Jerzy Kociatkiewicz

Monika Kostera
email: monika@kostera.pl

Grand plots of management bestsellers: Learning from narrative and thematic coherence

Keywords: grand plots, management discourse, narrativity, popular management textbooks, sensemaking

Barbara Czarniawska and Carl Rhodes have argued that managers and entrepreneurs o en learn from popular culture. e dominant plots off er the accepted interpretations and guide for actions, whereas alternative plots, available but not most prominent, provide schemes for possible departures from the common wisdom. In this article, we propose that not only works of ction serve this purpose; powerful ideas derive also from popular management books, not only in terms of explicit content but also as what we term, in homage to Lyotard, the grand plots: structures of meaning not usually seen as the overt message of this article. We present the results of our classi catory reading of popular management books, interpreting them in terms of the tacit notions of narrative development and cohesion, emplotted in the background. e contribution of this article is to show the ways in which the grand plots of popular management books are used to achieve coherence in presenting the books' total solutions for a variety of organizational problems and contexts. What their readers learn is not so much (or not just) how to manage but how to make narrative sense of management regarded as part of wider cultural context.

Introduction

Barbara Czarniawska and Carl Rhodes (2006) argue that managers and entrepreneurs o en use popular culture to guide their practice: the plots and images off ered by lms, books and media stories provide them with inspiration and sometimes with direct ideas that they use for everyday practice. e dominant plots, those which appear most o en or in the most prestigious sources off er the accepted interpretations and guide for actions, while alternative plots, available but not overwhelmingly popular, provide blueprints for possible departures from the common wisdom [START_REF] Czarniawska | New plots are badly needed in nance: Accounting for the nancial crisis of 2007-2010[END_REF]. In other words, popular culture can be regarded as a signi cant and not always consciously realized source for learning, including learning new and inspiring ideas about managing (e.g. Kociatkiewicz and Kostera, 2012;[START_REF] Panayiotou | Spacing gender, gendering space: A radical "strong plot[END_REF].

In this text, we propose that not only works of ction serve this purpose; popular management books also contain powerful ideas, expressed not only through explicit content, but also in the broader forms of expression: what we term, in homage to [START_REF] Lyotard | La condition postmoderne: Rapport sur le savoir[END_REF], the grand plots: structures of meaning not is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. usually seen as the main message of the text. ey are not intentionally hidden from the eyes of the reader, but serve as a background to the explicit argument and provide coherence and tone to the entire composition. Answering the call of Ann Cunliff e and Eugene Sadler-Smith (2014), we approach a strain of popular culture, relevant to management learning, in a critical and re exive manner. Critical, because we analyse and question what is o en taken for granted, in this case, that managers only learn from explicit plots and models. Re exive, because while doing so, we question our own approach to popular management literature as a fashion phenomenon, quite distinct from enlightened learning from research articles and books. is text proposes to use popular culture more consciously as a source for inspirational learning. Managers read popular books and they take in not only the models and knowledge they explicitly off er [START_REF] House | Change agents and systems thinking: e non-revolution in management rhetoric[END_REF], but also the plots and images that exist in the background. Standard management textbooks used in mainstream university level teaching o en provide only limited representations of managerial work, necessary to pass exams but failing to off er any guidance as to the context and generally present management in a disembodied way [START_REF] Knights | Management lives: Power and identity in work organizations[END_REF]. Popular books, o en bolstered by the authority of established management gurus [START_REF] Huczynski | Management gurus: What makes them and how to become one[END_REF], generously ll in this gap and may be a rich source of knowledge possible to be personalized and made experiential (e.g. [START_REF] Furusten | Popular management books: How they are made and what they mean for organisation[END_REF][START_REF] Collins | Narrating the management guru: In search of Tom Peters[END_REF]. Further on, we present the results of our classi catory reading of thirty-one hugely popular management books, driven by the attempt to identify not only the explicit knowledge (such as ideas about management, change, or power) presented in such texts, but also the tacit notions of narrative development and cohesion, important for the reader, and thus in uential in management practice, yet emplotted in the background and thus hidden from most common forms of management discourse analysis (e.g. [START_REF] Alvesson | Varieties of discourse: On the study of organizations through discourse analysis[END_REF][START_REF] Fairclough | Discourse analysis in organization studies: e case for critical realism[END_REF]. It is our contention that the grand plots present in management literature serve as an important source of inspirational learning, based on imagination, which makes it possible to make sense of and act in complex, shi ing environments [START_REF] Morgan | Imaginization: New mindsets for seeing, organizing and managing[END_REF]. Morgan proposes to use such methods as mind games or brainstorms to develop this kind of learning; our suggestion is to read management books, but look beyond their super cial narrative line, and towards the grand plots. Not tied to any speci c theme or idea, grand plots establish rules for the construction of appropriate, or admirable, plotlines. is text aims to analyse the ways in which the grand plots of popular management books are used to achieve coherence in presenting the books' invariably total solutions for organizational problems as adaptable to diff erent environments, contexts, and varied organizational dilemmas. Besides mapping the ways of establishing coherence, we also compare them to the textual strategies of more literary-oriented genres, and postulate the desirability of more conscious use of literary schemata which, even when not consciously invited, nd their way into management books.

us, this text's contribution is to introduce the idea of grand plots, and to analyse the forms they take in some of the most popular and in uential management books. is concept may enable critical management researchers to explore potential sources of sensemaking processes that enable learning from management fashions presented in popular books. Furthermore, it may help re ective authors, including academics who wish to reach practitioner audiences, to address their audiences in ways that inspire learning that leads to change in attitude and/or practice.

Organizations and sensemaking

Following Karl Weick, we think of organizations as persistent processes, bringing together "ongoing interdependent actions into sensible sequences i.e. generate sensible outcomes" (Weick 1979: 3). e results of organizing are cycles linked together as loops rather than chains of causes and eff ects. Organizing, and particularly managing involves active and continuous sensemaking: devising workable interpretations of ongoing activity and enacting them as real [START_REF] Weick | Sensemaking in organizations[END_REF]. Organizing is complex and non-linear, it embraces people and artifacts [START_REF] Law | Organizing modernity[END_REF]. John Law describes it as a mode of ordering: an emergent strategy in which no single actor determines the outcome. Organizations are a way of life, a mindset, or nets of collective action, undertaken in an eff ort to shape the world and human lives. e contents of the action are meanings and things (artifacts). One net of collective action is distinguishable from another by the kind of meanings and products socially attributed to an organization (Czarniawska, 1992, p. 32).

Sensemaking processes, managing included, depend on mobilizing available resources [START_REF] Callon | Techno-economic networks and irreversibility[END_REF], be they physical, economic, or textual. It is in providing is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342.

such resources that we see the strongest signi cance of management bestsellers: they can serve as both a source of readily available interpretations for understanding organizational realities and as rhetorical tools for changing them (inasmuch as these processes can be separated).

e narrative form of these books thus impacts not only their rhetorical eff ect on the reader, but also their applicability for constructing and changing concrete organizational settings, and for being adapted to re ect the experiences of other actors as well as the reader. In his book dedicated to the narrative features of organizations, Kaj [START_REF] Sköldberg | Administrationens poetiska logik: Stilar och stilförändringar i konsten att organisera[END_REF] re ects upon various organizational forms in terms of their poetic logic. Bureaucracy, human network, system and culture are presented as manifestations of poetic logic based on the enactment of respectively, tragedy, romance, comedy and satire. ese dramas are each directed by a leading trope: metonymy, metaphor, synecdoche and irony. e book provides a rhetorical analysis of business administration ideas and the main styles of organizing.

e aims, and in particular the eff ectiveness seen as the ultimate goal of organizing are also depicted as features of the narrative genre. Each style of organizing has its own dominating ideal of eff ectiveness: eff ectiveness of input, personality, the system and the mission. Managers' day-to-day practices involve using extant sensemaking narratives (largely following the fundamental types delineated above), and rely on readily available accounts of ideal managerial activity, lending themselves to conceptual conservatism and the tyranny of the one best way. And yet, as Stewart [START_REF] Clegg | For management? Management Learning[END_REF] show, management has a potential to learn to develop away from tyranny and towards polyphony, via active translation from one or several sources. We propose that popular management books have the potential of serving as sources of managerial polyphony, but in order to examine that potential, we need to rst consider the very idea of a (popular) management, or organizational narrative.

Narratives in organization studies

Narratives have gained much interest as method and substance of research in social sciences [START_REF] Czarniawska | Narratives in social science research[END_REF], and in our own eld of organization studies [START_REF] Boje | Narrative methods for organizational and communication research[END_REF], studied as a way of experiencing social reality as well as of communicating, teaching, and learning these experiences. Kenneth [START_REF] Gergen | Realities and relationships: Soundings in social construction[END_REF], using a very broad de nition of the narrative as any temporal embedding, argues that experience invariably takes narrative form. Every event is conceptualized in some relation to the past and the future, and thus narrativized. is describes not only everyday perception but also the more "advanced" perception of scienti c research [START_REF] Bruner | e narrative construction of reality[END_REF]. Other researchers, like Yiannis [START_REF] Gabriel | Storytelling in organizations: Facts, ctions, and fantasies[END_REF], prefer to use the term narrative much more narrowly, as needing a clearly delineated plot. Seen this way, narrativity becomes only one of the possible forms of expressing experience; painting, music, and even some forms of writing, such as straight description, or a chronicle [START_REF] White | e value of narrativity in the representation of reality[END_REF], are seen as non-narrative. In a similar vein, David [START_REF] Boje | Narrative methods for organizational and communication research[END_REF] sees narratives as a form of processed, accommodated experience, while discerning some similar structures in what he terms the antenarratives-fragmentary and disjointed accounts of the lived experience which, although they lack formal structure and fail to cohere into continuous stories nevertheless contain an expressive mixture of events, reactions, and feelings that clings close to the perceived, and felt, social reality. e de nitional confusion is heightened by the debate on the narrative's ontological anchoring, much as in the case of the discussion on the existence of outside reality. Some scholars, like David [START_REF] Carr | Time, narrative, and history[END_REF] see in it the deep structure of the only reality humans have access to, others, like Hayden [START_REF] White | Metahistory: e historical imagination in nineteenth-century Europe[END_REF], view it as an arbitrary (but ingrained in our culture) way of making comprehensible the chaotic jumble of events. Our aim, however, is not to try and resolve this dilemma, but rather to examine some of the variety in narrative forms used to communicate management ideas. Studies in literary theory and linguistics have proposed large number of classi catory schemes for analysing narratives, be they Vladimir [START_REF] Propp | Morphology of the folk tale[END_REF] formalist dissection of folk tales, Greimas'(1983) attempts at identifying basic components of any discourse and Kenneth [START_REF] Burke | A grammar of motives[END_REF] dramatistic pentad. While originally intended for the study of literature and paraliterature, all of these schemes have found use in examining other forms of discourse, including that of social science and management, from discussing language used in organizations [START_REF] Rhodes | Writing organization: (Re) presentation and control in narratives at work[END_REF][START_REF] Tietze | Understanding organizations through language[END_REF] to classifying academic texts [START_REF] Monin | Re-navigating management theory: Steering by the star of Mary Follet[END_REF]Styhre, 2005). In regards to the latter issue, Barbara Czarniawska (1999) proposed examining diff erent kinds of academic writing as genres, and raised the possibility of fruitful is copy does not follow journal layout or pagination. Originally published in 2016 in Management comparisons between academic and literary genres. Using a de nition of genre as "a system of action which has become institutionalized and is recognizable by repetition" (p. 15), she speci cally points out parallels between organization theory and detective ction, including realist style, focus on problem-solving, and concern with social context. She also retroactively labelled [START_REF] Burrell | Sociological paradigms and organizational analysis[END_REF] model of sociological paradigms in organization theory as an exercise in genre analysis, which seems to take an overly broad understanding of the notion of genre: Burrell and Morgan's study deals mostly with authorial stances rather than with writings themselves. We understand genres as types of utterances, or texts, and thus, in as much as our own analysis concerns genres, we subscribe to Tzvetan Todorov's description of a genre as "a codi cation of discursive properties " (1990, p. 18). At the same time, we are not interested in genres as deployed in the original context of their de nition. Jerzy Kociatkiewicz and Monika Kostera (1999) looked at the possibility of translation between ction writing and academic texts, pointing out the leeway present even in the relatively strongly codi ed form of a journal article, and arguing that the long history of experimentation and innovation in storytelling can be mobilized to enrich the o en incredibly boring academic writing.

is article also concerns generic translation, but directed at diff erent texts. Management bestsellers, produced at the edge of the academia are o en written by academics but addressed primarily to non-academic readers: managers or wouldbe managers. In attempting to draw and hold the readers' attention, these texts employ a wide variety of textual strategies, and our aim is to establish generic characteristics of a range of these books, show the correspondences between the narratives presented therein and established genres of ction-writing and, in particular, to investigate the variant ways in which these texts maintain coherence despite covering a varied range of topics.

Learning new ideas

e discussion of whether management ideas are being propagated by diff usion or translation is vibrant and ongoing (see e.g. [START_REF] Van Veen | Diff usion, translation and the neglected role of managers in the fashion setting process: e case of MANS[END_REF]Örtenblad et al., 2011;[START_REF] Clegg | For management? Management Learning[END_REF]. In this text, we follow the tradition of Bruno [START_REF] Latour | e powers of association[END_REF], according to which cultural notions travel and gain acceptance by means of translation, that is through recontextualization requiring active engagement of the social actors involved. e process of translation is complex, and the outcome (that is, the translated ideas and their reach) is never fully predictable [START_REF] Latour | Messenger talks[END_REF], but rather a "result of a blend of intentions, random events and institutional norms, all processed in a collective apparatus of sense-making" (Czarniawska and Sevón, 1996, p. 11). It involves deterritorializing an idea, or removing it from its network of contexts [START_REF] Deleuze | Nomadology: e war machine[END_REF], transporting or transposing it and, nally, reterritorializing it in a diff erent setting. e idea is not material, even though at any given time it is expressed through concrete, almost physical attributes, by the use of verbal, visual, or material symbols. ese symbols make it ready to be put into action through the reterritorializationin relation to a new web of meanings, and the whole process involves intense and continuous sensemaking.

As we have argued above, an important channel of propagation of management ideas involves popular management literature, and we would like now to turn to the authors who have studied the processes involved. Staff an [START_REF] Furusten | Popular management books: How they are made and what they mean for organisation[END_REF] shows how management fashions, presented in the most popular of management bestsellers are translated from scholarly studies to management practice. He nds that the authors of popular books propose models only partially based on contributions from scholarly studies, models which at the same time form rather crude simpli cations of real conditions and problems. While not providing ready-made solutions to practical problems, these ideas are attractive to practitioners because they serve the role of fashion icons, linked with virtues, ideologies, notions and standards. Furusten describes these ideas as providing sets of managerial lifestyles, complete and ready for use. Andrzej [START_REF] Huczynski | Management gurus: What makes them and how to become one[END_REF] likewise envisions management learning as a propagation of fashions and styles, rather than just knowledge, through the pronouncements made by management gurus, such as the famous consultants respected by business practitioners.

ese statements are accepted as an attractive source of learning because they off er a sense of personal and professional worth at the same time as they provide the readers with ready looking "recipes" for success. In a chaotic world, they off er a sense of control and predictability or, in the terms we have used in this text, tools for managerial sensemaking. Finally, the is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. gurus are skilled in using such cultural expressions that resonate well with the values and expectations of their audiences. [START_REF] Furusten | e managerial discourse: A study of the creation and diff usion of popular management knowledge[END_REF] off ers an explanation to one of the sources of this resonance. Popular management books are o en based on the narrative structure of the heroic myth, thus connecting their teachings with a profound symbolism which may be very attractive to readers aiming at tasks which have to do with control of uncertainty and making sense in an increasingly complex world, and such is the current context in which managers operate.

is is why archetypical images are so intensely appealing nowadays, even though the humanities have been all but erased from modern management curricula [START_REF] Kostera | Organizations and archetypes[END_REF]. David [START_REF] Collins | Narrating the management guru: In search of Tom Peters[END_REF] provides an in-depth analysis of the writings and public speeches of Tom Peters, whom he considers to be one of the most prominent management gurus of all times. e enormous popularity of his ideas is due to his talent as storyteller. Indeed, Tom Peters has changed the vocabulary of management, providing practitioners with symbols and expressions that not only off er them a fashionable language, but inspire them to trying out new endeavours through an ability to provoke new thoughts. Peters has in uenced the way we think and talk about work, as well as how we manage others and ourselves; indeed, we now have "a new way of speaking about management which insists that managing is, not so much a job as, an heroic way of life" (Collins, 2007, p. 8).

e problem of how the ideas are deterritorialiazed and reterritorialized has been much discussed in social science and management literature. e narrative has been pointed to as a particularly powerful sensemaking device used in organizations [START_REF] Weick | Sensemaking in organizations[END_REF]. Speci cally in our area of interest, Isabelle Corbett-Etchevers and Eléonore Mounoud (2011) presented a narrative framework for conceptualizing how management ideas are reterritorialized. Plots are adopted and used for their distribution, from abstract concepts to individual and organizational experience. Eff ective emplotments are interactive, they occur at many levels simultaneously, continuous and manifold. is texts aims to show some of the possible ideas used in emplotment processes of the kind depicted by [START_REF] Corbett-Etchevers | A narrative framework for management ideas: Disclosing the plots of knowledge management in a multinational company[END_REF], that is, some sources for translatable ideas that managers have been using in their everyday sensemaking related to several central notions of modern management. Ann Cunliff e and Chris Coupland (2011) address the issue of reterritorialization by embodied narrative sensemaking. e authors conclude that managers take into account other voices to acquire legitimacy and narrative coherence. is is a temporal and iterative process, occurring in everyday interactions, which are always embodied and experienced, not just realized in formal decision making moments.

Managers, decision-makers and leaders therefore need to understand that we make sense in every¬day ordinary interactions as well as formal forums because we continually feel, make judgments and evaluations and try to construct some sort of narrative rationality (ibid., p. 8).

Embodiment is part and parcel of this narrative rationality, utilized to translate ideas into a new context by sensemaking, which we address in the next section.

e contribution of this text builds on the research cited above, as we propose an additional important vector of propagation of signi cant management ideas and experiences: grand plots, or the background structures of coherence we identify in the bestselling management books we analyse. Unlike structuralists [START_REF] Greimas | Structural semantics: An attempt at a method[END_REF][START_REF] Lévi-Strauss | La Pensée sauvage[END_REF], we do not assume grand plots or any other narrative structures off er primary meanings that override other conceptual considerations. We do, however, believe both the obvious and the obscure facets of the story can matter, if they off er compelling interpretive tools for the reader to use [START_REF] Iser | Prospecting: From reader response to literary anthropology[END_REF]. Moreover, as our study demonstrates, the grand plots of management literature are shared with literary genres of much older provenience, and thus our familiarity with, and established scholarship on such genres can help in understanding the rhetorical values of popular management texts.

Methodology

In this article, we present an analysis of the discourse of popular management, as instanced in some of the bestselling books of the genre. In selecting the empirical material for this study, our goal was to establish a suffi cient corpus of in uential management texts spanning the history of popular business literature to render our investigation worthwhile. We did not attempt to survey the entire eld of popular management literature, nor to arrive at a representative sample of this eld: such an endeavour would certainly lie beyond the scope of this study, and we are doubtful whether increasing the studied volume would position us better to examine the mechanism of coherence at work. is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342.

In the rst stage, we collected from twenty-four MBA students, eight non-student management practitioners, and twelve academics involved in executive education and working in Poland, Sweden, and United Kingdom, lists of three to ten popular management books they deemed the most important or in uential. Out of these nominations we selected thirty-one books mentioned most.

e selection method does not attempt to provide any de nitive list, but ensures that the books we study are all in uential texts, widely read (or at least widely bought) by aspiring and practicing managers. While not all of the books we have chosen for analysis remain as in uential as they initially were, even the oldest titles, Frederick Taylor's (1911) e Principles of Scienti c Management and Dale Carnegie's (1936) How to Win Friends and In uence People are still commonly used to interpret and evaluate existing organizations, to plan changes, and to justify sweeping managerial decisions. Nineteen-eighties are by far the most prominently represented decade, with thirteen publications, and the newest book on the list is Sheryl Sandberg's Lean in, published in 2013. While the list is certainly biased by the selection process, we are con dent that all the analysed books constitute signi cant tools in the repertoire of organizational sensemaking [START_REF] Weick | Sensemaking in organizations[END_REF]; we see this as a suffi cient criterion for conducting our analysis.

is approach follows an established tradition of in interpretive social science studies to focus on what is considered useful (and/or beautiful) by the actors in the eld [START_REF]Narration or science? Collapsing the division in organization studies[END_REF].

e methodological approach we use in the study comes from the broad tradition of discourse analysis: we aim to examine processes by which management texts are made meaningful through careful and structured analysis of these texts (Philips and Hardy, 2002). More speci cally, we employ the techniques of distant readings [START_REF] Czarniawska | Distant readings: Anthropology of organizations through novels[END_REF], reading the studied material semiotically, with the intent purpose of deciphering the connections between various plot and theme elements in the text. We proceeded by reading (in most cases, re-reading) each of the selected books, paying attention to how background features of the texts turn into (grand) plots, or overarching narratives of the books , and to the ways in which disparate themes and sections are connected: the sources of coherence in management books. In this, we were guided by Roman [START_REF] Ingarden | O dziele literackim: Badania z pogranicza antologii, teorii języka i lozo i[END_REF] model of phenomenological text analysis, according to which a text should be read on several levels in order to uncover the diff erent layers of meanings and symbols.

e result was a series of short, reductive summaries of the analysed books and a list of categories, or keywords representing our understanding of the structural features of the texts. In comparing these, we have found that we relatively quickly reached data saturation, having established four major genres of grand plots which form the basis of our discussion in the next section. We decided that the best way to describe these grand plots, which we found diffi cult to delineate, is by showing analogies with established genres of ction. While we maintain that the analogies between the analysed management books and representatives of ction genres are structural and present on a number of possible levels of interpretation, the necessary brevity of this text has forced us to sum up these similarities in brief summaries and comparison of pithy quotes from both kinds of works. We hope our Readers will be willing to look beyond the metonymy of the presentation. Because our analysis yielded four distinct categories of grand plots, and in order to be able to present some context to our reading, we selected just four books out of the thirty-one bestsellers (listed in their own section of the bibliography) used to reach our ndings. ese serve as exemplars of grand plots of the management genre in the subsequent section.

e subsequent section off ers the discussion of our second level of analysis, focusing on the diff erent ways in which management bestsellers achieve coherence. In it, we examine two important sources of coherence: narrative and thematic unity, and show how they are instantiated in the grand plots of popular management literature.

Grand plots of management bestsellers

James Kouzes and Barry Posner's (1995) e Leadership Challenge is the most tightly focused of the management books we have analysed, being centred squarely on describing its protagonist, the leader. e book's own recapitulation de nes its theme as "about how leaders get extraordinary things done in organizations" (p xvii). rough the text, these extraordinary things are le relatively vague, though they seem to entail getting subordinates working hard to realize goals set by the leader. A few of the examples provided give more speci c descriptions of the successes such as creating a voluntary is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. organization of 100000 members or drastically reducing the cost of production.

ough most of the cases described come from business organizations, the word pro t does not appear in the book (at least, we haven't been able to nd it and it does not feature in the index). Non-pro t organizations are discussed (and feature in the index), if not at length. In terms of its narrative structure, the book starts with an apocalyptic vision of the current, fallen society where the cynics are winning. People are fed up. ey're angry, disgusted, and pessimistic about their future. Alienation is higher than it's been in a quartercentury (p. xvii-xviii).

Such society is clearly in need of a messianic gure, or at least of strong moral leadership, and thankfully the leader is there to provide it. Most of the book is devoted to delineating the positive qualities of the leader, and it ends with strong praise for the protagonist, envisioned as a Moses-like gure leading the people out of the wilderness:

We've said that leaders take us to places we've never been before. But there are no freeways to the future, no paved highways to unknown, unexplored destinations. ere's only wilderness. To step out into the unknown, begin with the exploration of the inner territory. With that as a base, we can then discover and unleash the leader within us all (p. 340). e tight focus, and the way in which reported cases are always but illustrations of the leader's transformative powers, means the book can be understood to follow that most rigid benchmark of internal coherence, the rule of three unities which came to dominate neoclassical drama of the seventeenth and eighteenth centuries. First formulated in Lodovico Castelvetro's Poetica d' Aristotele Vulgarizzata et Sposta from 1570 (Spingam, 2011), though derived from Aristotle's comments in Poetics, the three unities postulate that a drama should concern a single consistent story (unity of action), take place in one setting (unity of place) and in a continuous span of time (unity of time). Signi cantly, while Aristotle prescribed the unity of action, he only noted the unity of time (as a prevalent characteristic of tragedies) and did not address the unity of place. e notion of the three unities became popular throughout the sixteenth and seventeenth century, and is particularly prevalent in the plays of the French authors of the era (as well as present in Shakespeare's e Tempest and e Comedy of Errors). In our reading, e Leadership Challenge clearly adheres to the three unities. e leader's transformation of the organization provides the unity of action (all of the other characters' described activities are either instantiations of said change or are noted to illuminate the leader's transformative powers). e reference frame of the end times and of the possibility of salvation through leadership ful ls the requirement of the unity of time, and though short reminiscences from other successful leadership process enrich the book with additional background, they do not appear to shi the action to their settings. e unity of place is somewhat more diffi cult to determine, as there is very little concrete scenery described. Leader's actions take place in relation to their constituents and customers. Some of the reminiscences contain details on their settings, but are always interspersed by generalized statements about the leader (sometimes referred to in the plural) and his or her relationship with non-speci c other actors (occasionally divided into constituents and customers).

One more resemblance with neoclassical drama bears further comment, though it does not concern the narrative structure as such: the leader's apparent and highly lauded morality reminds us much more of Molière's Tartuff e, that paragon of hypocrisy, than of any religious gure. us, a section entitled e Secret of Success Is Lo e is illustrated by statements from two diff erent army generals (though the military does not otherwise gure much in the book), and includes the following excerpt:

Vince Lombardi, the unforgettable coach of the Green Bay Packers, believed in love. In a speech before the American Management Association, he made these remarks: 'Mental toughness is humility, simplicity, Spartanism. And one other, love. I don't necessarily have to like my associates, but as a person I must love them. Love is loyalty. Love is teamwork. Love respects the dignity of the individual. Heartpower is the strength of your corporation.' Retired General H. Norman Schwarzkopf emphasizes love as well. When Barbara Walters asked him, during a TV interview, how he would like to be remembered, he replied, ' at he loved his family. at he loved his troops. And that they loved him' (p. 305).

e Spartan ideal of love among soldiers (homosexual relationships within Spartan regiments were strongly encouraged in the belief that they would engender stronger ties and loyalty on the battle eld) bene ts, of course, from over two thousand years of history, but it is rare to nd Spartan society lauded for its moral composition (even if just because most descriptions of such come from the largely antagonistic Athenians). And just as love is explained through its relation to war, is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. so the leader's commitment to trust is framed only as the necessity for subordinates to trust the leader, and the leader's desire for constant learning is described only in terms of looking for external sources of expertise and knowledge. e possibility of knowledge bene cial for the leader to learn existing within the organization is not even raised. Peter Senge's (1993) e Fi h Discipline is a much more sprawling book than e Leadership Challenge. It features a collective protagonist serving as the active narrator (addressed in rst person plural), but also numerous other characters including humans and named business organizations. Various topics, characters, and associated narratives are woven through the book-they appear early on, then disappear for a hundred or more pages, only to reappear again for further insight and perhaps a resolution. e complex story of a Beer Game forms the central topic of chapter 3 (p. 27-54), then vanishes from the book (with a single mention on page 89) only to reemerge around page 390 to inform the argument. DC-3, introduced on p. 5, is mentioned only in passing three times over the next three hundred pages, but resumes central position and makes a signi cant contribution to the plot on pages 342-343. At the same time, the story never feels disjointed: while there is no obvious single thread connecting all the varied scenes and characters of the book, there are usually clear links between each scene, its predecessor and its follow-up. Consecutive chapters introduce more abrupt shi s in setting and plot, jumping from the limitations of linear thinking to the movie Spartacus or from the horror of self-re ection to the hunting for snakes under a carpet. Nevertheless, threads from previous chapters are picked up in later exposition, and the book clearly tells a single, though convoluted, story. In this regard, it resembles a realist novel with its convoluted plot and large ensemble of characters who disappear and reappear in the story. While the paragon of the genre seem to be the nineteenth century novels of the writers such as Dickens, Dumas, or Hugo, e Fi h Discipline bears the closest resemblance to much more recent writings. e plot structure, charting the protagonists' complex encounters with organizations and organizational actors, leads not just to the inevitable (largely) happy conclusion, but to the transformative apotheosis so o en found in the twentieth century science ction novels of Arthur C. Clarke. Childhood's End [START_REF] Clarke | Childhood's end[END_REF], written very much in the form of a realist novel, charts the vicissitudes of human encounter with the wider galactic community culminating in the human species' pseudoevolutionary transformation into new form existence beyond the con nes of planetbound biology. Similarly, 2001: A Space Odyssey shows the almost supernatural transformation of human beings by the encounter with an alien artifact. e concluding sentence of e Fi h Discipline could have served just as well as an epigram to either of these books:

Something new is happening. And it has to do with it all-the whole (Senge, 1993: 371).

W. Chan Kim and Renée Mabourgne's (2005) Blue

Ocean Strategy is even wider in its thematic scope. e book contains a multitude of business success stories, each following an almost invariant pattern: description of a novel market off ering sharply diff erent from all the competing products complemented by a glowing review of its success. While purporting to illustrate various aspects of planning a winning strategic move (the titular blue ocean strategy), most of these vignettes could be switched around without detracting from the coherence of the book in any noticeable way. Even the central concepts, blue ocean and value innovation, have an inconstant presence as the reader keeps being distracted (or entertained) by one success story a er another.

e authors it between rst person plural, second and third person narration throughout the text, allowing for a clear understanding of who the model authors and the model readers are (to use Umberto Eco's notion of the author and the reader as documented in the text).

e authors present themselves primarily as academics at the end of a large research project, characterized by their vast expertise. us, the possessive pronoun "our" appears quite commonly, but is usually only applied to research and study, with a single pairing each with assessment, discussion, interviews, and experience (as well as a single mention of "our networked society" and of "our managerial expression of procedural justice theory"). In contrast, the reader stands out as a more complex, and better de ned gure, a manager at the helm of a company (possessive pairings such as "your company, " "your industry, " "your product, " and "your strategic planning process" abound), whose possessions can include aconsigliere-a highly respected insider-in your top management team, or only a CFO and other functional head heads (ibid.: 168).

But descriptions of innovative products also reveal a more human side to the model reader. Most products, such as cheap wine, books, circus performances or is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. insulin pumps are described in terms of their appeal to the customer. But time-shared private jets and smartphones are presented as off ering their value directly to the reader. Interestingly, the reader also appears to be female, as she shows interest in the off er of female-only gyms, but none in a new line of barbershops. Overall, the book reminds us of a traveloguechronicling the authors' tour of what they themselves describe as blue oceans, full of strange and exotic businesses whose activities range from selling cement in Mexico to information systems for New York Stock Exchange traders. While the authors make some attempt to link these into a single story, the connections remain tenuous. ere is signi cant repetition in terms of the sights viewed: a er some time, all the innovative products that rede ned their industry begin to look alike. ere is also a clear degree of choice in terms of business stories recounted, much as most travel diaries focus on the traveler's interests, be it natural beauty, local cultures, or feats of architecture.

e oldest of our chosen exemplars, omas Peters and Robert Waterman's (1982) In Search of Excellence, stands out from the others through the emotional weight of its contents. e managers described therein (and the protagonists are clearly identi ed as managers) are full of passion that manifests itself in unexpected and even violent ways. One executive furiously asserts the highest quality of his brand of toilet paper, another endures three years of obsessing about building better skis. An entire organization is "fanatic about service" (p. 159), and another "fanatical about cleanliness" (p . 173). Yet another zealously pursues the building of a better product. Words like faith, transcendence, obsession, zeal, and fanatic appear over and over again. It is not surprising that Peters' next book [START_REF] Peters | A passion for excellence: e leadership diff erence[END_REF] was entitled A Passion for Excellence. Paradoxically, because of the strong emphasis on (equally strong) emotions and commitment, the companies and managers featuring in the book tend to blur together-they are driven by the same passions, and it is the strength, rather than the direction, of these passions that lies at the heart of Peters and Waterman's argument. In keeping with the religious imagery of faith and zeal, the main theme of the book is framed as a quest for an ever retreating goal, even as many of the presented companies are described as already excellent. e managers, and the more engaged workers, are shown as continually looking for the possibility of improving their product and their company. ere is also no clear plot holding the story together, as the book focuses on attitudes rather than on actions (though, of course, some actions are described-they just do not cohere into a single narrative structure as actions of one manager in one excellent company neither relate to nor re ect the actions of another). In terms of parallels from literature, In Search of Excellence most resembles a hagiography collection-a book of saints' lives such as the late medieval Golden Legend (Legenda Aurea) by Jacobus de Voragine. Full of marvelous stories and upli ing moral message, the Golden Legend presents a hodgepodge of accounts held together by sanctity of the subjects and the strength of their faith rather than by any other common theme or narrative pattern. us, the reactions of St. Anthony on nding misplaced silver A er this, as St. Anthony went in desert he found a platter of silver in his way; then he thought whence this platter should come, seeing it was in no way for any man to pass, and also if it had fallen from any man he should have heard it sound in the falling. en said he well that the devil had laid it there for to tempt him, and said: Ha! devil, thou weenest to tempt me and deceive me, but it shall not be in thy power. en the platter vanished away as a little smoke. And in likewise it happed him of a mass of gold that he found in this way, which the devil had cast for to deceive him, which he took and cast it into the re and anon it vanished away (de Voragine, 2012, n.p.).

are not far removed from the actions of Forrest Mars, the chief executive of Mars food empire when confronted with mispackaged candy:

He is given to ts of unbridled rage, such as the time he discovered an improperly wrapped batch of candy bars and hurled the entire inventory, one by one, at a glass panel in a boardroom while frightened aides looked on (Peters & Waterman, 1982, p. 181).

We have shown how the grand plots in popular management books carry plotlines that are much heavier than the medium of popular literature seems to be. However, as [START_REF] Czarniawska | Strong plots: e relationship between popular culture and management theory and practice[END_REF] point out, popular culture perpetuates strong plots from mythologies and other monumental cultural sources. Emplotment of the disparate ideas makes them more than titbits of fashionable knowledge: they hold a content that brings a sensitivity to a whole range of related contexts [START_REF] White | e content of the form[END_REF].

Sources of coherence

In this section we read the analysed books on a second is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342.

level [START_REF] Ingarden | O dziele literackim: Badania z pogranicza antologii, teorii języka i lozo i[END_REF], concerning the ways in which the texts achieve coherence.

Our aim here is to examine the interplay of narrative and thematic coherence in constituting diff erent genres of organizing, the authorial role of diff erent organizational actors, and the temporal organization of the resulting stories. To that aim, we set out by outlining the features of each scheme of coherence and their possible combinations, providing exemplars from the literary tradition that, in turn, can serve as metaphors for the diff erent genres of organizing.

Without even attempting to resolve the dilemma of ontological grounding of narratives (we do not believe any nal resolution to the latter dilemma is possible), we can largely circumvent the general problem of the structuring of experience by assuming narrativity as an important, but not the sole, source of coherence found in experiences and stories-understood, a er Yiannis Gabriel, as "narratives with simple but resonant plots and characters, involving narrative skills, entailing risk, and aiming to entertain, persuade and win over [the listeners]" (2000: 22). is is re ected in the analysed books where, for example, e Fi h Discipline followed a clearly discernible storyline while In Search of Excellence did not. Following Karl [START_REF] Weick | Sensemaking in organizations[END_REF] we call this source of consistency the narrative coherence. Linguistic research uses the related notions of subject, topic, and theme to denote forms of indicating the referent in a particular utterance or discourse. Subject and topic are usually understood as grammatical categories denoting the direct referent and the context and meaning of an utterance respectively. eme, the least o en used category (and yet the most relevant for the present text), organizes meaning of a larger chunk of discourse (Ochs [START_REF] Keenan | Topic as a discourse notion: A study of topic in the conversations of children and adults[END_REF]. It can be explicitly invoked right at the outset, or it can emerge as a common ground for diff erent contributions to the discourse. eme can thus be understood as the atemporal and non-causal linkage between various ideas that enables them to be interpreted as forming a coherent entity. We call this structuring the thematic coherence.

ematic and narrative coherence coexist within any given discourse, although their importance can vary wildly from genre to genre, and also between diff erent manifestations of any given genre. Nevertheless, a common pattern can be discerned, and the interplay between diff erent kinds of coherence can be analysed to gain a clearer understanding of a particular grand plot.

We can thus establish four basic grand plots named a er the literary genres we used as analogies, and distinguished based on the consistency of plot (narrative coherence) and theme (thematic coherence): Classical drama, novel, travelogue, and hagiography.

Low Narrative Coherence

High Narrative Coherence

High ematic Coherence

Hagiography

Classical Drama

Low ematic Coherence

Travelogue Novel

Tab. 1. Literary coherence

We do not claim that narrative and thematic coherence are the only available ways of creating and maintaining rhetorical cohesion, be it within discourse of literature or of organization. One other very obvious feature which does not inform our current analysis is formal coherence: the rules and constraints on permissible discourse within a given context. us, a sonnet is circumscribed by the rhythm and structure of its verses. At the same time, the proposed scheme gives us enough information to allow us to comment on the scope and adaptability of each of the examined books. Of the four literary genres we invoke, classical drama, circumscribed by the three unities presents the highest possible levels of both narrative and thematic coherence.

is is the work focused on exploring one particular issue and its manifestation in a concrete setting: Molière's Tartuff e is thus an exploration of hypocrisy, but set rmly within the high bourgeois milieu of Ancien Régime France. While the play continues to be performed to this day, many productions involve signi cant rewriting to update and adapt the work to suit the tastes and the understanding of modern audiences. Similarly, e Leadership Challenge is circumscribed not only by its subject matter, but also by the hierarchical corporate governance structure implicitly assumed as the context of leadership (and despite drawing in quotes and illustrations from sport teams and the army). Any attempt to transpose this message to a diff erent setting would require signi cant adaptation.

e coherence of the novel comes from its narrative structure: its plot cannot be ignored and reading the chapters out of sequence is likely to confuse the reader (in contrast, Peters and Waterman speci cally guide the is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342. reader in the introduction in regards to which chapters can be safely omitted). A book such as Childhood's End spans many diff erent settings, and cannot be considered a thorough exploration of any of them. In the same vein, e Fi h Discipline also tells an engaging story, but a very convoluted one. Even the titular h discipline, one of the ve areas of competence for building a successful learning organization, is confusing, as it is presented to the reader as the rst of the ve disciplines. Consequently, the book reads better as an account of organizational learning (and a fascinating one at that) than as its explicit goal of forming a blueprint for a learning organization. Jacobus de Voragine's Golden Legend has had a long history of serving as an indispensible tool for personal inspiration, and as a target for ridicule as to the veracity of its claims. e same can be said of In Search of Excellence, where many of the companies singled out for their supposed excellence went into sharp decline soon a er the book's publication. Yet does the dubious accuracy of its assessment nullify the passion and zeal forming both books' real contribution? Over one thousand extant medieval copies of the hagiography and continuing sales of the management inspirational point towards spiritual relevance that transcends any criticism, at least in the short term (the decline of interest in the Golden Legend coincides with the change of attitudes accompanying the coming of the Renaissance).

Low Narrative Coherence

High Narrative Coherence

High ematic Coherence

In Search of Excellence e Leadership Challenge

Low ematic Coherence

Blue Ocean Strategy e Fi h Discipline

Tab. 2. Coherence in selected management bessellers Finally, the travelogue and Blue Ocean Strategy both share low levels (but not the complete lack) of narrative as well as thematic coherence, and are best seen as collections of entertaining if not very closely linked excerpts. It should be noted that Blue Ocean Strategy, like many other management bestsellers of the 1990s and 2000s, had its roots in a Harvard Business Review article (Kim and Mauborgne, 2004) expanded (or padded out) to form a book. But a more charitable interpretation sees the book as a grab bag of possible inspirational stories which, while held together by a tenuous claim of explaining value innovation, can nevertheless serve as points of reference and resources for sensemaking in disparate organizational contexts. And, a er all, Kim and Mauborgne themselves claim that their research did not uncover any consistently highly performing companies, only occasional successful strategic moves.

Coherence in management grand plots e four management books are presented as exemplars, illustrating the four modes of achieving coherence and showing how the grand plots of classical drama, novel, travelogue, and hagiography function when used to enunciate the concerns of management literature. While there is some variation that can be found among the thirty-one books forming our study material, we found no diffi culty in diff erentiating between them based on which grand plots they were using. None of the books we scrutinized challenged this typological scheme, though, as noted before, adding additional dimensions of cohesion, such as formal coherence, could have produced a more nuanced categorization and more tightly de ned grand plot descriptions. Table 3 summarizes the results of our typologization.

Conclusion

We have presented what we call the main grand plots, situated in the background of much more prominent and well-known readings of the popular writings on management. ey provide a rich source for inspiration for managers as ideas for translation of ideas into practices. We showed how two main types of coherence of these plots: narrative and thematic, are kept throughout the composition. We would now like to address the question why we believe their existence provides an important condition for learning of how to make (narrative) sense of management. Contemporary organizations are a way of life (Czarniawska, 1992), and so is management, the rigorous, focused and purposeful mode of organizing [START_REF] Sjöstrand | (ed) Organisationsteori på svenska[END_REF]. Seen as part of wider cultural context, learning how to make sense of organizational and managerial realities has to be embedded in a wider context [START_REF] Argyris | Organizational learning: A theory of action perspective[END_REF]. Coherence of the grand plot serves this purpose: thematic, by providing a sense of identity [START_REF] Weick | Making Sense of organization[END_REF], and narrative, by off ering a sense of action, or meaningful cycles -processes of is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342.

overly ambitious publications remain so popular (see e.g. [START_REF] Klincewicz | Management fashions: Turning bestselling ideas into objects and insitutions[END_REF]. However, we agree with the critics of fashionable management books that other kinds of ideas would be welcome if we are to look forward to genuine organizational change, through double loop learning [START_REF] Argyris | Organizational learning: A theory of action perspective[END_REF]. To achieve this we need what Barbara Czarniawska and Carl Rhodes (2006) call avant-garde management writing which "experiments rather than repeats; it disrespects the canon rather than either following or opposing it; much of it vanishes but that which stays can revolutionize the institutional patterns" (ibid.: 215). It is consciously iconoclastic and refrains from a repetition of strong plots and will neither emulate nor the hackneyed distinctions between popular culture and high culture -instead their exemplarity and originality will lie in their refusal to follow the plots that are handed down to them from either (ibid.: 215).

We need "avant-garde management writing" in order to exercise the imaginative capabilities, which Morgan (2003) regarded as crucial in complex and shi ing environments. In order to solve problems under such conditions, inspirational learning based on imagination is necessary. We live in what [START_REF] Bauman | Liquid modernity[END_REF] calls liquid times, ever exible and free from restraining stable structures.

e simultaneous fragmentation renders sensemaking a precarious and perhaps futile eff ort for many, giving the illusion of freedom, yet delivering further injustice and suff ering instead. Imaginative management may be our hope for solving some of liquid modernity's accumulating problems, as the current linear and rationalistic methods seem to work in a counterproductive fashion [START_REF] Bauman | Collateral damage: Social inequalities in a global age[END_REF]. It is our contention that the grand plots present in management literature serve as an important source of inspirational learning, based on imagination, which makes it possible to make sense of and act in complex, shi ing environments [START_REF] Morgan | Imaginization: New mindsets for seeing, organizing and managing[END_REF]. Morgan proposes to use such methods as mind games or brainstorms to develop this kind of learning; our suggestion is to read management books, but look beyond their super cial narrative line, and towards the grand plots. Not tied to any speci c theme or idea, grand plots establish rules for the construction of appropriate, or admirable, plotlines. In this text we have shown the ways in which the grand plots of popular management books are used to achieve coherence in presenting the books' invariably total solutions for organizational problems as adaptable to diff erent environments, contexts, and varied organizational dilemmas. Besides mapping the ways of establishing coherence, we also compared them to the textual strategies of more literaryoriented genres, and postulate the desirability of more conscious use of literary schemata which, even when not consciously invited, nd their way into management books.

In other words, we propose that critical management researchers use narrative devices to explore the sources of some management fashions trough the concept of the grad plot. In management education, we believe we should also try to in uence these fashions in the directions that [START_REF] Clegg | For management? Management Learning[END_REF] advocated, i.e. towards a polyphonic and contextualized management mindset. is can be done by the writing of avant-garde management books, with high thematic and narrative coherence, suitable for the development of imagination and inspire a mode of learning leading to greater awareness and change. Human learning processes rely on stories to provide the otherwise missing experiential context necessary for learning [START_REF] Bruner | Actual minds, possible worlds[END_REF][START_REF] Neuhauser | Corporate legends and lore: e power of storytelling as a management tool[END_REF]. Popular (and, to an extent, high) culture provides many such stories [START_REF] Czarniawska | Strong plots: e relationship between popular culture and management theory and practice[END_REF], but management books off er a source of relevant narratives that are easier to interpret in regards to management practice. rough this text, we propose a more conscious use of management texts for the stories they tell rather than just for their informational content, in the design and delivery of inspirational management education. To conclude, while we remain critical of many of the texts we have analysed, we call for more -not less -popular management books. But we call for books engaging in conscious, rather than accidental, storytelling. We ask for inspiring management books (and lms, and talks, and articles) that contain more than a simple linear narrative. We need management stories that acknowledge our rich storytelling heritage, stories heedful of their reliance on grand plots of thematic or narrative coherence. We ask for popular texts that enable learning through contextualised sensemaking. We address this call to good and talented academic writers, Critical Management scholars, humanists and artists, all who are willing and able to engage with the imagination of managers. Oscar Wilde once said that life imitates art -observe he did not say: linear logo-scientistic writing -so let us produce texts able to inspire management learning for making life better.

is copy does not follow journal layout or pagination. Originally published in 2016 in Management Learning 47/3: 324-342.

organizing [START_REF] Weick | e social psychology of organizing[END_REF]. In that way, the grand plots hidden in the background off er a powerful device for organizational sensemaking, both in terms of identities and processes. e constancy of a plot of this kind throughout each of the popular books makes it possible to make sense and engage, while reading the book, in the full translation continuum: deterritorializing an idea, transporting it and reterritorializing it in a diff erent context [START_REF] Deleuze | Nomadology: e war machine[END_REF], to be put into action in relation to a new web of meaningswhich is the point of much of organizational learning [START_REF] Argyris | Organizational learning: A theory of action perspective[END_REF]. In line with [START_REF] White | e content of the form[END_REF] observations on the signi cance of the narrative form, we argue that the success of translation, and thus of management learning achieved through popular literature, depends on the successful embedding of grand plots in the story presented to the reader. What this analysis shows is how important for management learning is the existence and availability of books able to provide a more engaged level of reading, one involving a successful grand plot. Standard management textbooks deliver limited and linear representations of managerial work, devoid of context and disembodied [START_REF] Knights | Management lives: Power and identity in work organizations[END_REF] and are, for that reason, unable to ful ll the role of providers of a contextualized learning experience. Acontexualization is strongly criticized by [START_REF] Parker | Against Management: Organisation in the Age of Managerialism. Cambridge: Polity Press. is copy does not follow journal layout or pagination[END_REF] as one of the reasons why management is becoming a totalitarian practice, false at heart in its universalizing promises. Bringing back context is very important, if we wish managers to learn polyphony in order to become "talented and creative players in many simultaneous and complex games" (Clegg et al., 2006: 19). Managers look to popular books to ll in this gap [START_REF] Pagel | Charting managerial reading preferences in relation to popular management theory books: A semiotic analysis[END_REF] and so it should, perhaps, cease to astonish us, academic observers, that these not


Ems Lord

Andreas J Stylianides

Strategy choices and formal algorithms: A mixed methods study

Keywords: Calculation, strategy, fluency, gender, confidence

Although making appropriate strategy choices is arguably a key indicator of calculation fluency, recent curriculum reforms in England prioritise the teaching of formal algorithms. The impact of this policy on students' calculation choices is currently unknown. This paper, which derives from a wider sequential mixed methods explanatory study, consisting of a large-scale survey (N=590) followed by individual interviews (n=23), casts some light on this issue by investigating the strategy choices of the first cohort of Year 6 students (10-11-year-olds) studying under the curriculum reforms. The survey findings showed that gender, prior attainment and confidence were all significant predictors of the use of formal algorithms. The interview findings revealed knowledge of multiple strategies and a willingness to choose alternative strategies as other key variables.

Background

This study was motivated by recent curriculum reforms in England (DfE, 2013a) which compelled schools to prioritise the teaching formal algorithms (Figure 1) over and above other calculation strategies. Those reforms signposted a dramatic shift away from previous policy that had encouraged the teaching of a wider range of calculation strategies (DfES, 2007). Alongside the curriculum reforms (DfE, 2013a), corresponding adjustments were made to the assessment procedures; incorrect calculations would receive half marks if and only if students attempted a formal algorithm. The reforms swiftly appeared to have an impact on classroom pedagogy: McClure (2014, para. 3) noted that "Many schools are already interpreting this as practice, practice, practice of formal algorithms." Although procedural fluency is recognised as a key factor of calculation fluency, the relevant literature highlights other factors too.

Theoretical framework

The notion of calculation fluency (also known as computational fluency) has been defined in the literature as requiring students to satisfy several different criteria. For example, the US-based National Council of Teachers of Mathematics (NCTM, 2000) stated:

Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. (NCTM, 2000, p. 152) The NCTM's definition was consistent with the way we conceptualised calculation fluency in this study as requiring accuracy, efficiency, flexibility and understanding of the chosen strategy. In light of the DfE's (2013a) reforms prioritising formal algorithms, flexibility received special attention in our work; due to the particular curricular context and policies, students in this study were deemed to be working flexibly when they deviated from choosing the formal algorithm. Examining the impact of teaching formal algorithms on 9-10-year-old boys in Belgium (N=21), [START_REF] Torbeyns | Efficient and flexible strategy use on multi-digit sums: A choice/no-choice study[END_REF] reported that most of the students prioritised formal algorithms within a year of their introduction to those strategies, even for calculations suited to other strategies such as 482 -299. The DfE's (2013a) reforms prioritising formal algorithms in primary schools were accompanied by an increased focus on problem-solving in secondary schools. The DfE's reforms across both levels of schooling appeared to assume that they satisfied the needs of all students. However, [START_REF] Villalobos | The importance of breaking set: socialized cognitive strategies and the gender discrepancy in mathematics[END_REF] argued that the gender differences in mathematical attainment observed in US schools could be explained by the different curricula that students experienced in their primary and secondary schooling. Her model predicted that young girls might respond positively to the increased focus on formal algorithms but their early success might hamper their later mathematical attainment studying under a problem-solving curriculum. Indeed, significant gender differences already existed in UK schools before the reforms; the DfE (2013b) released data indicating that similar numbers of girls and boys consistently achieved age-related expectations in primary mathematics, yet boys were outperforming girls at higher levels. Examination of the assessment descriptors (DCSF, 2009) revealed that pupils working at age-related expectations were expected to satisfy objectives addressing number recall and performing written calculations whereas pupils working above agerelated expectations were expected to demonstrate more problem-solving skills.

The literature also revealed gender differences in calculation strategies. For example, [START_REF] Carr | Gender differences in arithmetic strategy use: a function of skill and preference[END_REF] conducted a choice/no-choice study with 6-7-year-old students in the US (N=84) comparing their addition and subtraction strategies; the boys tended to prefer counting in their heads whereas the girls were more likely to choose counting on their fingers. Also, [START_REF] Hickendorff | Individual differences in strategy use on division problems: Mental versus written computation[END_REF], investigating the division calculations of 12-year-old students in the Netherlands (N=362), reported that boys tended to prefer informal written calculation strategies whereas girls were more likely to adopt formal strategies. Furthermore, when the researchers asked the students to record their division strategies, the boys tended to record fewer steps and work more intuitively than the majority of the girls in the sample. However, the reforms (DfE, 2013a) adopted a 'one size fits all' model which ultimately expected all pupils to use the formal algorithm and did not appear to take into account the differences described above. Moreover, the Programme for International Student Assessments (OECD, 2009) confirmed that 15-year-old English students had one of the largest gender differences favouring boys in mathematical performance.

The role of confidence in the calculation choices of boys and girls remained unexplored in the literature despite evidence revealing that confidence could interact with gender in shaping students' dispositions, decisions, or achievement. For example, [START_REF] Brown | I would rather die": Attitudes of 16-year-olds towards their future participation in mathematics[END_REF] reported that almost twice as many UK 16-year-old girls than boys indicated that they would not consider studying mathematics post-16 because it was perceived as 'too difficult.' Moreover, US-based [START_REF] Heilbronner | The STEM pathway for women: What has changed?[END_REF] found that confident students were more likely to continue studying mathematics post-16 than their less confident counterparts. Exploring the factors surrounding gender participation in the various STEM-related career paths, Heilbronner also reported a gender imbalance across the STEM-related subjects where females were less likely to choose engineering or mathematics than males. Hence confidence was regarded as a key issue in this study. For the purposes of this study, we adopted the definition of mathematical confidence as being an individual's belief in their ability to 'do' mathematics (Fishbein & Azjen, 1975).

Research design was another concern. Prior calculation studies tended to adopt choice/no-choice designs which limited their opportunities to explore calculation choices. Few studies explored the reasons behind the strategy choices of the students. Moreover, the DfE's (2013a) reforms prioritised formal algorithms for the four operations but prior studies tended to focus on a single operation, such as addition. The limited number of studies which did address all of the four operations did not consider gender or confidence. Hence this study adopted a sequential explanatory mixed methods research design which addressed the following research question: To what extent do gender, prior attainment and confidence predict use of formal algorithms across all of the four operations?

Method Participants

For the quantitative phase, 19 schools were randomly selected from a larger cohort taking part in a regional Mathematics Specialist Teacher (MaST) programme, an initiative which aimed to place a Master-level trained teacher in every primary school. This approach resulted in a potential sample of 670 10-11-year-olds. The actual sample consisted of 590 students (324 boys, 266 girls) with 79 students removed (35 -newly arrived in the UK with English as a second language, 33 -working below the required level, 6 -absent, 1 -poor behaviour and 4 -no evidence of parental permission).

Data collection

The quantitative survey consisted of a workbook containing 16 calculations, a mathematics Confidence Questionnaire (CQ) and the prior attainment scores from students' most recent national assessment at age 7 (Level 1 = below average, Level 2 = average, Level 3 = above average). The class teachers delivered the materials under national assessment test conditions.

The workbooks reflected the overall focus of the study by including some calculations which were deemed suitable for using formal algorithms (456+372, 5412+2584, 632-154, 27x63, 568x34 and 517÷19) and others which were regarded as suitable for other approaches, such as rounding to the nearest multiple of ten or counting the difference between two numbers (299+532, 245+256, 500-76, 702-695, 382-199, 20x46, 35x99, 693÷3, 480÷20 and 401÷25). The draft workbooks were piloted, revised and validated by five education professionals who were asked to confirm their suitability for the use of formal algorithms or alternative strategies; they were also asked to confirm their age-appropriateness, and their scores exceeded the minimum score of 0.8 recommended for new measures [START_REF] Rubio | Objectifying content validity: conducting a content validity study in social work research[END_REF].

The CQ was adapted from an existing measure which addressed mathematical competence as well as views on the importance of mathematics [START_REF] Eccles | Age and gender differences in children's self-and task perceptions during elementary school[END_REF]. The original version consisted of ten questions with a five-point Likert-style response scale which had been extensively trialed with similar age groups. For example, students were asked 'How well do you expect to do in math this year?' and 'How good in math are you?' The questionnaire could be efficiently administered by teachers to their whole class, but the terms math and student were replaced for my UK-based study. The internal consistency of the revised questionnaire was confirmed using Cronbach Alpha testing, achieving a high rating (10 items; α=0.88).

Twenty-four potential interviewees (12 boys, 12 girls) were drawn from three of the schools from the initial phase. This purposeful sample consisted of 12 high attaining students (6 boys, 6 girls) and 12 low confidence students (6 boys, 6 girls). One student, a high attaining girl, was absent which resulted in an actual sample of 23 interviewees. Each pupil was individually interviewed by the first author and the interview was audio recorded (video recording was not possible due to school policies). Since the purpose was to elicit the reasons underlying the students' strategy choices, semistructured interviews were deemed the most suitable approach; after a few introductory questions to confirm their name and willingness to participate in the project, the students were asked a series of questions addressing different aspects of their calculation fluency such as the reasons behind their strategy choices, their knowledge of alternative strategies and their checking procedures.

Data analysis

The initial quantitative data analysis informed the subsequent qualitative analysis. Each workbook was checked for accuracy and the individual calculations were coded according to the chosen strategy. An individual's flexibility was determined by the total number of times they chose formal algorithms across the 16 calculations. Quantitative analysis was conducted using ANOVA to compare the accuracy rates of different strategies and Multiple Linear Regression (MLR) to predict flexibility; the three predictor variables were gender, prior attainment and confidence, and the dependent variable was their use of formal algorithms.

The interviews were transcribed and coded using framework analysis (Richie & Spencer, 1994). This accommodated a priori issues from the quantitative phase as well as other themes emerging during the analysis. It began with a familiarisation stage, reading and re-reading the transcribed notes in order to become totally immersed in the data. The a priori themes were calculation accuracy, use of the formal algorithm (which reflected the flexibility aspect of calculation fluency), conceptual understanding, efficiency and the most accurate calculation strategies. The notes taken during this stage were organised into a draft thematic framework which was trialled and refined with a limited number of the transcripts, and the revised framework retained its original themes. Charting the data moved the analysis from working with individual transcripts towards analysing the whole data set. Each chart represented a single theme and the data was organised into the subthemes identified in the previous stages of the processthese completed charts allowed the data to be analysed both vertically (by sub-theme) and horizontally (by individual pupil). The charts enabled counting of the total number of coded items as well as consideration of the actual text.

Findings

Although formal algorithms were the most frequently selected strategy for each of the sixteen calculations, ANOVA tests confirmed that other strategies were significantly more accurate for three of those calculations (702 -695, 401 ÷ 25 and 517 ÷ 19) and formal algorithms for two others (456 + 372 and 693 ÷ 3). The MLR analysis revealed a statistically significant regression equation (F (4, 585) = 11.98, p<0.001), R 2 = 7.57% (Table 1) for predicting use of the formal algorithm.

Use of formal algorithm = 5.5212 + 0.8893(girl) -1.3026(Level 2) -1.6688(Level 3) + 0.1439(Confidence).

The MLR analysis confirmed that gender, prior attainment and confidence were all significant predictors of flexibility, but the most significant factor was confidence. If a student rated their mathematics confidence with the maximum score of 50, then their predicted use of formal algorithms increased by seven calculations. However those findings did not explain why the confident students tended to choose formal algorithms. Nor did they either explain why the girls tended to choose formal algorithms for one more calculation than the boys, or explain why the high attaining pupils tended to choose formal algorithms for two fewer calculations than the others. Due to the sequential nature of this study, each issue was addressed in the subsequent qualitative analysis. Moreover, the regression model indicated that just under 8% of the variance in choosing formal algorithms was explained by the three predictor variables so the qualitative phase also offered an opportunity to explore other possible variables to account for the remaining variance. Consider the quantitative finding that the more confident students tended to choose formal algorithms: this finding might imply that those students were either confident in their abilities to apply those strategies or they felt confident because they were following their teacher's approach. Alternatively, this finding might appear to imply that the low confidence students drew upon a wider range of calculation strategies than their counterparts by not relying on formal algorithms. However, the interviews revealed that the situation was more complex than it initially appeared; two-thirds of the low confidence interviewees admitted that they only knew a single strategy for some of their operations, some of them had yet to encounter formal algorithms and others were unwilling to attempt such strategies due to their lack of practice with the strategies. In particular, when asked to suggest another strategy for working out their answers, most of the low confidence students struggled to name an alternative strategy for multiplication or division calculations.

Coefficient

For gender, the quantitative findings showed that the girls were more likely to choose formal algorithms than the boys, and the interviews revealed that the girls preferred to use the same strategy for calculating and checking too. When the girls did know another strategy, such as rounding for 35 x 99, several of them either did not identify suitable opportunities to apply it or were reluctant to apply it. Several students stated that their choice of strategy was influenced by their knowledge of the assessment procedures for national tests. However, most of the boys were willing to adopt different strategies such as applying their knowledge of divisibility rules or checking their answers using inverses.

The quantitative findings also showed that the high attaining students were less likely to choose formal algorithms than other students, and their interviews revealed that they knew a greater range of strategies than the other students which enabled them to select alternative approaches. This was most noticeable when the high attaining students were discussing how they checked their answers; half of them employed more than one checking procedure or estimated their answers. Their flexibility ensured that they had a higher mean accuracy score than the other students too.

The interviews also shed further light on the unaccounted for variance in the regression model. Knowledge of multiple strategies and checking procedures emerged as important factors to consider regarding use of formal algorithms. More specifically, the transcripts revealed that students checked their calculations in different ways and at different times, and that those differing strategies might account for different accuracy rates too. The most accurate students were the minority who checked at least some of their answers using multiple strategies such as divisibility rules and using inverses; the majority simply checked each of their calculations by repeating their initial strategy. The students also checked their answers at different times but most of them checked as they went along. Around a fifth of the students, mostly boys, delayed checking their answers until they had finished all of their questions. However, the findings relating to the optimum time for checking their calculations were inconclusive, due to the small numbers of students involved. The interviews also highlighted the potentially negative influence of national testing on calculation flexibility; several students said that their choice of formal algorithms was influenced by national tests.

Discussion

Exploring different calculation strategies offers an opportunity for young students to experience working flexibly in the mathematics classroom, rather than relying exclusively on formal algorithms. However, the findings revealed that formal algorithms were the most frequently selected strategy for each of the 16 calculations in this study, including those deliberately included due to their suitability for other strategies. The subsequent interviews revealed that less confident students tended to be unaware of multiple strategies for multiplication or division calculations, possibly indicating that the renewed emphasis on formal algorithms might have steered some schools towards teaching a narrower range of strategies. The interviews also revealed that failing to recognise an opportunity to work flexibly often resulted in students choosing a less efficient, potentially error-prone, strategy.

The finding that the girls were more likely to choose formal algorithms than the boys was consistent with the early stages of Villalobos' (2009) theoretical model whereby young girls experience strategy socialization when they choose to follow algorithms. If the model is correct, those girls may struggle to adapt to the demands for more flexible approaches of later mathematics courses, such as those related to problem-solving. The results also showed that the high attaining students were less likely to choose formal algorithms than others. Their willingness to work flexibly would present a clear advantage for those high attaining students when problem-solving; knowing more than one strategy would enable them to adopt a different strategy if they got stuck [START_REF] Russell | Developing computational fluency with whole numbers in the elementary grades[END_REF].

Moreover, the most accurate students were the minority who checked at least some of their answers using multiple strategies, including estimation which was highlighted as important in the literature (e.g., Doreneles, Duro, Rios, Nogues, & Pereira, 2017). Readiness to consider other strategies was also recognised as a key aspect of fluency [START_REF] Mcclure | Developing number fluencywhat, why and how[END_REF]; comparing two answers from different strategies would allow students to identify any possible errors which might not have been noticed by simply repeating their initial strategy.

All study designs have their limitations. Although this project focused on gender, prior attainment and confidence, we accept that future studies might address social class or the enacted curriculum. Due to financial and time restraints, the student interviews were limited to three schools; widening the range of schools might uncover further factors too.

The above findings have clear implications for schools, researchers and policy makers. The decision to focus on all four operations, contrary to most prior research, exposed differences in the extent of students' knowledge of multiple strategies between operations. Also the sequential explanatory mixed methods research design, another notable difference from most prior research, enabled further exploration of the initial quantitative results by revealing potential issues arising from focusing too heavily on formal algorithms. Such issues include: low confidence students lacking knowledge of multiple strategies, restricting their options when they encounter difficulties; girls prioritising algorithmic fluency above all other aspects of mathematics, possibly to the detriment of their future mathematical development; and, students limiting themselves to a single calculation and checking procedure, reducing their opportunities to spot errors. Next steps in this study involve disseminating these findings to a variety of audiences, especially policy makers through contributions towards parliamentary access groups, national conferences and teaching publications.

Figure 1 :

 1 Figure 1: Formal algorithms for the four operations (DfE, 2013a, pp. 46-47)

Table 1 : Summary of revised coefficients for predicting use of the formal algorithm

 1

		Estimate	Standard	t-value	p-value
			Error
	Intercept	5.5212	0.9884	5.5862	3.56E-08
	Girl	0.8893	0.3091	2.877	0.0040
	Level 2	-1.3026	0.5379	-2.4217	0.0158
	Level 3	-1.6688	0.6225	-2.6806	0.0076
	Confidence	0.1439	0.0229	6.2793	6.63E-10