Nicolas Henckes
email: nicolas.henckes@cnrs.fr

Infrastructures of schizophrenia: transforming psychiatric diagnoses at the local and global level in the twentieth century

Keywords: schizophrenia, infrastructures, psychiatric diagnosis, history of psychiatry

This article uses the concept of infrastructures of diagnosis to propose a framework for telling the history of schizophrenia as a global entity in the twentieth century. Infrastructures of diagnosis include the material and architectural arrangements, legal prescriptions and professional models that organize the way patients come to clinics and navigate in the world of schizophrenia, as well as clinicians organize their diagnostic work. They organize the way schizophrenia was identified as a disorder. The article then explores three moments in the history of the infrastructures of the diagnosis of schizophrenia in the twentieth century. The first is German psychiatrist Kurt Schneider's discussion of first and second rank symptoms in the interwar period. The second is the work on the criteria for defining schizophrenia in the framework of the WHO International Pilot Study of Schizophrenia at the turn of the 1970s. The last moment concerns recent discussions on deconstructing psychosis the in the framework of the development of the fifth edition of DSM.

Infrastructures of schizophrenia: transforming psychiatric diagnoses at the local and global level in the twentieth century

When in 1954 the American psychiatric profession developed one of its innumerable quarrels over the meaning of schizophrenia, a participant to the discussion proposed to write to Manfred Bleuler, the son of the originator of the concept, Eugen Bleuler, and his successor at the Zurich university psychiatric clinic on the Burghölzli hill, to ask his opinion on the "diagnostic criteria which had been established at Burghölzli with reference to the diagnosis of schizophrenia, schizoid states "pseudoneurotic schizophrenia", and allied conditions" [START_REF] Johnson | The Concept of Schizophrenia[END_REF] . In his response, published in the American Journal of Psychiatry, Manfred Bleuler took pain at explaining the meaning of the various labels crafted by his father, recalling the ways these labels were used at Burghölzli [START_REF] Bleuler | The Concept of Schizophrenia[END_REF]. For mid-century psychiatrists, the truth of schizophrenia was to be found in a single place. The intimate connection Manfred Bleuler had with his father's work had made him a guardian of the clinical tradition Eugen Bleuler had created, a role he would keep until his death in 1994. This role entailed both moral and scientific dimensions. Bleuler personified a humanistic vision of schizophrenia, a vision that had roots in his long term study of the course of the disorder as well as in the bound he had created with his patients and their families over his life spent at Burghölzli since his childhood. (see for instance [START_REF] Rosenthal | Introduction to Manfred Bleuler's "The offspring of schizophrenics[END_REF] My point in recalling this episode is to stress the fact that schizophrenia has always been, in a certain sense, a global category: a category which circulated in and was shaped by networks of people extending over continents. A crucial question for a global history of schizophrenia then relates to the shape of these networks: both their extension and the type of channel they were for a variety of entities. Where was schizophrenia used as a concept? What sorts of concepts and instruments were mobilized in these settings to diagnose and discuss schizophrenia? Who were the authorities in these discussions and how did their authority extend to various contexts? And how did the replies to these questions impact the very nature of schizophrenia as an entity? In this article I would like to insist on the materiality of the professional and scientific networks behind schizophrenia. Networks are not only a matter of circulating people, ideas, and things. They also involve in decisive ways a series of infrastructures and more generally material arrangements which make these circulations simply possible. These infrastructures were not only necessary in order to transport people, things and concepts. They also helped these people, objects and concepts retain a meaning across contexts.

By insisting on these dimensions I wish to offer a new framework for understanding the history of schizophrenia in twentieth century. There are a number of good historical, anthropological and sociological analyses of the changing phenomena that have been labelled as schizophrenia across the twentieth century. [START_REF] Woods | The Sublime Object of Psychiatry : Schizophrenia in Clinical and Cultural Theory[END_REF][START_REF] Mcnally | A Critical History of Schizophrenia[END_REF][START_REF] Noll | Feeling and smelling psychosis: American alienism, psychiatry, prodromes and the limits of 'category work[END_REF]2011;[START_REF] Barrett | The Psychiatric Team and the Social Definition of Schizophrenia : an Anthropological Study of Person and Illness[END_REF][START_REF] Garrabé | La schizophrénie : un siècle pour comprendre[END_REF][START_REF] Guillemain | Schizophrènes au XXe siècle[END_REF][START_REF] Bernet | Schizophrenie. Entstehung und Entwicklung eines psychiatrischen Krankheitsbilds um 1900[END_REF] Most of this scholarship focused on the changing representations of both schizophrenia and the people concerned: which symptoms defined schizophrenia and schizophrenic patients; what sort of person these were. By contrast the question that interests me in this article is the ways in which clinicians identified the disorder they were calling schizophrenia. What were the structural, institutional and practical conditions that framed the clinical experience of schizophrenia at each single moment? I draw on research of infrastructures and more generally on the insistence in Science and Technology Studies (STS) on the material dimensions of clinical work in order to highlight both the highly contingent nature of clinical judgment and the way it is structured by the conditions of psychiatric work. With this inquiry I do not intend to downplay the argument that fundamental human processes are behind schizophrenia. [START_REF] Jenkins | Schizophrenia, Culture, and Subjectivity : the Edge of Experience[END_REF] Rather I see the analysis as an attempt to offer another supplementary perspective on the social life of that disorder.

Outlining an account of the changing infrastructures of psychiatric diagnosis across the twentieth century would by far exceed both my capacity and the scope of this article. Rather my strategy will be to illustrate aspects of this analysis by focusing on three moments in the history of the diagnosis of schizophrenia in the twentieth century. The first is German psychiatrist Kurt Schneider's discussion of first and second rank symptoms in the interwar period. The second is the work on the criteria for defining schizophrenia in the framework of the WHO International Pilot Study of Schizophrenia at the turn of the 1970s. The last moment concerns recent discussions on deconstructing psychosis the in the framework of the development of the fifth edition of DSM. I take these discussions as revelatory moments in which the arguments that are exchanged, the nature of the criteria and the type of the definitions they offer, make visible the infrastructures behind diagnostic work. Before turning to these analyses, the first section of the article offers some broad theoretical and historiographical considerations on the changing infrastructures of psychiatric diagnosis in the twentieth century. 1

Infrastructures of psychiatric diagnosis

This article proceeds from the assumption that what is global in a condition such as schizophrenia derives as much if not more from shared infrastructures of clinical work as it does from shared understandings and representations, circulating numbers and concepts, common biological and psychological processes. I draw my understanding of infrastructures from Susan Leigh Star's and colleague pioneering work on information systems (Star, 1999;[START_REF] Star | Steps Toward an Ecology of Infrastructure: Design and Access for Large Information Spaces[END_REF]Bowker, et al., 2016). Infrastructures are things that are embedded and transparent, that are learned as part of becoming a member of a community, that extend over several sites and are, and that only comes to the fore when they break down. They can be found virtually everywhere there is work. Social science interest in infrastructures derived from an attention paid to mundane and taken for granted dimensions of professional and scientific work, many of which related to the use and maintenance of infrastructures. [START_REF] Graham | Out of Order. Understanding Repais and Maintenance[END_REF][START_REF] Lynch | Scientific practice and ordinary action : ethnomethodology and social studies of science[END_REF] Geoff Bowker and Leigh Star's own work on the International Classification of Disease offers a series of analytical clue as well as a series of concrete examples on some infrastructures behind that lay behind diagnostic work. (Bowker and Star, 1999) In the line of decades of research on categories and labelling, one of their central questions was how people managed to map a complex reality onto a limited set of categories. I suggest in this article to expand the analysis to a wider range of infrastructures that contribute to organize and shape practices in the field of schizophrenia. These infrastructures do not only consist in the instruments that are specifically used to sort pathological conditions and disease entities, but they also encompass a range of material and architectural arrangements, legal prescriptions and professional models that organize the way patients come to clinics and navigate in the world of schizophrenia, as well as professionals organize their work. Among these infrastructures are the paper technologies and informatics infrastructures that are used to record clinical notes [START_REF] Hess | Case and series: medical knowledge and paper technology, 1600-1900[END_REF][START_REF] Borck | Sorting things out : classification and its consequences[END_REF][START_REF] Berg | Practices of Reading and Writing: The Constitutive Role of the Patient Record in Medical Work[END_REF], the architectural and institutional models that structure the landscape of mental health institutions [START_REF] Keating | Biomedical platforms : realigning the normal and the pathological in late-twentieth-century medicine[END_REF][START_REF] Laget | L'hôpital en France: histoire et architecture[END_REF], or the professional standards as well as legal models that define the role and scope of mental health professions [START_REF] Freidson | Profession of Medicine[END_REF][START_REF] Abbott | The system of Professions[END_REF].

By insisting on infrastructures I do not want to reduce diagnosis making to the mere application of routine procedures that would be solidified in these infrastructures. A key theme in the analysis of infrastructures is in fact the gap between their normative dimensions and the creativity of social practices. On another hand while infrastructures impose their structure on work activities they themselves derive from the way this work is thought of and conducted. We may also think of the relationship between infrastructures and clinical work with the help of the notion of moral economies as it was defined by historian of science Lorraine Daston. In science Daston defined moral economies as "webs of affect-saturated values that stand and function in well-defined relationship to one another" and that are integral to the very ways in which scientific research is done. [START_REF] Daston | The Moral Economy of Science[END_REF] In the same way, in the field of psychiatric work, a given infrastructure both reflects and shapes a series of moral values and norms that organize the ways in which clinicians conceive of themselves and behave as professionals. For instance the development of an array of tests and interview schedule was founded on a new ethos of exactitude and discipline that profoundly affected both the psychiatric profession and its relationship to its patients.

With the concept infrastructures I also insist on the incremental nature of changes in the domain of psychiatric diagnosis across the last century. A central theme in the history of schizophrenia is the impact of past descriptions of the disorder on current concepts. The distinction German psychiatrist Emil Kraepelin made between dementia praecox and manic depressive continues to be called upon in virtually every discussion of the diagnostic problems of schizophrenia and in 2011 the centenary of the publication of Eugen Bleuler's Schizophrenie, which introduced the term, was celebrated with due recognition of the enduring influence of a classic [START_REF] Carpenter | One hundred years[END_REF]. Such celebrations represent more than rhetorical deference due to a glorious past. Many clinicians and theoreticians seek the truth of the disorder in observations published decades ago that seem to embody their authors' clinical concepts. While one may want to see in this enduring influence the acumen of past clinicians, it also reflects the permanence of some core dimension of the infrastructures of diagnoses across the century. Despite decades of deinstitutionalization and more broadly transformations as a result of an expanding field of psychopharmacology and transforming societies, psychiatric practices are still structured by the institutional and normative arrangements that were created in the 19 th century in most European and American countries. Both the sort of phenomena that are labelled schizophrenia and the way they are remain intimately related to what they used to be a century ago.

By contrast one might want to see in the advent of the biomedical complex in the second half of the twentieth century a series of epochal transformations that have profoundly affected psychiatric diagnosis making. The creation of new psychopharmacological therapies, the multiplication of tests and scales, the development imaging and genetic engineering not only molecularized the representations of psychiatric disorders. STS scholars Peter Keating and Alberto Cambrosio would perhaps argue that these developments were behind the emergence of new arrangements between laboratory techniques and clinical practices taking place on "biomedical platforms" [START_REF] Keating | Biomedical platforms : realigning the normal and the pathological in late-twentieth-century medicine[END_REF][START_REF] Garrabé | La schizophrénie : un siècle pour comprendre[END_REF]. While I agree with them that we should be watchful for the new ways of practicing psychiatric that are emerging within the biomedical complex, I do not believe that these are necessarily based on a dilution of the clinical gaze. On the one hand the psychiatric research complex has had a major impact in transforming diagnosis making over the last decades through the dissemination of schedules and guidelines or the multiplication of reference centers that tend to create new polarities in the landscape of mental healthcare. On another hand, contrary to Keating and Cambrosio's observations in the field of cancer, psychiatric disease entities notoriously resist reduction to biomarkers. Even in research settings a striking dimension of psychiatric decision making remains its reliance on clinical judgment. Despite a number of prophetic calls the impact of genetics or brain imaging might not be so much to challenge psychiatric expertise than to negotiate it in new ways.

In the line of these remarks a major theme in the history of schizophrenia is the possibility to produce universal knowledge on the disorder through localized experience. In the past phenomenological approaches have promoted the role of the clinician's personality in the evaluation of symptoms, and some of these approaches even asserted that diagnosing schizophrenia relied on a "praecox feeling" that could not be objectified [START_REF] Rümke | The Nuclear Symptom of Schizophrenia and the Praecoxfeeling[END_REF]. If these ideas may have receded in the recent period, they have not disappeared and one may argue that they continue to shape the perspectives of many clinicians over the disease. They reflect the enduring tension between the lack of specificity of the disorder and the irreducible experience represented by its encounter. Schizophrenia was from the beginning and still is at once a vague and unmistakable thing. The equation many people still see between schizophrenia and madness is a dimension of this. Yet schizophrenia is something else than pure madness. It is the attempt at framing madness within biomedical reason. This tension shaped schizophrenia as both a global and a local entity throughout the last century. The question for historians is how this experience has been shaped by the social, material, organization and institutional organization of psychiatric work. I now turn to the first moment of my analysis.

Clinical schizophrenia in the interwar period

In his Klinische Psychopathologie published between 1939 and 1950, probably one of the most influential book on schizophrenia in the 20 th century after Bleuler's Dementia praecox oder Gruppe der Schizophrenie, Kurt Schneider pointed to the particular position schizophrenia occupied in psychopathology [START_REF] Schneider | Star, Susan Leigh 1999 The ethnography of infrastructure[END_REF]. In the domain of so-called endogenous psychoses, schizophrenia was the remaining option once a clinician was sure the condition was not manic depression (Schneider, 1950:11). Yet at the same time Schneider also suggested that schizophrenia could be ascertained in many cases on the basis of the presence of specific symptoms (Schneider, 1950:138-139). These perspectives were less contradictory than it may seem. In Schneider's view schizophrenia was conceived of in relation to other disorders; it was a salient pattern against the background of the ordered set of pathological phenomena that constituted the realm of psychiatry. This take on schizophrenia reflected Schneider's wider position on diagnosis. Schneider saw individual psychiatric disorders as "types", in the sense given by Max Weber to that concept, which helped organize psychiatric diagnosis making but should not be taken at its face value. "With this [notion], the classification of endogenous psychoses will be more relative, with this notion 'accuracy' loses its strength, the struggle between systems and schools loses its pungency, with this notion for instance it does not make sense any more to fight over the question of whether regression melancholia 'belongs' to manic depressive madness, but the question is only whether it is practical to count it as such, or whether it is handier not to do it." [START_REF] Schneider | Star, Susan Leigh 1999 The ethnography of infrastructure[END_REF] In this perspective diagnostic criteria did not aim at ascertaining a diagnosis. Rather they helped a clinician recognize a condition in order to take action. The "first rank" and "second rank criteria" he listed for the diagnosis of schizophrenia followed this philosophy. [START_REF] Schneider | Star, Susan Leigh 1999 The ethnography of infrastructure[END_REF]; also see: [START_REF] Cutting | First Rank Symptoms of Schizophrenia: their Nature and Origin[END_REF] They were a list of symptoms which were typically there in patients with the disorder and as such they indicated the presence of that disorder when they were there, but they were neither a sufficient nor a necessary condition for it.

Schneider's relativistic stance on diagnosis is usually taken as an expression of the influence of phenomenology over his thinking. A colleague and friend of Karl Jaspers, his psychopathology was also influenced by his reading of Max Scheler as a philosophy student in Tübingen. [START_REF] Cutting | Max Scheler's influence on Kurt Schneider[END_REF] More pragmatically his intellectual project also reflected a concept of mental disorders where the main question was not so much whether a case was schizophrenia or another psychosis, but whether it was madness or not. (on this way of framing the problem of psychiatric diagnosis, see [START_REF] Noll | Feeling and smelling psychosis: American alienism, psychiatry, prodromes and the limits of 'category work[END_REF] This explained his and his fellow psychiatrists' ways of thinking about classification. The key, central category for mid twentieth German psychiatrists was that of "endogenous psychoses". These were characterized within two series of distinctions. On the one hand psychoses distinguished themselves from psychopathy or abnormal personalities: while psychopathy was conceived of as a deviation from the normal, psychoses were seen as illnesses resulting from an underlying pathological process. On another hand, within the realm of psychoses, German psychiatrists distinguished between organic psychoses, for which a biological cause was known, and endogenous psychoses for which there was no known biological etiology. Diagnosing organic psychoses was supposed to be relatively straightforward: by definition they relied on the presence of a number of definite signs, which could be ascertained by biological testing properly done. By contrast the identification of endogenous psychoses relied on an ability to decipher less univocal psychological and behavioral signs that was the realm of psychiatry. [START_REF] Henckes | Performing doubt and negotiating uncertainty: diagnosing schizophrenia at its onset in postwar German psychiatry[END_REF] The role of forensic psychiatry was determinant in this way of thinking [START_REF] Hess | Die Buchhaltung des Wahnsinns. Archiv und Aktenführung zwischen Justiz und Irrenreform[END_REF]. In the midtwentieth century the main use of psychiatric classifications was still to decide about the fate of a patient in the asylum system or in the court. This is why they were highly idiosyncratic. The way psychiatrists addressed the problem of nosology was shaped by the specific institutional and judicial arrangements on which the psychiatric system was founded at the national level. These arrangements were in turn reflected in the paper technologies in use locally. Local ways of doing with these technologies remain to be investigated by the historiography. [START_REF] Hess | Case and series: medical knowledge and paper technology, 1600-1900[END_REF] In France, for instance, the "certificates" psychiatrists had to write to justify a decision to commit a patient aimed less at labeling a disorder than at making explicit the arguments for or against seclusion. (on the creation of the psychiatric certificate : Castel, 1988:139-141) Clinicians had to provide a short description of the disorder in order to justify confinement. This created a style of writing that consisted in picturing traits in order to produce a global impression of the case. Diagnosis was not the determinant feature and as a result it was virtually absent from medical records. By contrast the specific take German psychiatrists had on diagnosis was shaped by the organization of the university clinic, a urban institution created at the end of 19 th century that served both as an entry in the psychiatric system for patients, as a training center for medical students and as a research institution. [START_REF] Engstrom | Clinical psychiatry in imperial Germany[END_REF][START_REF] Hess | Psychiatrie in der Stadt. Die Poliklinik als Schwellenphänomen einer urbanen Moderne[END_REF] In this system diagnosis was a crucial instrument at the juncture of knowledge making and patient management, a position that was reflected in the very structures of German medical records [START_REF] Henckes | Performing doubt and negotiating uncertainty: diagnosing schizophrenia at its onset in postwar German psychiatry[END_REF][START_REF] Keuck | Diagnosing Alzheimer's disease in Kraepelin's clinic[END_REF]. The differential understanding of schizophrenia between both countries reflected these two widely different infrastructures: in France many psychiatrists saw schizophrenia as a catch all category that blurred the subtleties of individual tableaus and schizophrenia only made its way in French diagnostic practices after the 1930s [START_REF] Guillemain | Schizophrènes au XXe siècle[END_REF]; by contrast schizophrenia had established itself as the determinant category for German psychiatric thinking from the 1910s.

The circulation of knowledge and categories was shaped by the specificities of local infrastructures of psychiatric work. Categories and classifications were useful for communicating across contexts and the first efforts at crafting an international classification of madness can be traced back to the late 19 th century. Yet locally what was important were the ways in which singular concepts found a niche in the institutional infrastructure of psychiatric work. While the diffusion of categories in the colonial world also followed this pattern, it was also shaped by the specific relationships colonial administrations had with autochthone people, its goals as well as the shape local colonial and indigenous infrastructures. Speculations about and research on the universal nature of dementia praecox famously began with Emil Kraepelin's journey to Indonesia in 1904. [START_REF] Bendick | Emil Kraepelins Forschungsreise nach Java[END_REF]) However colonial psychopathologies were shaped by a melting pot of influences which included metropolitan theories as well as vernacular concepts, resulting in hybridity rather than translation. [START_REF] Ernst | Idioms of Madness and Colonial Boundaries: The Case of the European and "Native" Mentally Ill in Early Nineteenth-Century British India[END_REF][START_REF] Vaughan | Curing their ills colonial power and African illness[END_REF][START_REF] Sadowsky | Imperial Bedlam. Institutions of Madness in Colonial Southwest Nigeria[END_REF] The identity of schizophrenia as a disorder across contexts made in fact little sense in a world where classifications were so much related to the local infrastructures of healthcare.

Schizophrenia redefined by the research complex in the 1960s and 1970s

The International Pilot Study of Schizophrenia (IPSS) is usually considered as a decisive moment in the history of transcultural psychiatry: the demonstration that schizophrenia affected people in the same ways in all parts of the globe; the proof of the global nature of mental disorders. [START_REF] Patel | Global mental health : principles and practice[END_REF] Another less commented aspect of IPSS is its role in the emergence of a new concept of schizophrenia characterized as the conjunction of two syndromes, one consisting of "positive symptoms", the second of "negative symptoms". (Strauss, et al., 1974) This concept would become the main framework for the research on the disorder for the next forty years. [START_REF] Marneros | Negative versus positive schizophrenia[END_REF] These two aspects reflected the profound changes in the ways psychiatry addressed its entities in general and schizophrenia in particular from the 1960s on. While what counted for Schneider and his contemporaries was the position of a category in a classification, the main question raised by schizophrenia was now its internal consistency. In this new problematization a key role was played by an emerging infrastructure of institutions, protocols and technologies supporting schizophrenia research.

Schizophrenia research was in a sense a typically American cause. It reflected both the importance taken by schizophrenia in the American intellectual and cultural life and the specific ways in which biomedical research was funded in this country. [START_REF] Woods | The Sublime Object of Psychiatry : Schizophrenia in Clinical and Cultural Theory[END_REF][START_REF] Metzl | The protest psychosis : how schizophrenia became a Black disease[END_REF] The creation of the National Institute of Health and then of institutes dedicated to research on specific health conditions is usually interpreted as the governmental response to increasing public demands from for public funding of biomedicine: while successive US governments rejected the idea of creating a universal healthcare coverage at the scale of the country, funding research seemed less expensive than funding care. [START_REF] Starr | The social transformation of american medicine[END_REF][START_REF] Harden | Inventing the NIH: federal biomedical research policy[END_REF][START_REF] Hannaway | Biomedicine in the twentieth century : practices, policies, and politics[END_REF] When the National Institute of Mental Health was created in 1949 its main task was to monitor the reform of the US psychiatric system. [START_REF] Farreras | Mind, brain, body, and behavior : foundations of neuroscience and behavioral research at the National Institutes of Health[END_REF][START_REF] Grob | The National Institute of Mental Health and Mental Health Policy, 1949-1965[END_REF] By the 1950s it had established a series of intramural research units devoted to basic as well as clinical research and was funding a wide range of projects across the US as part of its extramural program.

The idea that the research effort in the field of mental health should focus on singular disorders rather than on mental health in general began to be expressed in the late 1950s. At that time schizophrenia already attracted a significant share of the research money distributed by the NIMH, but it was not singled out among the numerous programs coordinated by NIMH grantees. (Studies of Schizophrenia, 1954) Highlighting schizophrenia was thought of as a way of prioritizing research on a particularly dreadful disorder as well as a way of promoting psychiatric research and demonstrating to the congressmen who voted the budget of the NIMH the utility of the money spent for it: while mental health was a rather abstract concept, schizophrenia pointed to the tens of thousands people affected by the disorder who for the most part lived on state or federal money. In 1957 in a letter to the editor of the American Journal of Psychiatry, psychiatrist Stanley R Dean thus proposed that a program of research for schizophrenia was established at the NIMH: "Until now, public support has been directed towards the all-inclusive field of mental health. But psychiatry has long outgrown such swaddling clothes, and the phrase "mental health" now seems too diffuse, too ambiguous, too inadequate to clothe its constituent parts. That is especially true of one of its largest segmentsschizophrenia -which many believe may provide the key to all mental disease. It is therefore deserving of much closer public and even professional scrutiny than it has previously received." [START_REF] Dean | Focus on Schizophrenia: The Role of R.I.S.E. and the Dean Award[END_REF] Dean subsequently contributed to raise funds for schizophrenia research and he created an award for outstanding researchers. [START_REF] Dean | Focus on Schizophrenia: The Role of R.I.S.E. and the Dean Award[END_REF] These efforts and others led to organize and institutionalize the field of schizophrenia research. By the mid-1960s a series of funding bodies including the NIMH and several private foundations were significantly involved in that effort. In 1966 a reorganization of the NIMH led to the creation of a bureau specifically dedicated to coordinating work in the field, the Center for the Studies of Schizophrenia (CSS). [START_REF] Mosher | Special Report on Schizophrenia[END_REF] The role of the CSS was to produce coherence among programs and foster synergies between researchers. The Center organized meetings between researchers and monitored a series of programs while its head advocated the cause of schizophrenia among NIMH officials and the wider public. In 1969 the CSS also created the Schizophrenia Bulletin which rapidly developed into the major journal in the field. By the end of the 1970s schizophrenia was the sole psychiatric disorder with a significant coordinated research effort specifically devoted to it. In other countries schizophrenia research never reached this level of institutionalization but it also distinguished itself as a key fundraiser cause.

In a way the main question asked by schizophrenia research was what had become of a disorder that had lost its natural boundaries. The demise of the psychiatric institution beginning in the 1950s in the US and the advent of neuroleptic treatment in 1952 had blurred the symptomatic tableau of schizophrenia. Chronic schizophrenia did no longer mean the catastrophic course resulting in a combination of delusional states and intellectual deterioration that had been observed earlier. (Strauss and Carpenter, 1974) On another hand some forms of schizophrenia became harder to distinguish from a wealth of conditions located on the side of personality disorders with which they shared many traits. [START_REF] Gunderson | Borderline and schizophrenic patients: A comparative study[END_REF] An answer to these evolutions was the rejection of diagnosis, a temptation that had a strong appeal on the European continent to psychiatrists with a variety of theoretical orientations. [START_REF] Pilgrim | The survival of psychiatric diagnosis[END_REF][START_REF] Henckes | Mistrust of numbers: The difficult development of psychiatric epidemiology in France, 1940-1980[END_REF] In the US the same phenomena had as a consequence an extensive understanding of the label, which was used for an ever increasing group of patients, a problem that began to cause a stir among the psychiatric profession in the 1960s and eventually became a major impetus behind both diagnosis research and the larger movement that led to the DSMIII. [START_REF] Demazeux | Qu'est-ce que le DSM ? : genèse et transformations de la bible américaine de la psychiatrie[END_REF][START_REF] Decker | The making of DSM-III: a diagnostic manual's conquest of American psychiatry[END_REF] In this context the objective of schizophrenia research was to identify core phenomena that would help better characterize and understand the disorder. A basic methodological approach was to constitute samples of patients and to test them against controls for a variety of psychological and biological variables. [START_REF] Mosher | Special Report on Schizophrenia[END_REF] The idea that schizophrenia was processual and that the processes behind the disorder would be better identified when observed through time also led to the success of longitudinal approaches. In these approaches researchers sought to create samples of patients either suffering from schizophrenia or supposed to develop schizophrenia in order to test them repeatedly and see how the disorder was evolving. Research on subjects at high risk of schizophrenia, which would become one of the main programs of the NIMH in the field of schizophrenia in the 1970s, typically exemplified this approach: in this research patients supposed to be particularly at risk of schizophrenia were followed from childhood to adulthood to observe the disorder as it blossomed. [START_REF] Reinholdt | Anticipating psychosis: The Copenhagen High Risk Project and the dream of the prevention of schizophrenia[END_REF] High risk subjects were chosen among children of patients with schizophrenia, a condition that was known to be associated with a heightened probability to develop the disorder since the work of European geneticists in the immediate post-war period. Other longitudinal studies conducted in the US and German speaking countries also looked at the long term prognosis of the disorder. [START_REF] Bleuler | Die schizophrenen Geistesstörungen im Lichte langjähriger Kranken-und Familiengeschichten[END_REF][START_REF] Huber | Schizophrenie. Verlaufs-und sozialpsychiatrische Langzeituntersuchungen an den 1945-1959 in Bonn hospitalisierten schizophrenen Kranken[END_REF] These researches stressed the diversity of schizophrenia both synchronically and diachronically. Yet the objective was to channel diversity rather than suppressing it.

In contrast with earlier discussions over diagnosis in Germany, a characteristic of schizophrenia research in the 1960s was that it was in a sense working from within a clinical definition of the disorder. The diagnosis of schizophrenia was a departure point for research protocols. Another central feature was that it did not seek to suppress the variety of perspectives upon the disorder. A key challenge of schizophrenia research was the increasingly diverging perspectives taken by different segments of the psy world over the nature and mechanisms of the disorder. Schizophrenia research seemed to be a chaos of programs, theories and hypotheses, institutions and actors that barely converged. However until the mid 1970s NIMH officials did not seek to suppress this diversity. Rather the strategy was to aggregate the different perspectives in order to derive the best from each of them. This was true of both the intramural program of the Institute which was thought of as an interdisciplinary endeavor, and its extramural research which extended to all the sensibilities in the profession. As Robert Cohen, the Director of Clinical Research at the NIMH wrote in his 1960 annual report:

The interaction at the regular staff conferences over the eight years of our existence has had a noticeable impact. The individual social or biological scientist no longer approaches a representative problem even in his own discipline without some consideration of its broader implications. Such thinking, by taking into account a wider range of possibilities, leads to a more critical evaluation of the phenomena we are attempting to understand. As the range and depth of our studies show, this atmosphere has not had a stifling effect upon individual initiative; rather, it has promoted careful attention to methodology, precise evaluation of results, and, what is most important, a search for more powerful conceptualizations. (National Institute of Mental Health, 1960:[590]) Another aspect of this way of thinking was that clinicians were left to decide about the definition and limits of schizophrenia. Until the 1970s and the work on Research Diagnostic Criteria, attempts at standardizing diagnosis were limited to the collection of data. The first questionnaires that circulated in the 1950s were used to structure clinical interviews and make sure that all the relevant data was collected. Clinicians were needed to pass questionnaires and to make a diagnostic decision. Diagnostic standardization organized the perspective of clinicians but it did not seek to suppress it.

The work undertaken in the framework of the IPSS reflected this style of doing research. Even before investigating the prevalence of the disorder in different parts of the world, the first objective of the study was to evaluate the possibility to conduct epidemiological research in a transcultural context. (World Health Organization., 1973:3-4) The study relied on clinical evaluations conducted simultaneously in nine centers by teams consisting of local clinicians. To ensure that local teams would diagnose the same phenomena, they were required to use the same instrument for collecting the data, namely the Present State Examination. Discussions over the comparability of the results of the different centers of the study usually focus on the translation of the instruments used for clinical interviews. However another source of variability came from the fact that local clinicians were left alone to make diagnostic decisions. While the investigators tried to harmonize diagnostic practices both within and between centers by organizing sessions where clinicians were asked to diagnose together the same patients, the procedure left much room for the expression of the idiosyncrasies of individual clinicians. In a subsequent phase of the analysis a factor analysis was applied to the data collected to create different groupings of patients. Clinical judgment was required at all stages of the procedure, from the definition of variables to the final validation, but the procedure introduced some standardization in the ways patients were classified. The main outcome of all this work was the delimitation of a core group of patients defined by the fact that they were labelled with schizophrenia by local clinicians as well as by the statistical calculation. This "concordant group of schizophrenics" was judged sufficiently coherent to demonstrate the consistency of diagnostic procedures across centers and to validate the research.

The very existence of that group relied on the shared assumption that there existed something called schizophrenia that could be recognized by every clinician across the world. Work on positive and negative symptoms of schizophrenia by the US team of the IPSS followed on a similar philosophy. The method consisted in analyzing the frequency of a series of symptoms among the US patients of the study. [START_REF] Bartko | The diagnosis and understanding of schizophrenia. Part II. Expanded perspectives for describing and comparing schizophrenic patients[END_REF] These were then allocated to subgroups reflecting different distributions of the symptoms as demonstrated by a cluster analysis. Eventually the symptoms were grouped into categories that contributed more or less to each group. The analysis thus suggested the existence of three categories of symptoms: positive and negative symptoms, and disorders of personal relationship. Eventually the author suggested that they reflected different processes behind schizophrenia. (Strauss, et al., 1974) In the end the research did not so much aim at decomposing schizophrenia than it sought to test its internal consistency.

Databased schizophrenia in the early 21 st century

In the early 21 st century schizophrenia may be losing its preeminent position in global mental health. Multiple causes contribute to this phenomenon: contestations of the label by both researchers and service users across the world [START_REF] Lasalvia | Should the label "schizophrenia" be abandoned?[END_REF][START_REF] Van Os | Salience syndrome' replaces 'schizophrenia' in DSM-V and ICD-11: psychiatry's evidencebased entry into the 21st century?[END_REF], results from basic research demonstrating the continuum between schizophrenia and both other psychotic disorders and normal conditions [START_REF] Tamminga | Deconstructing psychosis : refining the research agenda for DSM-V[END_REF], as well as findings suggesting that schizophrenia is not the first contributor to the burden of psychiatric disorders, including in southern countries [START_REF] Whiteford | Global burden of disease attributable to mental and substance use disorders: findings from the Global Burden of Disease Study 2010[END_REF]. Behind all these phenomena lay new ways of mapping psychopathological phenomena onto new infrastructures, namely databases. These in turn organize new representations of psychopathologies that challenge the very idea of psychiatric disorders. Yet despite these challenges the schizophrenia label continues to be needed to characterize a range of seemingly irreducible clinical experiences. This creates a series of tensions that profoundly affect current debates over the diagnosis.

Databases are the main infrastructures behind a new organizational form that emerged and came to organize the field of psychiatric research over the last two decades, namely the research consortium. Consortia may be defined as collaborative networks of researchers sharing similar methodologies. While such networks existed since the 1950s in other branches of medicine, and most notably in cancer [START_REF] Keating | Biomedical platforms : realigning the normal and the pathological in late-twentieth-century medicine[END_REF], in psychiatry the origin of consortium research may be traced back to the first collaborative clinical trials organized under the aegis of the NIMH in the early 1960s. (The National Institute of Mental Health Psychopharmacology Service Center Collaborative Study Group, 1964) However these first collaborative studies were planned to work on the short term with definite research objectives, even though with time some of them came to constitute databases that were made available for further analyses. By contrast consortium research had a wider scope and it was based on much looser organizations. Moreover its field was not restricted to treatment research but rather encompassed more generally research on etiology. In the field of schizophrenia one of the early examples was a consortium created in 1973 as an umbrella for the high risk studies funded by the NIMH [START_REF] Garmezy | An early crossroad in research on risk for schizoprhenia: the Dorado Beach Conference[END_REF]. In the spirit of 1960s and 1970s schizophrenia research this early consortium aimed at fostering discussions among its members about methods and results. Research teams did not share data and as we mentioned above they had widely divergent views over both the nature of the disorder and the processes they were interested in. In fact members of the consortium only had contacts on the occasion of meetings organized more or less regularly. Except for a series of special issues of the Schizophrenia Bulletin, the only joint publication was an edited book with chapters from single projects published in 1984. [START_REF] Watt | Children at risk for schizophrenia : a longitudinal perspective[END_REF] Later consortia shared the same philosophy but they managed to produce a much higher degree of integration among participating centers. The ultimate objective was to mutualize data in order to increase their analytical power. Several factors accounted for the creation of those consortia, including the availability of funding at the Federal or international level, the new possibilities opened by communication technologies as well as the need to create larger samples of patients to strengthen analyses as new methodologies were developed. In the 1980s genetics provided the first such consortia under the aegis of the NIMH genetics initiative with the objective to map the genes involved in major psychiatric disorders. While the first of these consortia gathered a small number of centers, by 2007 consortium research in the field of psychiatric genetics entered a new dimension with the creation of the Psychiatric Genomics Consortium (PGC) as part of the broader Genetic Association Information Network [START_REF] The | New models of collaboration in genome-wide association studies: the Genetic Association Information Network[END_REF]. Described by one of its protagonist as the coming of "big science" to psychiatry [START_REF] Sullivan | The psychiatric GWAS consortium: big science comes to psychiatry[END_REF] this creation aimed at powering GWAS study of major psychiatric disorders. The GPC now claims to be the biggest consortium in the field of schizophrenia research with more than 800 participating teams and a total number of more than 900 000 individuals involved as research subjects2 .

In the subsequent years brain imaging also produced a need for similar collaborations and more and more consortia came to be created with a variety of research goals and methodological designs, often aggregating several more or less independent sub-groups. One of the biggest consortia working in the field of schizophrenia studies in Europe in recent years, the EU-GEI study, is in fact a big coalition of research groups from all over Europe funded by the Seventh Framework Program of the European Union. Its website indicates as its broad objective to investigate "the interactive genetic, clinical and environmental determinants, involved in the development, severity and outcome of schizophrenia"3 , however this objective conceals several relatively independent scientific agendas led by its various subgroups.

A crucial ingredient of consortium research is the ability to share large sets of data within extended networks of researchers. Beyond databases, communication technologies and laboratory techniques, the infrastructures that make this happen include an array of standardized tests, interview schedules and questionnaires that are used to generate data from clinical interviews. Using these infrastructures requires large amount of calibration work from participating researchers to ensure the comparability of local data sets: harmonization of criteria, training sessions, supervision, and ongoing quality control. In fact the standardization of data collection is a trend that affects psychiatric research beyond consortia. To enable replication or the inclusion of published results in meta-analyses, journals tend to require from researchers that they make their data available for further analyses. While there are usually a number of tests or interview schedules available in the literature to assess a given psychopathology domain or psychological function, researchers are also encouraged to use a small number of standard instruments even though they may find that these instruments are less handy than others or that they do not correspond to their own concept of the phenomena. In a sense the whole field of psychiatric research may be now seen as a giant consortium.

As a result, it has become nearly impossible to map the field. This observation does not so much refer to the size of the psychiatric research industry although it has more than significantly increased over the last quarter century. The total budget of NIMH was multiplied by three between 1993 and 2017, from half a billion USD to more than 1,5 billion USD. In Europe funding opportunities have multiplied at the level of both States and the European Union in the wake of the Lisbon strategy launched in 2000 [START_REF] Keeling | The Bologna Process and the Lisbon Research Agenda: the European Commission's expanding role in higher education discourse[END_REF]. Several journals are now publishing research exclusively on schizophrenia and this condition is also the raison d'être of several research associations worldwide including the Schizophrenia International Research Society. Yet mental health research continues to attract modest amounts of funding particularly from private interests [START_REF] Forsman | Public mental health research in Europe: a systematic mapping for the ROAMER project[END_REF]. In the field of schizophrenia, the total number of studies is limited and most studies are small in scale. The complexities of the field rather derive from its loose organization. Participation to a consortium often means little more than sending data to a centralized bureau which will be then in charge of dispatching it for analysis to statisticians. The whole process might be relatively informal. Local participating teams usually only need to add to an ongoing study protocol a series of tests required by the consortium and revise their inclusion criteria. Contact between teams may be limited to a few training sessions to use specific instruments and a series of emails upon sending data.

For patients this turns participation to research into a particularly opaque experience. Patients may be included at the same time in several studies corresponding to several consortia. Their data may circulate in widely different networks in which they will be submitted to different types of analyses. Some of these analyses may take place years after inclusion and may concern questions that are only remotely related to the reason they had been indicated on inclusion. Even though patients are supposed to sign a consent form for each study they are in, they usually have limited awareness of the way their data will be used.

For participating clinicians and scientists, networking is a central activity at all levels. Local groups need to be integrated into international consortia to simply exist in the world of psychiatric research. Participation to these consortia gives them access to publications in major journals and, as a result, to funding. On another hand they also need to keep contact with the local infrastructure of psychiatric care in order to get access to patients. Most of psychiatric research centers rely on primary care services for recruiting patients, to which they need to demonstrate their usefulness. Diagnosis and more generally evaluations are the primary products they can offer them. Some of them provide expert care to patients but they rarely do in the long term.

There are also several ways of organizing these networks. For instance two competing clinical and research networks have been created in the early 2010s in France under the leadership of the two main figures of psychiatric research in the country. These networks now gather most psychiatric teams in French university hospitals. They are competing for funding as well as for patients. Both aim at creating large databases that may fuel future analyses and generate new research hypotheses. The first is organized around a series of pathology-oriented reference centers established in University clinics. These reference centers offer standardized assessments to patients addressed by community services but they do not provide treatments. The second network is somewhat looser. It is organized in the framework of a Groupe de Recherche which provide both a framework for launching collaborative projects and a database infrastructure set up to collect data from individual centers. Despite this competition, teams from both networks often contribute to the same international consortia and they sometime have to cooperate within single projects. Another model has been established in Germany in the 2000s where the main psychiatry university departments organized in a series of pathology oriented networks. The schizophrenia network was described to me as a loose organization that aimed at creating synergies among participating teams and fostering collaboration in consortium projects. However the network has played an important role over the years as a window of German schizophrenia research and its chair has been also chairing the workgroup in charge of the definition of psychotic disorders in the ICD11 and he also participated to the workgroup on the same issue for the DSM5.

While earlier schizophrenia research sought to aggregate singular perspectives on schizophrenia, consortium research seeks to create new perspectives from within the data accumulated. If the efforts of clinicians and researchers previously aimed at stabilizing a familiar schizophrenic tableau, the objective is now to destabilize this tableau in order to generate a better representation of the patients' conditions. Several iconic projects have embodied this ambition in recent years including the controversial RDOC project launched by the former director of the NIMH [START_REF] Insel | Research domain criteria (RDoC): toward a new classification framework for research on mental disorders[END_REF] or a range of even more speculative endeavors in the field of "phenomics" [START_REF] Cuesta | Current psychopathological issues in psychosis: towards a phenome-wide scanning approach[END_REF]. These projects are developed amidst concerns over the "validity" of clinical categories such as schizophrenia. [START_REF] Tsuang | Toward reformulating the diagnosis of schizophrenia[END_REF] Yet interest in this research also derives from the recognition of the limits of available psychopharmaceutical treatments on a wide share of symptoms. The head of the clinic where I was conducting my observations titled one of her projects: "Better descriptions for better treatments". Diagnosis research is in fact closely with research on new therapeutic strategies such as psychedelic drugs, various types of brain stimulation technologies or cognitive-based psychotherapeutic intervention.

While the prospect for a radical transformation of psychopathology might be far ahead, this research already begins to destabilize the ways clinicians and patients are used to understand and deal with psychopathological conditions. An aspect of these evolutions is the role in the diagnosis and treatment of schizophrenia of what sociologist David Armstrong called "distal symptoms", that is symptoms such as functioning, quality of life or even cognitive symptoms that are the revealed by questionnaires and scales [START_REF] Armstrong | Health-related quality of life and the transformation of symptoms[END_REF]. As I was told by a psychiatrist in the center where I was conducting my fieldwork: "We are working with a new symptomatology". This center is now known for treating schizophrenia with off label prescriptions of Methylphenidate, a drug normally used in attention deficit disorders. Standard treatment procedures for schizophrenia also include motivational group techniques and cognitive remediation that are used to help patients cope with their lack of concentration or difficulty with planning and organization.

Researchers seek to reach these objectives by generating large amounts of data that can be computed with new types of statistical analyses, such as machine learning or Bayesian techniques. The nature, the quality as well as the quantity of data are crucial to the process. The limited number of included subjects in most studies is compensated by the large numbers of data that can be generated for each single patient thanks to an accumulation of tests. It is not rare that recruited patients have to undergo week-long sessions of tests and interviews. On another hand the quality of the data also relies on the way researchers are disciplined to administer tests and report the results of their observations in the shared database. This involves an amount of tedious work to supervising the group, correcting the data, looking for missing data that is performed by the clinicians themselves or by a data manager.

Good data also means that patients have to satisfy to stringent inclusion criteria. As Steven Epstein forcefully demonstrated a politics of inclusion determines with whom and for whom biomedical research is conducted [START_REF] Epstein | Inclusion : the politics of difference in medical research[END_REF]. An aspect of this politics concerns the psychopathological conditions that are researched. This is why disease entities continue to play a key role in the organization of the research. In order to be able to demonstrate the presence teams need to recruit patients presenting neat psychopathological tableaus. This requirement contradicts the notion that psychiatric diagnoses lack validity: in many respect they are the unique valid ways of constituting samples. In order to overcome this contradiction, some publications are now arguing for the creation of samples of "unselected patients" that would not correspond to given tableaus. [START_REF] Uher | Genomics and the classification of mental illness: focus on broader categories[END_REF] Another tendency is to create transdiagnostic samples of patients on the basis of symptomatic criteria. The emergence of a series of entities such as attenuated psychosis that are defined by the mere presence of a series of symptoms is an aspect of this trend. This is only one aspect of the tensions that arise between the relentless logic of categorical thinking and the type of representations that is emerging from the research. These tensions are expressed in different ways. Locally, in research centers, an aspect is the gap between the way patients are evaluated for research and the clinical discussions they are stimulating. Robert Barrett's analysis of the construction of schizophrenia as a case situated at a distance from the patient might be useful here. [START_REF] Barrett | The Psychiatric Team and the Social Definition of Schizophrenia : an Anthropological Study of Person and Illness[END_REF] Another tension derives from the fact that most of the research is concentrated in European, North American and to a lesser extent East Asian institutions. Patients from southern countries are underrepresented in the research and while there is a growing awareness of the cultural dimensions of psychiatric disorders, including in the DSM5, this has had little impact on the way mental illness is approached within research.

All these tensions surfaced in the debates over the definition of schizophrenia in the DSM5. Interestingly enough, for the first time the work group in charge of the question included non American psychiatrists. Some of them are fierce advocates of a "Deconstruction" of psychosis that would lead to abandon the concept of schizophrenia. Much of these discussions focused on the introduction on forms of "dimensionality" in the structure of the DSM. However there are many ways to understand the idea: one might be to use "dimensions" to organize the description of psychopathological conditions; one might also reorganize the descriptions of psychopathological conditions in order to stress the "continuum" between these conditions or the "spectrum" they constitute. Both solutions may have immense consequence for the ways we conceive of psychiatric disorders and treat them. In a 2014 editorial announcing the intention of his journal to publish studies on the boundaries between schizophrenia and bipolar disorder, the editor of Schizophrenia Bulletin summarized his position as: "We intend to broaden the mission without damaging the brand." [START_REF] Carpenter | Porous Diagnostic Boundaries: A New Emphasis for the Bulletin[END_REF] As this quote hinted this is more than an issue of the valid basis for diagnosing people. The question is also that of the very image of the disorder in the wider public.

Conclusion

In this paper I have tried to offer a prismatic view on the changing status of schizophrenia over the last century. I have suggested that a focus on the changing clinical and research infrastructures might help shed a new light on these transformations. What is at stake in this story is the very sort of entity that schizophrenia has been through time: not only the symptoms, signs, criteria and more generally the wider clinical and social representations that defined it, but the inner and outer consistency of that category and its position in psychopathology at large. While schizophrenia represented in many ways the archetype of asylum pathology in the first half of the twentieth century, deinstitutionalization and the emergence and development of a research complex is now producing new definitions of the very sort of phenomena that once constituted the disorder.

There is much more to tell about the infrastructures of psychiatric diagnosis than I was able to do in this article. Rather than drawing a full picture I have attempted to heuristically delineate a framework that may be used for further research. At the same time I have also sought to highlight a series of discussions and debates that relate to the enduring difficulty of objectifying psychiatric diagnoses. While we need detailed studies of the very ways in which clinical work and psychiatric research have been done in various ways in a diversity of settings by different types of collective I hope to have outlined a first roadmap for these futures studies.

https://www.med.unc.edu/pgc, consulted 05/09/2018. Other figures are mentioned in other publications however, a variation that might be explained by the fact that participating to the consortium is a relatively informal process. See below.

See: http://www.eu-gei.eu/about-the-project, consulted 05/09/2018.


Hussein Sabra

The connectivity in resources for student-engineers: the case of resources for teaching sequences

Keywords: connectivity, resources in engineering education, mathematics for engineers, sequences

This paper concerns the teaching of mathematics for student-engineers. We focus on the theme of sequences in the first year of engineering education. We claim that teaching sequences in the first year of engineering education requires different kinds of connections: connecting different topic areas, different concepts, and different registers. We use here the concept of connectivity, to analyze resources in the case of an engineering school in France. We provide elements from interviews showing that the teachers can strengthen some forms of connections during their use of resources.

Context of the research

The present paper concerns the teaching of mathematics in the context of engineering. We present an analysis of resources collectively designed by teachers in a French Engineering School (undergraduate education). We address the issue of the connections made in mathematics for student-engineers. We focus on the theme "sequences".

The textbook is a crucial artifact for university teachers [START_REF] González-Martín | From resource to document: scaffolding content and organising student learning in teachers' documentation work on the teaching of series[END_REF]. However, the appropriateness of the content offered by textbooks in some academic paths remains a controversial issue; [START_REF] Randahl | Engineering students approaching the mathematics textbook as a potential learning tool -opportunities and constraints[END_REF] shows that student-engineers do not perceive the mathematics offered by the textbook as relevant for the engineering context. She considers that the issue of how the textbook is combined with the context of lectures and task solving sessions might "provide learning opportunities with meaningful use of the textbook" (Randahl, 2016, p.67).

Research literature highlights the gap between the mathematics taught in mathematics courses and the use of them in engineering courses [START_REF] Biehler | Conceptualizing and studying students' processes of solving typical problems in introductory engineering courses requiring mathematical competences[END_REF]. Minding this gap supposes to understand the reasons behind it. Research evidences also the necessity of making explicit connections between theory and practice to make the mathematical content in engineering education relevant to students [START_REF] Flegg | Students' perceptions of the relevance of mathematics in engineering[END_REF]. According to [START_REF] Gueudet | Making connections" in the mathematics courses for engineers: the example of online resources for trigonometry[END_REF], engineers in the workplace identify missing links in the mathematics taught during their studies: links between mathematics and the real world, and between different mathematical contents.

All these sources suggest that the teaching of mathematics in engineering education should propose specific "connections". The main question we address here is: what type of connections is present in the resources used and in teaching practices regarding mathematics for engineering students?

Connectivity in resources: topic areas, concepts and semiotic representations "Connections" can be related with (at least) three issues that could influence the teaching of mathematics; some of them are specific to the context of engineering education.

(1) Within mathematics, the networking between mathematical objects and their representations [START_REF] Hiebert | Learning and teaching with understanding[END_REF], identified as essential for the understanding of mathematical facts.

(2) The need to build links between mathematics courses and engineering courses.

(3) The modifications of learning processes in the digital era prompted [START_REF] Siemens | Connectivism: a learning theory for the digital age[END_REF] to introduce the concept of connectivism. He considers learning as an "actionable knowledge" that can reside outside ourselves. The learning in this case depends on the ability to build a network of connections between, and across, the available resources (or databases) and users of these resources.

Based on these works, we have proposed the concept of connectivity [START_REF] Gueudet | E-textbooks and connectivity: proposing an analytical framework[END_REF] developed in the frame of e-textbooks analysis. This connectivity has two components: "macro-level connectivity" that refers to the potential of linking to and between users and resources outside the textbook (practical aspect); and "micro-level connectivity", where the focus is on a particular mathematical topic within the e-textbook to look for connections in, between, and across individuals' cognitive/learning tasks and activities. We define therefore connectivity in a set of resources for teaching a mathematical theme as a linking potential for a given user (student or teacher) both practically as well as cognitively. We only use here micro-level connectivity. We indeed consider, in the case of sequences, the connections present in resources between different topic areas or mathematics fields, between different concepts, and between different semiotic representations.

For [START_REF] Duval | A cognitive analysis of problems of comprehension in a learning of mathematics[END_REF], semiotic representations are productions constituted by the use of signs belonging to the same "register" (natural language, formalism, algebraic formula, graph, figure, etc.). A register of semiotic representation allows the following activities: to represent a concept; to treat representations within the same register; to convert representations from a given register into another. According to [START_REF] Duval | A cognitive analysis of problems of comprehension in a learning of mathematics[END_REF], the conceptual acquisition of a mathematical object necessarily passes through the acquisition of one or several semiotic representations. However, the connection between different representations, seems absent in engineering programs. [START_REF] Quéré | French engineers' training and their mathematical needs in the workplace: interlinking tools and reasoning[END_REF] interviewed French engineers about their mathematical needs in the workplace. They declared that the teaching of mathematics they received during their studies "did not make enough connections" particularly connections between different mathematical contents and between different representations.

From the institutional point of view, the mathematics taught are shaped by the institution where they are taught [START_REF] Chevallard | Approche anthropologique du rapport au savoir et didactique des mathématiques[END_REF][START_REF] González-Martín | From resource to document: scaffolding content and organising student learning in teachers' documentation work on the teaching of series[END_REF]. We consider, as [START_REF] Quéré | French engineers' training and their mathematical needs in the workplace: interlinking tools and reasoning[END_REF], that in engineering education, mathematics courses constitute an institution different from engineering courses. Different institutions could shape the teaching of mathematical topics in different ways. Moreover, teachers' personal relationship with those topics, which results from their experiences in different institutions [START_REF] Chevallard | Approche anthropologique du rapport au savoir et didactique des mathématiques[END_REF][START_REF] González-Martín | From resource to document: scaffolding content and organising student learning in teachers' documentation work on the teaching of series[END_REF], could shape the mathematics taught. Indeed, the teaching actually implemented by a teacher using a given resource can offer more connections than this resource. Teachers might develop an "unexpected" connectivity in practice, by their discourse, examples produced "on-the-spot", and how they show proofs, etc. Here, there is the issue of the combination between potential connectivity and effective connectivity developed in use, which could be also related to the teacher's perception of students' needs and difficulties.

Our aim here is to consider the connectivity in the case of teaching sequences in the first-year in a French Engineering School. Therefore, we reformulate our general question as follow: Q1: Which connections concerning sequences appear in resources for a mathematical engineering course? Q2: Which is the effective connectivity of the curriculum implemented by different teachers using these resources?

Sequences in the French curriculum and in the engineering education

Our choice of to focus on sequences is related to its importance in some engineering paths. Within mathematics courses, sequences constitute an entry for other concepts (single and double integrals, series, etc.). They are also essential for studying Fourier series. In engineering courses, sequences are needed in a different way: in the study of some processes of discretization (transferring of continuous models into discrete models), in numerical analysis (numerical resolution of differential equations or heat equations, etc.), and in the "signal processing" course.

In France, the first encounter of students with sequences happens in grade 11. The curriculum recommends that the teaching of sequences in grade 11 goes through the modelling of real-life situations. Connections in terms of registers are recommended. For instance, the curriculum requests using the spreadsheet (numerical representation) or the calculator (algorithms) to compare the evolution of arithmetic and geometric sequences, as well as to represent the term of a sequence graphically. According to the curriculum, in grade 12 the concept of "limit of a sequence" should be studied in order to prepare the introduction of "limit of a function".

In different engineering education paths, the introduction of sequences usually appears in the calculus courses. [START_REF] Randahl | Engineering students approaching the mathematics textbook as a potential learning tool -opportunities and constraints[END_REF] notices that calculus is part of the basic mathematics courses for engineering students, and it has many formal aspects. Compared to the secondary level, more time is dedicated for mathematical reasoning and the use of formal representations. Research literature on the teaching and learning of sequences acknowledges the existence of strong links between both concepts "limit" and "sequences" [START_REF] Alcock | Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role[END_REF][START_REF] Roh | Students images and their understanding of definitions of the limit of a sequence[END_REF]. Regarding the concept of "convergence", studies highlight the importance of the graphical representation to make sense of it, as well as to facilitate the appropriation of its formal representation [START_REF] Alcock | Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role[END_REF].

Context of the study and methodology

The context of our study is a French Engineering School. It is one of the three technological universities in France. Mathematics teachers in this Engineering School have different statuses (teacher-researcher, full-time teacher, etc.) and various specialties (mathematicians, engineers, physicists, etc.). Four semesters structure the first and second academic years, where there are "basic science courses", including mathematics, physics and chemistry. There are four mathematics courses. Each of them followed in consecutive semesters. Sequences are introduced in the first chapter of the mathematics course of the second semester. In this context, our methodology consists in two parts: 1) collection and analysis of resources on sequences; 2) interviews with 3 teachers and their analysis.

The resources collected are collectively designed and used by teachers. They contain the textbook's lesson distributed to students; the slideshow projected during the lecture sessions; the tutorial that contains tasks to solve and problems; and the Practical Work tutorial (PW) composed of online exercises on a moodle platform.

To analyze the resources, in terms of micro-level connectivity, we used the grid developed by Gueudet et al. (2018). We adapted it to our case, according to the definition of connectivity we discussed above. We then analyzed the resources following four steps. In the first step, we identified concepts used in the resources, we mentioned the connected concepts and the way they are connected by definitions, propositions, theorems, examples, and/or exercises. Within this step, we studied the connections that concern "progression" chosen by the designers (connections with previous knowledge and further knowledge). In the second step, for each concept (or connected concepts), we characterized the different moments of their appropriation (lesson, examples, exercises, problem solving, or practical tasks); we considered also the context of this appropriation (different topic areas within mathematics, different disciplines, real-life situations, etc.). In the third step, for each concept (or connected concepts), we identified the registers of semiotic representation used or that can be used in solving tasks; we characterized them in terms of the three cognitive activities "to represent", "to treat", or "to convert" [START_REF] Duval | A cognitive analysis of problems of comprehension in a learning of mathematics[END_REF]. In this step, we determine, where appropriate, the connections made with particular tools (software, calculator, etc.). The fourth step concerns particularly the exercises; we determined the different strategies to solve them, and the variations of the same exercises. The fourth step allowed us to understand the connections that the designers emphasize between concepts, registers and mathematics topic areas.

We also conducted interviews with three teachers. We chose teachers with contrasting profiles in terms of their specialties and academic education, and in terms of their status. T1 is a physicist, he has a PhD in theoretical physics and modeling, he teaches mathematics, modeling and physics; T2 is an engineer, he has a PhD in Engineering, he teaches mathematics and engineering courses; T3 is a mathematics teacher, he has an "agrégation" in mathematics (French competitive examination that must be passed to teach at university). We hypothesize that the contrasted profiles can inform us on different forms of connectivity developed in implementation of mathematics resources.

The interview grid covers four axes, according to which we analyzed the teachers' declarations. The first concerns the connections to make across the different mathematics topic areas, across different disciplines, or with real-life problems. The second axis concerns the teachers' point of view on students' difficulties, which influences the connectivity they could emphasize in their use of resources. The third axis concerns the place of the examples they add, which allows to make connections between concepts or to use the registers of semiotic representation. The fourth axis concerns the place of mathematics proofs in engineering education, and their role in enhancing connectivity. We aim by the analysis of the interviews to identify elements on the effective connectivity of the curriculum implemented by different teachers using the same resources. Nevertheless, we are limited here to what teachers declare about the use of resources.

Potential connectivity in resources for teaching sequences

We identified in the resources for teaching sequences: 7 definitions, 10 theorems, 29 exercises, and 9 examples. The PW contains three exercises, where the use of Wiris CAS calculator is requested.

In terms of previous knowledge, some basic concepts from secondary school are reintroduced but in a formal register (convergence and limit of sequences). We note that continuity and limits of functions are taught in the first semester. We also note that the sequential definition of limits of functions is not taught. The order used to teach the concepts of "limit of sequences" and "limit of functions" is different from the choice made in the curriculum of secondary school (see above).

The connections between both concepts "limit of sequences" and "convergence" are emphasized. The resources also emphasize, in the properties and exercises, the connections between "convergence", "variation of sequences" and "bounded sequences". For instance, there is in the tutorial an exercise with nine different sequences; students are asked to study the convergence of sequences and calculate their limits when it is possible. The sequences given need different strategies to solve the proposed tasks (a sequence bounded by another one that tends to 0; a decreasing sequence and bounded from below by 0; a task that needs the use of properties about the quotient of convergent sequences; etc.). Recursive sequences are particularly emphasized in the different components of the resources. The exercises related to recursive sequences allow students to establish connections with "upper bound", "lower bound" and functions.

There is no connection between different topic areas within mathematics. In terms of different semiotic representations, the resources contain particularly one semiotic representation, the formal representation. In general, the treatment of tasks remains within the same representation. The resources contain rarely tasks where students are asked to represent mathematical objects in a given register. The PW constitutes an opportunity to make new connections between mathematics topic areas as well as between semiotic representations. Nevertheless, it is restricted to three exercises. The connections between semiotic representations are strengthened; there are, for example, tasks that need the graphical study of the given sequences. Besides, the algorithmic topic area changes to study the behavior of recursive sequences by dynamic representations (Figure 1). The use of Wiris CAS software offers the potential to make connections between algorithms and the graphical register.

In the analyzed resources, sequences constitute a theme where the mathematical materials are mainly limited to the calculus topic area. This is very similar to the content presented to mathematics majors. There are strong connections between concepts (convergence/divergence, limit of a sequence, function, upper/lower bound, recursive sequences). The tasks and activities propose mainly treatments within the formal register. In addition, there are no authentic situations, real life problems, or problems referring to other disciplines. All the examples, exercises and applications are intra-mathematical, which could strengthen a possible gap with the institution of engineering courses.

Analysis of interviews: towards effective connectivity in the enacted curriculum

Concerning the characteristics of a mathematics teaching well suited to engineering education, we identify three different trends in the answers of the interviewed teachers: T1 emphasizes the need for "contextualization"; T2 perceives his profile as interesting for teaching mathematics in engineering education; T3 perceives himself as a teacher who applies the mathematics as are "recognized in the university institution". T1 notices that teachers who are mathematicians have a reluctance to integrate problems referring to other disciplines. He supposes that they need some support in the design and the implementation of this kind of problems. T2 states he has "ability" to make connections between contents to ensure a continuum of learning between mathematics courses and engineering courses. He sees himself as a "specialist in mathematics for engineers". He says:

T2: Specialist of mathematics no, I am not a mathematician. Otherwise, am I a specialist in mathematics for engineers? I think I have a lot of experience to know how math tools are used in the workplace.

[Our translation]

He presents mathematics content as tools that have utility in the workplace of engineers:

T2: We try often to remind students that later on they will need mathematical tools and they have to build them. They have to be able to manipulate them properly. [Our translation]

T3 only considers the mathematics courses in terms of utility within mathematics.

In their answers about students' difficulties, the teachers referred to: 1) reasoning (T1, T2, T3); 2) treatment of tasks within the formal representation (T2, T3); 3) the capacity of abstraction (T1, T3).

It seems that the emphasis on formal representations in resources accentuates these difficulties.

According to their declarations in the interviews, the examples they add during the classroom sessions appear as revealing their will to support connectivity in different ways. Concerning proofs, all interviewed teachers stated that they do not do, in the classroom sessions, all the proofs given in the resources. The reasons they gave could be interpreted in terms of personal relationship with calculus [our translation]:

T1: the proofs I like are usually the useful proofs. I do not like for instance the "trapping" proofs for which if you do not have the right intuition, you cannot start.

T2: When you look at the theorem and the proof does not come to your mind right away, and you finally find out that the proof is based on tricks, I think this proof should be replaced by examples.

T3: If the proof requires little effort and seems important to me, I do it. I do not do it if I think we can understand the theorem without the proof, sometimes the proofs help to understand.

T1 and T2 show in class the proofs that can support the learning of a form of reasoning, which is, according to them, essential for future engineers. T3 shows the proofs that can help to understand theorems and properties, even if they sometimes require fastidious techniques. However, the interviews allowed us to identify criteria the teachers consider for choosing the proofs to do in the mathematics courses in engineering education: they can help improve the understanding of theorems; they allow highlighting the importance of a given theorem; they can help -during the proof -implement a mathematical reasoning. Each of these criteria could promote a specific form of connection between concepts.

The additional resources that the teachers design individually can strengthen specific connectivity in their teaching. T2, for instance, prepares examples to motivate the introduction of a given concept or to replace "tricky" proofs. T1 designs resources to show situations from other disciplines. T3 designs additional resources (exercises and examples) to strengthen links between mathematics concepts.

Discussion and conclusion

We present in this paper the issue of connectivity concerning a mathematics course in engineering education. We analyze the potential connectivity of resources, collectively designed, for teaching sequences theme. We highlight elements on effective connectivity that teachers, as users of these resources, could develop in their implementation.

The potential connectivity in resources for teaching sequences appears as restricted to the calculus topic area. The register of formal representation occupies an important space. According to two of the interviewed teachers (T1 and T2), making connections with engineering contexts, real-life problems or other disciplines "remains a dimension to enhance".

It appears by the interviews that the way the teachers use resources is likely to lead to an effective connectivity different from the potential connectivity, and this could be related to their personal relationship with the topic at stake. The teachers stated that students struggle with making sense of formal properties. Hence they attempt to support students by designing additional resources. They add examples and select separately the proofs to show in lectures sessions. These individual teachers' choices could strengthen some forms of connections. The physicist (T1) tries to enhance the connections in terms of other disciplines; the engineer (T2) constructs mathematical tools and tries to make connections with the engineering courses; the mathematics teacher (T3) tries to maintain connections within mathematics.

The analysis of the interviews draws our attention to the need to take into consideration the macrolevel connectivity (Gueudet et al. 2018), especially connectivity across disciplines, in terms of teachers' own resources, as well as in terms of teachers' and students' joint work. Besides, based on the analysis of the interviews, we highlight the necessity to observe how the teachers select and implement proofs in their sessions, which could tell us more about the effective connectivity built.

The issue of connectivity in resources and the connectivity developed by their use seems to be relevant in the context of engineering education, where the connectivity between theory and practice is crucial. Each of these elements requires further study with a larger sample of teachers, considering different mathematical topics and articulating the analysis of resources and classroom observations.

Figure 1 .

 1 Figure 1. It is required to act on the cursor "n" to relate the two dynamic representations (Wiris CAS).

  Each teacher, in his preparation of the course, designs his own examples. T1 says that the examples he designs should enhance the meaning of the concepts at stake. He presents examples referring to other disciplines. T2 says that he gives examples particularly during the introduction of concepts, "intra and extramathematical examples". According to T1 and T2, examples referring to other disciplines of real life situations are opportunities to make sense of the contents. T3 says that he gives examples after having stated a theorem. He uses examples to illustrate the "operability of the theorem".