. 91), so that we can refuse subjection and the one, to constitute ourselves from new forms of subjectivity and through multiple forms of life.

Essay writing: the (de)formation of the trajective self

The post-structuralist perspective "[...] not only questions this notion of truth; it more radically abandons the emphasis on 'truth' in order to highlight, instead, the process by which something is considered to be true" (^{Silva, 2007}, p. 123-124, emphasis added). In this way, in our Master's research, we moved through a teacher's exercise in hypercriticism in order to problematize the discourses and truths of an educational scenario of colonized-schooled education for the deaf.

We understand these truths, based on Foucault's contributions, as the constitution of a strong and perverse discursive production, insofar as "[...] discourse is nothing more than the reverberation of a truth being born before your very eyes [...]" (Foucault, 2014, p. 46) that produces ways of educating and relating to deaf people.

Seeking to explore these truths in the production of teaching, we found a connection with essay writing because it "[...] neglects indubitable certainty, but also renounces the ideal of this certainty [...] through the march of its thought, which takes it beyond itself" (^{Adorno, 2003}, p. 32). Thus, we decided to try to resist the fundamentalist cloisters of knowledge-power-truth to which we are subjected through essayistic writing that puts unquestionable truths on hold a priori in favor of a mobilization of thought.

In addition, Bell Hooks urged us to think that "[...] there can be no intervention [in/by life] that challenges the status quo if we are not willing to question the way in which not only our pedagogical process but also our self-presentation is usually shaped" (Hooks, 2017, p. 245). To this end, we envision a different kind of deaf education that (de)forms its existence-doctrine through essayistic writing and the experiences-marks lived with deaf students at school, constituting itself unpredictable from a trajectory movement of research.

Based on the studies of ^{Larrosa (2003}) and ^{Adorno (2003}), we understand essayistic writing as an experimentation of thought, a life-writing in rehearsal of itself, which allows a subjective and trajective immersion in and through writing in the first person, since "[...] to write is to trace, to always become another. Writing is sculpting the raw material with words [...]" (^{Rolnik, 1993}, p. 246).

The essay, in its writing-becoming, makes it possible to blur the boundaries between Science, Philosophy, Literature and Art, giving the researcher greater freedom. According to ^{Larrosa (2003}, p. 111), "[...] the essay is fragmentary, partial and selects fragments as its material. The essayist selects a corpus, a quotation, an event, a landscape, a sensation, something that seems expressive and symptomatic, and gives it great expressiveness".

We would like to point out that the teacher-researcher wrote an essay that included excerpts from the literary work Grande Sertão: Veredas, by Guimarães Rosa, after all, "[...] sertão. You know: sertão is where people's thoughts are stronger than the power of the place" (^{Rosa, 2019}, p. 25). In addition, she used photographic records in scenes from her daily life as art experiments to think about the movements of the present with the theorizations of her research, producing powerful subjective encounters with these different languages and their trajectories.

The essay arises when the possibility of a new experience of the present opens up. Firstly, when the past has lost all authority and can therefore be read again from the present, but without any reverence or submission. Secondly, when the future appears as something so uncertain, so unknown, that it is impossible to project oneself into it. Thirdly, when the present itself appears as an arbitrary time, as a time that has not been chosen, as a time that can only be taken as a contingent and provisional abode, in which we will always feel like strangers; as a time that constantly slips out of our hands, resisting any of our attempts to fix it, to solidify it, to trace its shape and profile (^{Larrosa, 2004}, p. 33).

The photographs chosen to compose the essayistic writing experimented in the Master's research depict unconventional spaces for thinking about education, showing the trajectivity being lived by what is possible to produce "[...] in the relationships, in the 'between', whether between the images and the researcher, between the images and the text, between the images and the reader, in the crossings of the modes of readings and productions of meanings" (^{Neuscharank & Barin, 2018}, p. 55, emphasis added). We have therefore selected two photographic experiments to share in this study (Figures 1 and 2).

Source: ^{Dell' Osbel (2022})

Figure 1 Photographic record of costume 1 

The choice of essay writing triggers a movement of micropolitics of life and desire, since it aims to "[...] problematize the way in which the politics of truth and the images of thought and knowledge, dominant in the academic world, impose certain modes of writing and exclude others, including the essay" (^{Larrosa, 2003}, p. 102). Thus, we understand that essay writing can be constituted as a writing-combat against the dominant methodological models of doing research and in favor of a more active subjectivity of the researcher through the movement of experience and thought:

That's why criticism in the essay is unquestionably an exercise in freedom or liberation, an asceticism of freedom. The essayist can only entrust himself critically to his own experience, all he has to do is experiment, see and make people see how far it is possible to speak and think differently, how far it is possible to live differently. This is why the essay is not about comparing reality with ideas, but about comparing experience in relation to the truth of power and the power of truth (^{Larrosa, 2004}, p. 39).

Source: ^{Dell' Osbel (2022})

Figure 2 Photographic record of costume 2 

^{Aquino (2011}, p. 633) provoked us into this exercise of freedom by advocating "[...] a writing-combat that challenged determinations of multiple orders, that altered destinies already traced, that transformed lives indelibly. A writing-arrebentation, so to speak [...]", of a self (de)forming itself in its own writing process, constantly moving through encounters with the subjects and events of its research. It is also a writing of rapture which, in its courage, forges new methodological possibilities through its ability to "[...] deterritorialize thought, that is, to pull thought out of the dimension of the thinkable in which it finds itself and launch it in search of other dimensions [...]" (^{Lopes & Veiga-Neto, 2010}, p. 159) not thought of, not experienced, but emerging through the force of the environment, of the encounter of a trajective existence and, therefore, open to new transits, to crossings.

In this sense, essay writing helped us to rehearse the liberation of a more active subjectivation, after all, in and through research it was possible to "[...] abandon the marks that constitute us, even for a few moments, allowing other forces to compose us, undoing the sovereign 'I' and holder of the truth that inhabits us, taking writing as creative becoming and artful speeds" (^{Olegario & Munhoz, 2014}, p. 157, emphasis added). From this, it was possible to dig new encounters with ourselves and the other through the deterritorialization of a thought that found strength in trajectivity.

Essay writing is a becoming-research, constituted by the between and its intertwining with the thoughts and affections of the investigative journey. A becoming-research corroborates the resistance "[...] as an insistence on existing alive, re-existing in movements that create meaning, moving, reluctant [...]" (^{Aspis, 2012}, p. 74) to methodological paths supported by regimes of truth that, epistemologically, direct us to certain perspectives and ways of doing research.

Since "[...] the real is neither at the exit nor at the arrival: it becomes available to us in the middle of the crossing [...]" (^{Rosa, 2019}, p. 53), we understand essay writing as a movement of crossing oneself, a trajective self that discovers itself in the middle, tracing the investigative path, (de)forming itself, transforming itself through the becoming-research that it is composing.

Finally, we believe that essay writing makes it possible to transgress the norms and prescriptions of dominant methodological models, since "[...] to move we write and to write we move" (^{Kohan, 2002}, p. 124). In other words, an essayistic writing that constitutes a trajective self that always finds itself unpredictable in the encounters with itself, with others and with the knowledge it produces.

Invitation-desire to continue thinking: trajectivities and the composition of a writing-life-research

For the - hopefully not final - considerations of this article, we propose to share an invitation-desire. An invitation because the post-structuralist perspective urges us to expand, fracture and open up to new ways of researching and being in education. A desire because we announce the power of a trajective teaching as a pedagogical thinking and acting for new relationships with deaf people, in favor of their living, active and mutating subjectivities, transgressing a hegemonic and colonial discursive production about deaf people and their schooling processes. After all, desire implies "[...] all forms of the will to live, the will to create, the will to love, the will to invent another society, another perception of the world, other value systems" (^{Guattari & Rolnik, 2005}, p. 261).

We found strength in the words of ^{Corazza (2007}) to present this invitation-desire, which was the result of a research practice we experienced as

[...] a way of thinking, feeling, desiring, loving, hating; a way of questioning, of arousing events, of exercising the capacity to resist and submit to control [...]; of confronting those procedures of knowledge and those mechanisms of power; of being inserted in particular processes of subjectivation and individuation. Therefore, a research practice is implicated in our own lives. The 'choice' of a research practice, among others, concerns the way in which we have been and are subjectivized, how we enter into the game of knowledge and how we relate to power (^{Corazza, 2007}, p. 121, emphasis added).

In order to enhance this invitation-desire, we return to the objective of this writing - to present the notion of trajectivity as a theoretical-methodological operator, aligned with a post-structuralist perspective - recognizing it as the composition of a writing-life-research that produces and is produced from an ethical and aesthetic movement of the researcher. The teacher-researcher can shape her research problem, problematizing events experienced in her teaching with deaf people. We understand that trajectivity "[...] has no beginning or end, but always a means by which it grows and overflows" (^{Deleuze & Guattari, 2014}, p. 43). A powerful means to keep thinking between the objective and the subjective, to seek out new experiments, to produce something different from what one is. Through trajectivity, the researcher enhances insurgencies by transgressing the already indicated, legitimized and true ways of doing research, in order to risk new transits.

Thus, essay writing becomes an important element in the production of trajectivities as a possibility of crossing life with oneself, but also crossing life with the other. According to ^{Aquino (2011}, p. 647), essay writing enables "[...] the exact point of culmination between writing and life, in which the former offers itself as a mode and occasion for the dizzying multiplication of forms of the latter". In this sense, in the context of the research, such writing has made possible journeys in and through life for active subjectivities of the self and the other, for the possibilities of becoming, seeking to problematize the determinations of various orders, the subjections that are already traced, the educational processes and their mainstream.

Through the theoretical-methodological movement of trajectory, it was possible to identify in my Master's research the experiences and marks of a colonizing-hearing educational process in teaching with deaf students in common schools, recognizing marks that cause subjection to deaf modes of existence and modes of teaching in the school context. However, it was also possible to recognize experiences that potentiate other forms of coexistence, complicity and sharing of a community in the school territory, driven by trajectivities.

In this way, we believe that trajectivity as a theoretical-methodological movement for doing research is in line with Deleuze's statement about Nietzsche's contributions to philosophy: "[...] ways of life inspire ways of thinking, ways of thinking create ways of living. Life activates thought, and thought, in turn, affirms life [...]" (^{Deleuze, 1994}, p. 17-18), constituting another way of doing research.

In the encounter with the post-structuralist perspective as the theoretical-methodological grid of this study, we felt resonance in what makes us "[...] tread paths different from the established ones, makes us resist practices and knowledge that are placed as permanent, meanings that are presented as fixed, times and spaces that seem too linear" (^{Tedeschi & Pavan, 2017}, p. 13). The post-structuralist perspective has mobilized us to "[...] a necessary courage in our [research], methodologies, to find ways out of the imprisonment and fixity of meanings, essentialisms, 'this is it' or 'it should be done this way'" (^{Meyer & Paraíso, 2012}, p. 32, emphasis added), a courage to do research, to think and be in teaching and education in a composition of life that is always unpredictable and incessant.

In an effort to think about trajectivity as the production of a different kind of teaching and education with deaf people in common schools, we presented some clippings of the teacher-researcher's wanderings in her Master's thesis which, in a trajective movement, signaled other ways of living and being in education with deaf people in ordinary schools. By composing a writing-life-research in which life activated thought, the teacher-researcher found the opportunity to delve into her teaching, immerse herself in her process of subjectivation, digging fissures in the given, in the instituted.

At the same time, thought affirmed life in order to "[...] de-eternize the ways in which things are made known and can be known, as well as trying to reposition the subject in relation to themselves and others - their destiny caught up in the weaves of knowledge-power-truth" (^{Carvalho, 2010}, p. 64). In this way, it was possible to operate in and through the trajectivity of an existence-doctrine lived by the teacher-researcher through the subject matter, in order to seek breathers for other teaching in the affirmation of the deaf presence-life and in the trajectivities as others-united in the common school.

We operate with the life-presence of deaf people and others-united in education, in the common school, as effects and relationships emerging from trajectivities. Trajectivities incite coexistence, the possibility of horizontalizing relationships, pluralizing knowledge and, through this, an education 'with' deaf people and not 'of' deaf people' in common schools is affirmed. Through this movement, we resist subjection and production by relations of knowledge-power-truth, so that we can fight for micropolitics with the deaf, because "[...] if we broaden the horizon of our gaze to encompass the surface of the world as [...] it is configured today, we will see that we are facing the micropolitics of a life, individual or collective, that manages to reappropriate its power" (^{Rolnik, 2018}, p. 65).

We thus glimpse the production of trajectivities as resistance and (re)existences that leak incessantly, deterritorializing, affecting and being affected, (de)forming those involved and producing other inventions of the self, of the other and of education, causing cracks in the machinery of knowledge-power-truth relations and their macropolitical ways of combating difference and multiplicities.

Trajectivity in and through writing-life-research invites us to new forms of a teaching-existence, to a different kind of deaf education, through the micropolitics of life and desire. It contributes to achieving "[...] other ways of educating, other ways of relating to and in education; [...] of drafting intentions that move to risk doing the new, doing oneself anew" (^{Carvalho & Gallo, 2022}, p. 156-157). So, we invite you to think about: what trajectivities have we produced and can we still produce? And we also reaffirm our desire: what can a life-doctrine-research driven by trajectivity do?