This article draws from the work of scholars in Critical Whiteness Studies to provide a nuanced analysis of ‘white shame’ in anti-racist education. In particular, it is argued that antiracist politics and pedagogy can be enriched by recognizing the affective and political complexities emerging from white shame and shaming. The purpose is to suggest that white shame has different manifestations depending on context and subject/group, and that those manifestations are related to feelings about white privilege, white ignorance, white fragility, and (...) white complicity. The author uses examples of white shame to discuss the pedagogical principles that inform the development of strategies for anti-racist education, emphasizing how educators can capitalize on teachable racial moments in the classroom that: move beyond white students’ tendency to default to shame; and, move beyond white students’ affective investments to racial inequality, while critically equipping white students to explore responsible ways of inhabiting their whiteness. (shrink)

In order to reach a better understanding of relationships in pedagogical practices the authors believe their language about relationships needs to be broadened and deepened. This chapter draws upon American philosopher Harry G. Frankfurt who writes about ‘care’ and how what we care about represents a volitional drive. It explores his notion of love in relation to his notion of care, and elaborates more fully what is at stake in our pedagogical interactions. The chapter also offers some thoughts (...) on why a more complex theory of actions is needed in order to broaden and deepen our language of pedagogical relations and what this means for reimagining pedagogical relationships. Finally, it discusses two statements from two school leaders: ‘you have to give of yourself’ and keeping ‘an open door’. These led the authors to investigate some aspects of human relationships in education that are rarely touched upon in pedagogical literature. (shrink)

In this article Morwenna Griffiths argues that teacher education policies should be predicated on a proper and full understanding of pedagogical relations as contingent, responsive, and adaptive over the course of a career. Griffiths uses the example of the recent report on teacher education in Scotland, by Graham Donaldson, to argue that for all the report's considerable merits, it remains deficient because it does not attend to the complexity and contingency of pedagogical relations. The complexity arises (...) from the existence of (at least) four analytically distinguishable pedagogical relations, each of which interacts with the others. These relations are contingent on the embodiment of teacher and students and on the political and sociocultural context of the class. Therefore they are also contingent on time, as teachers age and as the political and sociocultural context changes. Griffiths concludes the article with suggestions for creating a teaching profession in which teachers are reflectively and critically adaptive during the course of their careers. (shrink)

This chapter outlines a case for why liminality is of educational and not only of pedagogical concern, building on James Conroy's notion of the liminal imagination and his emphasis on the importance of metaphor for calling our attention to the ontological spaces that make up educational practice. It then turns to developing how different metaphors may be mobilised to signify the particularly relational quality of becoming, drawing on Luce Irigaray's work to explore more closely the corporeal and spiritual aspects (...) of becoming in relation. The chapter also presents a more fulsome discussion of the significance of approaching pedagogical relationships in education in this way and what this signifies for the teacher‐student encounter in particular. Finally, it argues that exploring the existential dimensions of pedagogical relationships between body and spirit similarly requires a language of in‐betweenness, or liminality, that gives full weight to the complex processes of human becoming. (shrink)

An ongoing collaborative project between art and science, Taming the Forest (2022) was implemented by a team of students, artists and researchers charting an interdisciplinary project among bioeconomics, environmental history, policy and artistic practice. In this article, the project acts as a case study for researching the conflicting narratives of history and economics about biodiversity in general, and specifically about forests. It shows how different blends of methodologies in artistic-cum-scientific research can become relevant for both realms, opening new creative pathways (...) and pedagogical registers while repeatedly returning to a specific forest’s microhistory. Moreover, the article stresses the need for a new sensibility and complex knowledge, moving beyond an objective study and becoming attentive to different dimensions of research and its outputs that emerge through the introduction of artistic thinking and methodologies. This kind of transdisciplinary approach becomes necessary in order to tackle the manifold large-scale problems such as the climate and biodiversity crises, which call for both acting decisively and transforming radically, above all with regard to how humans perceive, relate to and manage nature. (shrink)

The importance of pedagogy as a science is in exploration and improvement of education as an integral part of the social reality. Theory of education, General pedagogy and Methodics of educational work are the scientific disciplines that are most directly related to examining the educational work, and represent its theoretical and methodological basis in the process of its realization. Educational work provides the essence of the overall education process, since it refers and unites the knowledge, skills, attitudes, beliefs and values (...) of the individual, and its results are seen in developing student’s unique personality. In this paper the focus is on the Methodics of educational work, as a pedagogical discipline which is most closely related to the process of realization of educational work. The aim is through analysis of the basic theoretical and terminological aspects to emphasize its role in the overall education process. Taking into consideration the complexity of educational work and difficulties related to the process of assessment of the outcomes, application of the taxonomy of the affective domain is suggested as a possible approach. Also, the importance of some topics that are particularly relevant in pedagogy is emphasized, but which, due to terminological inconsistencies, are not sufficiently recognized as part of the Methodics of educational work. (shrink)

An Organisation for Economic Cooperation and Development research priority, innovative learning environments have been translated into policy and practice in 25 countries around the world. In Aotearoa/new Zealand, learning spaces are being reconceptualised in relation to this policy work by school leaders who are confronted by an impetus to lead pedagogic change. The article contributes a conjunctural analysis of the milieu around the redesign of these education facilities. Recognising that bodies and objects entwine in pedagogic spaces, we contribute a new (...) materialism reading of ILEs as these are instantiated in New Zealand. New materialism recognises the agential nature of matter and questions the anthropocentric narrative that frames the post-enlightenment conception of what it means to be human. The decentring of human subjects through a materialist ontology facilitates a consideration of the power of objects to affect the spatial politics of learning environments. The article traces a relationship between the New Zealand strategic plan for Education 2015–2021 and principal conceptions of ILE as the lived spaces of this policy actualisation and the disciplinary/control society conjuncture. Informed by theories of spatial practice, we argue that principals’ understandings of ‘space’ are integral to pedagogic approaches within open-plan spaces. A conjunctural analysis can expand the capacity to act politically. By examining the complex conditions of a political intervention, in this case ILEs, we trace the displacements and condensations of different sorts of contradictions, and thus open up possibilities for action. (shrink)

Much recent work in the study of popular culture has emphasized the extent to which it is not only a site of signifying practices, myths, meanings and identifications, but also an arena of intensities, of affective flows and corporeal state-changes. From this perspective, many areas of popular culture (from calisthenics to social dance to video gaming) can be seen as sites at which rich and complex—if sometimes dangerous—processes of embodied learning/teaching take place. By comparison, the world of formal education (...) can seem hopelessly clumsy in its inattention to such issues. From a personal perspective, I can attest that nothing surprises my students more than when I try to get them to think about the ergonomics of studying, or advise them that getting some exercise and cutting down on sugar will probably improve their work as much as further studying will, or when I advise graduate students that their mood and physical state will make as much difference to the quality of their lectures as will their level of formal preparation; and yet experience has convinced me of the accuracy of these assertions. I would aver that I have learned more about successful lecturing—in particular about the improvisational skill of ‘reading’ a room, and adjusting an affective–informational flow accordingly—from DJing in dance clubs than from any formal training in pedagogy that I have received. What conclusions could be drawn from these observations, and how do they relate to existing strands of pedagogic theory? These are the questions which this article will ultimately seek to address. (shrink)

This paper rereads John Dewey's works in the light of complexity theory and self‐organising systems. Dewey's pragmatic inquiry is posited as inspirational for developing a logic of education and learning that would incorporate novelty and creativity, these artistic elements being part and parcel of the science of complexity. Dewey's philosophical concepts are explored against the background of such founders of dynamical systems theory as Ludwig von Bertalanffy, Ervin Laszlo, and Erich Jantsch. If, in this process, Dewey's thought appears to undergo (...) some transformation, this would only confirm Jim ) belief that Dewey would welcome, in accord with his own philosophical project, the reconstruction of his own ideas so as to better respond to contingencies and challenges of new times, places and contexts. The paper introduces some elements of non‐linear dynamics, relating them to the problematic of learning and the transformation of habits. Finally, the paper addresses a delicate balance between novelty and confirmation in a self‐organised system, positing it as an issue of pedagogical significance. (shrink)

This paper discusses Butler’s theory on the possibility of precarity to serve as the nexus of ethical relations, while also exploring some of the pitfalls of her theorization to reconceptualize the pedagogical implications of a critical pedagogy for precarity. In particular, the paper asks: How can precarity—understood as an ambivalent concept, as a paradoxical nexus of both possibilities and constraints—function pedagogically in a way that challenges its moralization? How can educators engage with precarity in ways that ‘re-frame’ it (...) so that both the dangers and prospects of ethics and politics of precarity are properly acknowledged and critically interrogated in pedagogical practice? The risks and possibilities of a critical pedagogy for precarity are addressed, highlighting that there are several complexities involved as much as there are opportunities for ethical transformation and political action in school and beyond. (shrink)

Agamben’s notion of the ‘paradigm’ has far-reaching implications for educational thinking, curriculum design and pedagogical conduct. In his approach, examples—or paradigms—deeply engage our powers of analogy, enabling us to discern previously unseen affinities among singular objects by stepping outside established systems of classification. In this way we come to envision novel groupings, new patterns of connection—that nonetheless do not simply reassemble those singular objects into yet another rigidly fixed set or class. Agamben sees this sort of ‘paradigmatic understanding’ as (...) our richest source of intelligibility. For Agamben the paradigm is ultimately about learning to see again, starting not with already perfectly known and categorized objects (or ideas), but rather with a fresh experience of one individual object and the analogical relations it may have to others, and to novel groupings that may arise. The paradigm is a method, a way in which educators might respond to a wide range of educational challenges. For a paradigmatic relation suspends while exposing, deactivates while revealing, complicates while clarifying. But articulating the enigmatic paradigmatic relation between example and class is far more than a method. It is epistemological (a way of knowing and conception of knowledge), ethical (a fostering of freedom from presupposed categories and reified principles) and ontological (a type of being that exposes the potential of knowing and communicating—their intelligibility and communicability). In these qualities, paradigms exhibit to educators a free, a new use of singularities. (shrink)

This paper presents a model for the implementation of educational activities involving musical improvisation that is based on a review of the literature on the psychology of music. Psychology of music is a complex field of research in which quantitative and qualitative methods have been employed involving participants ranging from novices to expert performers. The cognitive research has been analyzed to propose a pedagogical approach to the development of processes rather than products that focus on an expert’s use (...) of improvisation. The intention is to delineate a reflective approach that goes beyond the mere instruction of some current practices of teaching improvisation in jazz pedagogy. The review highlights that improvisation is a complex, multidimensional act that involves creative and performance behaviors in real-time in addition to processes such as sensory and perceptual encoding, motor control, performance monitoring, and memory storage and recall. Educational applications for the following processes are outlined: anticipation, use of repertoire, emotive communication, feedback, and flow. These characteristics are discussed in relation to the design of a pedagogical approach to musical improvisation based on reflection and metacognition development. (shrink)

The pedagogical function of science teaching may benefit from an analysis of the historical-epistemic dimension, without neglecting the socio-political context in which a given research was carried out. In the case of DNA structure, the background of its discovery is particularly complex. Starting from the analysis of some papers, the view on the circumstances that led to their drafting broadens. We try to answer the fundamental question for any educator: why teach all that? Ethics issues are related to (...) the general organisation of research, increasingly focused on speed and competition. Even teaching is affected by these dynamics, not only in higher education, but also at secondary level; students should be made aware of this trend. The history of science could therefore favour a more general awareness. _SUNTO_ La funzione pedagogica dell’insegnamento scientifico può trarre vantaggio da un’analisi della dimensione storico-epistemica, senza trascurare il contesto socio-politico nel quale una determinata ricerca è stata condotta. Nel caso della struttura del DNA, i retroscena della sua scoperta sono particolarmente complessi. Dopo l’analisi di alcuni articoli, si allarga gradualmente la vista sulle circostanze che hanno condotto alla loro stesura. Si cerca di rispondere a una domanda fondamentale per ogni educatore: perché insegnare tutto ciò? Le questioni etiche riguardano l’organizzazione generale della ricerca, sempre più tesa alla velocità e alla competizione. Persino l’insegnamento è influenzato da dinamiche simili, non solo in ambito accademico, ma anche a livello secondario; gli studenti dovrebbero essere a conoscenza di questa tendenza. La storia della scienza può dunque favorire una maggiore consapevolezza. (shrink)

In recent years new discourses have emerged to inform philosophy and pedagogy in early childhood. These range from various postfoundational perspectives to objectivist accounts such as neuroscience in relation to brain development. Given the variety of competing narratives, the field is complex and multifaceted with potential to revision early childhood pedagogy through varied paradigms and philosophical orientations. This special issue sought scholarship on a range of philosophical perspectives about early childhood education, particularly those related to issues of pedagogy. In (...) this article, we develop an argument for philosophically informed pedagogy to balance some of the psychological and empirical approaches that dominate the field. Based on the provocations of the seven articles that comprise this issue, we argue for greater attention to subjective and even mysterious approaches to learning that call for ontological orientations to pedagogy as a relationship rather than a response or an intervention. (shrink)

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relationsR,S, a componentwise reducibility is defined byR≤S⇔ ∃f∀x, y[x R y↔fS f].Here,fis taken from a suitable class of effective functions. For us the relations will be on natural numbers, andfmust be computable. We show that there is a${\rm{\Pi }}_1^0$-complete equivalence relation, but no${\rm{\Pi }}_k^0$-complete fork≥ 2. We show that${\rm{\Sigma }}_k^0$preorders arising naturally in the above-mentioned areas are${\rm{\Sigma }}_k^0$-complete. This includes polynomial (...) timem-reducibility on exponential time sets, which is${\rm{\Sigma }}_2^0$, almost inclusion on r.e. sets, which is${\rm{\Sigma }}_3^0$, and Turing reducibility on r.e. sets, which is${\rm{\Sigma }}_4^0$. (shrink)

This edited text recaptures many of Joe L. Kincheloe's national and international influences. An advocate and a scholar in the social, historical, and philosophical foundations of education, he dedicated his professional life to his vision of critical pedagogy. The authors in this volume found mentorship, as well as kinship, in Joe and express the many ways in which he and his work made profound differences in their work and lives. Joe's research always pushed the limits of what critically reflective and (...) informed teaching entailed, never diluting the import of comprehending the complexity of sociopolitical, cultural, economic, and educational discourses and practices. Dedicated to a praxis of social and political activism rooted in students' development as citizens and workers, the labor of teachers as action researchers, cultural workers, and social mediators is always at the heart of all he achieved. We who were so influenced directly and indirectly by him knew his genius and relished the generosity with which he shared his ideas, advice, encouragement, and art. The world is better because of Joe L. Kincheloe scholarship-inextricably related to "critical" critical thinking and enactment of education that tenaciously interrupts complacency, mediocrity, always responding thoughtfully to particular educational contexts. (shrink)

This paper elaborates a typology of universities in which each university is characteristically associated with diverse missions, different ways of producing knowledge and contrasting pedagogical configurations. Four university forms are identified, analysed and illustrated, namely the expert university, the non-elite university, the entrepreneurial university and the revolutionary university. It is suggested that the typology and the analysis of university forms offered here provide insight into the current positioning of universities in relation to the wider world and have potential in (...) prompting new forms of university for the twenty-first century. The paper further advances another possible university for the future, namely the complex university. The complex university is part of and respectful of diverse ecosystems. It creates new frameworks to understand the world and, in that way, supports social transformations. (shrink)

Pedagogy, power and practice ethics: clinical teaching in psychiatric/mental health settings Often, baccalaureate nursing students initially approach a psychiatric mental health practicum with uncertainty, and even fear. They may feel unprepared for the myriad complex practice situations encountered. In addition, memories of personal painful life events may be vicariously evoked through learning about and listening to the experiences of those diagnosed with mental disorders. When faced with such challenging situations, nursing students often seek counsel from the clinical and/or classroom (...) faculty. Pedagogic boundaries may begin to blur in the face of student distress. For the nurse educator, several questions arise: Should a nurse educator provide counseling to students? How does one best negotiate the boundaries between ‘counselor’, and ‘caring educator’? What are the limits of a caring and professional pedagogic relation? What different knowledges provide guidance and to what differential consequences for ethical pedagogic relationships? This paper offers a comparative analysis of three philosophical stances to examine differences in key assumptions, pedagogic positioning, relationships of power/knowledge, and consequences for professional ethical pedagogic practices. While definitive answers are difficult, the authors pose several questions for consideration in discerning how best to proceed and under what particular conditions. (shrink)

In this essay, Christiane Thompson addresses the question of evaluative practices, particularly student evaluation of teaching (SET), and their effects with respect to pedagogical relations in the university setting. In the first part of the essay, Thompson draws on Michel Foucault's analysis of power to show how university teaching has come to be defined according to notions of obligation, accountability, and assurance. The forgetfulness of pedagogical relations that results from the increasing use of SET prompts Thompson (...) to rethink the significance of pedagogical relations in the second part of the essay. Referring to the notion of “educational authority” and Foucault's framework of power, Thompson argues that education is about the continuous re-institution of pedagogical relation to the other. In the final section, Thompson reflects upon the professor's “authority” in terms of constituting a “community of inquiry”: specifically, the seminar is interpreted as a pedagogical setting that implies a different “being-with” than SET suggests. She concludes by considering what possibilities and limitations the seminar setting offers and how we can discuss this issue (by means of evaluative practice). (shrink)

This paper argues that public pedagogy—an educational activity that takes place outside of the traditional classroom setting—has had a potent impact on the history of racism in the United States of America (USA). Yet this paper questions why the education academy’s scholarship has not shown a commensurate focus on the subdiscipline of public pedagogy, particularly racialized public pedagogy. I explore these topics by first examining a fateful confluence of historical circumstances involving slave codes and indentured servant laws governing low-income white (...) workers, laws passed by the Barbados Assembly in 1661, that made their way across the Atlantic to be lifted, word for word, by leaders of colonial territories that became the USA. These laws ended up regulating not only the legal status of black slaves and white indentured servants in the USA, but also regulating social relations between those same black and white people. The resulting black–white social relations led to the evolution of racialized customs in what eventually became the USA, inspiring practices that undergirded black inferiority and white superiority for hundreds of years. Those customs contributed to the construction of what I have labelled a United States (US) values infrastructure dominated by racism, which I contend is a racialized values infrastructure that exists to this day. To gain more insight into this phenomenon, this paper considers the question: how might the complexity of racialized public pedagogy be addressed in the scholarship of education literature and be imagined in a way to fit into an anti-racist curriculum? (shrink)

We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris [2], Mayer-Wolf [5], and Weaver [8]. We show that this relation is Borel bireducible to the universal relation for Borel actions of Polish groups. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).

Moral distress is a common phenomenon among nurses and is related to the complicated work environments and complex nature of ethical situations in day-to-day nursing practice. Moral distress impacts nurses as well as patient care and the health care system. Few strategies have been identified for instructors to effectively engage with learners when communicating about moral distress. We discuss two key curricular and pedagogical strategies that should be utilized when learning about moral distress: difficult knowledge’ and ‘terror management (...) theory’. Whether it is with new nursing students or experienced nurses, there is necessary learning that needs to occur on moral distress. Difficult knowledge’ and ‘terror management theory’, when implemented, can provide a starting point for both the learner and the instructor to discuss the emotionally difficult and complex topic of moral distress. Knowledge about moral distress has the potential to mitigate its negative effects, therefore it is vital to consider educational strategies to teach nurses about this complex phenomenon. (shrink)

The relation between philosophy and pedagogy is complex and hard to grasp.1 Nonetheless, the tendency within much educational research influenced by the Anglo-American traditions of studying education is for philosophy to become a source from which educational researchers retrieve concepts, ideas, and critical methods for the analysis of empirical material, for formulating criticism of policy, or for developing curriculum theory. Philosophy is simply applied to educational research problems and questions. Such a relation can be prolific, but it risks resulting (...) in a formalistic study of education and an asymmetric relation in which philosophy contributes to pedagogy, but where pedagogy is not given a chance to speak... (shrink)

Drawing on Michel Foucault's writings as well as the writings of feminist scholars bell hooks and Jane Gallop, this paper examines faculty–student sexual relations and the discourses and policies that surround them. It argues that the dominant discourses on professor–student sex and the policies that follow from them misunderstand the form of power that is at work within pedagogical institutions, and it examines some of the consequences that result from this misunderstanding. In Foucault's terms, we tend to theorize (...) faculty–student relations using a model of sovereign power in which people have or lack power and in which power operates in a static, stable, and exclusively top-down manner. We should, however, recognize the ways in which individuals in pedagogical institutions are situated within disciplinary and thus dynamic, reciprocal, and complex networks of power, as well as the ways in which the pedagogical relation may be a technique of the self and not only of domination. If we reconsider these relations in terms of Foucault's accounts of discipline and technologies of the self, we can recognize that prohibitions on faculty—student sexual relations within institutions such as the university are productive rather than repressive of desire, and that such relations can be opportunities for development and not only for abuse. Moreover, this paper suggests that the dominant discourses on professor—student relations today contribute to a construction of professors as dangerous and students as vulnerable, which denies the agency of (mostly female) students and obscures the multiplicity of forms of sexual abuse that occur within the university context. (shrink)

__ Inclusive education is complex, multi-faceted and ever-changing and to date there has been no fixed definition of what is meant by the term ‘inclusion’, leading to confusion about what inclusive education actually means in practice. This key text introduces readers to the underlying knowledge and wider complexities of inclusion and explores how this can relate to practice. Considering inclusion as referring to _all_ learners, it surveys the concept of inclusive practice in its broadest sense and examines its implementation (...) in a variety of educational institutions. Throughout the book, international contributors consider this broader concept to critically evaluate the realities of practically implementing inclusive objectives. Each chapter assesses key theories and concepts alongside a range of examples to encourage students to think critically and reappraise their own experience as learners. Key topics covered include: • studying the definition of inclusion • the relevance of pedagogy in inclusive practice • how to lead and manage for inclusion • the issue of inclusion in early years, primary, secondary and post-16 settings • inclusive practice for families • international perspectives on inclusive practice. Fully illustrated with tasks, case studies, discussion questions and recommended reading, _Inclusive Education_ is essential reading for second and third year students looking to extend their research and writing, and to develop their critical and reflective thinking. (shrink)

This article discusses the hypothesis of a recovery of the phenomenological and literary paradigms of antiquity to cross the complexity of the existential, educational and relational experience in the digital contemporary world, focusing on the problems of the construction of identity and digital citizenship in social coexistence intended as a place of education.

The problem-oriented approach to teaching first-time philosophy students makes course design simple and makes the course content quickly recognizable to students, yet it fails to challenge them as readers and fails to convey the complex historical and social contexts out of which philosophical inquiry emerges. Presenting philosophical problems without context makes it harder for students to relate course material to their own lives and risks alienating students. In contrast, the authors argue, an interrogative and narrative approach to teaching philosophy (...) facilitates students’ ability to relate personally to philosophical texts and problems. This paper details a course designed by the authors which begins by studying the concept of narrative and subsequently frames the history of philosophy as a story with a setting (the intellectual conversation produced by canonical figures), characters (the philosophers themselves), theme (e.g. the question “How ought I to live?”), and plot (e.g. answers to the question “What is wisdom?”). Simultaneously, in addition to class structures which encourage questions, reading questions are assigned in order to make question-asking central to how students and teachers approach a text. Included are examples of the reading questions, as well as the authors’ method for using these questions and suggestions for how to motivate students to use them. (shrink)

This chapter contains sections titled: Teaching as vocational environment Batch processing, kitsch culture, and other obstacles to teacher vocation The syntax of educational claims The shape of humanistic conversation Horizons of educational inquiry Teacher education for practical wisdom.

We prove that if G is a Δ 0 -definable function on the natural numbers and F = Π i = 0 n G , then F is also Δ 0 -definable. Moreover, the inductive properties of F can be proved inside the theory IΔ 0.

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be (...) very complex in the following sense: for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

For ecofeminists within academic contexts, the classroom is another "contested terrain "where transformative eco-cultural work should be integrated. In our case, we are a part of communication studies and try to adopt ecofeminist insight as a position for questioning dominant discourses and practices. To do this, we "incorporate popular culture as a serious object of politics and analysis" (Giroux 1997, 148). It is our hope that popular culture can be used as an ecofeminist tool for interrupting hegemonic power relations (...) and encouraging critical-relational consciousness. This paper reports an exploratory effort aimed at combining ecofeminist critiques with popular culture to employ an ecofeminist pedagogy. It begins with an ecofeminist critique of the "animal-industrial-complex" (Noske 1989). In this critique, discursive moral agents are situated within the anthropocentric and androcentric culture (Payne 1994). It then articulates an ecofeminist teaching philosophy and describes how that philosophy was applied in one case using an episode from a prime time television cartoon. Finally, it draws conclusions about what is accomplished through this exploratory case. (shrink)

In the educational psychology literature, self-regulated learning is associated with empowerment, agency, and democratic participation. Therefore, researchers are dedicated to developing and improving self-regulated learning pedagogy in order to make it widespread. However, drawing from the educational philosophy of Paulo Freire, teaching students to regulate their learning can be tied to a curriculum of obedience, subordination, and oppression. Using Freire’s discussion of concepts such as adaptation, prescription, and dependence, I suggest that self-regulated learning: targets individual psychological changes that render individuals (...) adaptable to existing social orders; is guided by a logic to prescribe a certain kind of self; and produces a relationship of dependence as learners depend on teachers for learning the necessary scripts to regulate their learning. This analysis points to ethical complexities related to teaching students to academically self-regulate. (shrink)

Recent moral philosophy emphasizes both the particularity of ethical contexts and the complexity of human character, but the usual abstract examples make it difficult to communicate to students the importance of this particularity and complexity. Extended study of a literary text in ethics classes can help overcome this obstacle and enrich our students’ understanding and practice of mature ethical reflection. Jane Austen’s Persuasion is an ideal text for this kind of effort. Persuasion augments the resources for ethical reflection that students (...) bring to our courses, provides a multitude of fecund examples to inspire discussion, and introduces philosophical points of its own. I explain specific ways to integrate this novel into courses and why some approaches work better than others, and I highlight themes for three different levels of study: reflection on particular virtues and vices, illustration of broader ethical issues, and discussion of virtues that the philosophical literature neglects. In each case, I discuss a particular example in detail: the question of whether or not pride can be a virtue, the varieties of friendship and their relation to virtue, and the virtue of proper persuadability. These examples suggest ways in which ethics teachers might explore the resources of other literary works towards similar ends. (shrink)

We prove that the homeomorphism relation between compact spaces can be continuously reduced to the homeomorphism equivalence relation between absolute retracts, which strengthens and simplifies recent results of Chang and Gao, and Cieśla. It follows then that the homeomorphism relation of absolute retracts is Borel bireducible with the universal orbit equivalence relation. We also prove that the homeomorphism relation between regular continua is classifiable by countable structures and hence it is Borel bireducible with the universal orbit equivalence relation of the (...) permutation group on a countable set. On the other hand we prove that the homeomorphism relation between rim-finite metrizable compacta is not classifiable by countable structures. (shrink)

Films depicting educational relationships typically emphasize personal connections between students and teachers over the educational goals that such relations facilitate. In doing so, these films raise the question of how teachers stand in relation to their institutional roles in such a way as to inspire students’ desires for knowledge. In this paper, in order to examine the influence of institutional roles in defining teacher–student relationships, we analyze “The Paper Chase,” a film in which teacher and student have no personal (...) connection but in which the drama of student desire is nonetheless clearly featured. Drawing from Plato’s erotics, in which the soul is shaped by desire for that which it lacks, and from Jacques Lacan’s theories of desire and transference, we argue that “The Paper Chase” portrays educational desire as rooted in the differential of authority between teacher and student. (shrink)

Writing and reading are closely related and are thus likely to have a common orthographic representation. A fundamental question in the literature on the production of written Chinese characters concerns the structure of orthographic representations. We report on a Chinese character handwriting pedagogical corpus involving a class of 22 persons, 232 composite character types, 1,913 tokens, and 13,057 stroke records, together with the inter-stroke interval, which reflects the parallel processing of multilevel orthographic representation during the writing execution, and 50 (...) orthographic variables from the whole character, logographeme, and stroke. The results of regression analyses show that orthographic representation has a hierarchy and that different representational levels are active simultaneously. In the multilevel structure of orthographic representation, the representation of the logographeme is absolutely dominant. Writing and reading have both commonalities and individual differences in their orthographic representations. The online processing of the logographeme unit probably occurs at the ISI before the initial stroke of the current logographeme, which may also cascade to the first subsequent logographeme. In addition, we propose a new effective character structure unit for describing orthographic complexity. (shrink)

The article examines two forms of public pedagogies in a rural region of Southwest China—tourism and ethnic songs—to illustrate their contested roles in transforming local relations with natural and built environment. While tourism development daily alters the village landscape by spatial intervention, demolition, and construction, the ‘landscaping’ is both a visual and conceptual device that produces a pleasurable environment as the ‘other’ and signifies what is tourable and what is to be seen. On the other hand, the echoes of (...) the environment and human-nature relations are central elements in ethnic songs that have been sung for centuries as a major music genre to transmit ancestral, historical, and cultural understandings. Indigenous worldviews and ecological awareness are expressed in songs through imitation of nature and worship of various nonhuman forms of life. The paper argues that a nascent environmentalism and ecological significance of the ethnic songs are increasingly oriented towards instrumental development rationality, while at the same time revived and choreographed in staged tourism performances. Both tourism and ethnic songs offer powerful forms of public pedagogies through which to rethink how incommensurable discourses generate new environmental crises by drastically altering not only the vernacular landscape but also local cosmological beliefs. The short-lived developmental zest and the longstanding local ecological consciousness play out complex dynamics in ‘teaching’ the locals and the tourists about the changing environment of rural ethnic China, and the ambiguities and tensions that exist within the notion of sustainable development. (shrink)

This edited volume presents a post-humanist reflection on education, mapping the complex transdisciplinary pedagogy and theoretical research while also addressing questions related to marginalised voices, colonial discourses, and the relationship between theory and practice. Exhibiting a re-imagination of education through themed relationalities that can transverse education, this cutting-edge book highlights the importance of matter in educational environments, enriching pedagogies, teacher-student relationships and curricular innovation. Chapters present contributions that explore education through various international contexts and educational sectors, unravelling educational implications (...) with reference to the climate change crisis, migrant children in education, post-pandemic education, feminist activisism and other emergent issues. The book examines the ongoing iterations of the entanglement of colonization, modernity, and humanity with education to propose a possibility of education capable of upholding heterogeneous worlds. Curated with a global perspective on transversal relationalities and offering a unique outlook on posthuman thoughts and actions related to education, this book will be an important reading for students, researchers and academics in the fields of philosophy of education, sociology of education, post humanism and new materialism, curriculum studies, and educational research. (shrink)

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be (...) very complex in the following sense: for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. For model checking, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PS pace , NE xp T ime , and (...) even N2E xp T ime . Our analysis includes the versions of all these languages without atomic propositions, and also complete frames. (shrink)

Terence Mclaughlin’s essay addresses the conceptual and practical complexities involved in identifying and evaluating the nature, status, and institutional context of common education in pluralist societies. He explores some of the neglected burdens and dilemmas faced by common schools in pluralist, multicultural, and liberal–democratic societies. The potential weight and complexity of these burdens and dilemmas is reflected in Stephen Macedo’s observation that common schools give rise to questions relating to some of the ‘deepest divisions’ and ‘most intractable conflicts’ characterizing the (...) public lives of modern states. The chapter has five sections: Section 5.1 outlines some general considerations relating to common schooling and a conception of common education, pointing out that the relationship between the two is a contingent one – the adequacy of a particular institutional arrangement, such as the common school, depends critically on the extent to which it embodies an adequate conception of common education; Section 5.2 offers a sketch of some general features of such conceptions; in Sections 5.3 and 5.4, respectively, some of the burdens and dilemmas of common schooling are explored; Section 5.5 addresses neglected questions relating to the pre-eminently practical burdens and dilemmas highlighted in the previous two sections. McLaughlin’s chapter is especially helpful in identifying a number of the most important considerations in the presumption in favour of common schools as the most suitable arrangement for advancing common education, and his essay maps the conceptual, curricular, pedagogical, and policy issues that must be addressed in clarifying and defending the role of common schools and common education in liberal–democratic societies. (shrink)

The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...) as well. We prove that the equational theory of \ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

Although there have been various issues involving shame in the educational scene, little research in the field of philosophy of education has seriously investigated this topic. In my dissertation, a comparative philosophical study is conducted in an attempt to develop a better understanding of shame in moral education. This study explores when shame is morally appropriate and how shame is relevant to moral education, either positively or negatively, through historical and multidisciplinary reviews on the concept of shame and cross-cultural analysis (...) of shame-related matters within the context of moral education between South Korea and the United States. In the process of finding sources discussing shame and related issues, a variety of scholarly works in the humanities and social sciences, from classical to contemporary, are surveyed in early chapters of this dissertation. Accordingly, diversified concepts of shame and its complex nature concerning moral education are identified. The later chapters illustrate how shame is associated with education practices, pedagogical approaches, and curriculum by providing selected examples, not only observed by other researchers but also obtained from my own case studies—utilizing content analysis of Korean textbooks and semi-structured interviews with education practitioners in an urban area in central Oklahoma. As a result, this study shows that the moral value of shame is explicitly taught in the Korean education system and negative shame-related phenomena such as shaming are tightly guarded against in the American education setting. This leads to two different consequences: the misuse of shame is underestimated in South Korea, while the moral potential of shame is undervalued in the United States. Ultimately, the study prescribes the re-contextualization of shame in company with the promotion of intercultural awareness, which are both urgently needed for a well-balanced, high quality moral education in today’s multicultural and globalized age. Keywords: sense of shame, shame in moral education, moral pedagogy. (shrink)

We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel reductions between them. We motivate these concepts on examples and we set some basic general theory. We illustrate the new notion of reduction by showing that the Gromov–Hausdorff distance maintains the same complexity if it is defined on the class of all Polish metric spaces, spaces bounded from below, from above, (...) and from both below and above. Then we show that [Formula: see text] is not reducible to equivalences induced by orbit pseudometrics, generalizing the seminal result of Kechris and Louveau. We answer in negative a question of Ben Yaacov, Doucha, Nies, and Tsankov on whether balls in the Gromov–Hausdorff and Kadets distances are Borel. In appendix, we provide new methods using games showing that the distance-zero classes in certain pseudometrics are Borel, extending the results of Ben Yaacov, Doucha, Nies, and Tsankov. There is a complementary paper of the authors where reductions between the most common pseudometrics from functional analysis and metric geometry are provided. (shrink)

An application of the Method of Analysis of Relational Complexity (MARC) to suppositional reasoning in the knight-knave task is outlined. The task requires testing suppositions derived from statements made by individuals who either always tell the truth or always lie. Relational complexity (RC) is defined as the number of unique entities that need to be processed in parallel to arrive at a solution. A selection of five ternary and five quaternary items were presented to 53 psychology students using a pencil (...) and paper format. A computer-administered version was presented to 50 students. As predicted, quaternary problems were associated with higher error rates and longer response times than ternary problems. The computer-administered form was more difficult than the pencil and paper version of the test. These differences are discussed in terms of RC theory and alternative processing accounts. Together, they indicate that the relational complexity metric is a useful and parsimonious way to quantify complexity of reasoning tasks. (shrink)

Charles Sanders Peirce’s first rule of logic (EP 2.48, 1898) identifies the inception point of human inquiry. Taking a closer look at this principle, we find at its core a necessary relationship between emptiness and desire that underlies all genuine instances of human learning and adaptation. This composite relationship plays a critical role in the function or failure of learning but has received scant attention in the literature. As a result, the complexities of the first rule of logic are not (...) well understood, often being mistakenly conflated with the rule’s famous corollary, ‘do not block the way of inquiry’, or passed over with cursory definitions, including ‘wonder’, ‘doubt’ and ‘the will to learn’. Following a background discussion highlighting the nature of reflexive inquiry and fallibilism that situate human consciousness both within and beyond animal being, I draw on multiple layers of evidence from a range of disciplines to better reveal the complex dynamics intrinsic to the first rule of logic. These layers include a closer reading and exegesis of the original passage and surrounding text; a semiotic reanalysis of this reading in light of recent advances in the semiotic theory of learning; a resituation of these distinctions within broader contemporary discussions of emptiness ontology to which I contribute in part via an original semantic/rhetorical analysis of a linguistic construction in Laozi; the introduction of a closely related pedagogical tool under development in the context of my own university-level teaching in ethnography and research methods; and the dialogic situation of this diagram within discourses of psychotherapy, philosophy and literature. Building on these principles and distinctions, the paper closes with a perspective shift on obstacles and desire in human learning and an expanded reformulation of the first rule of logic. (shrink)

Calvino’s apology of multiplicity starts with the exposure, revealed by his take on typically modern novels, of some fundamental contradictions underlaying the modern quest for knowledge, which are definitely not alien to our day education. Then, when Calvino goes on to explore how twentieth century literature transcended those difficulties, he provides us with a valuable inspiration for how education could cope with its ambiguous relation to knowledge, still deeply rooted in the modern approach. Guided by Calvino’s readings, we are shown (...) that literature can succeed in its epistemological (r)evolution. Meanwhile, education, as it seems, is still struggling to overcome its entanglement with the unreachable goal of teaching everything about everything, to cope with the infinity and complexity of that everything, making reflecting upon education’s epistemological stance in the twenty-first century very much a necessity, one that I will try to pursue in the following pages After a methodological introduction, the paper starts by placing Calvino’s examination of beautiful, yet unsuccessful literary attempts at an exhaustive account of the world in the context of education, to show how their unattainable ambitions are mirrored in pedagogical practice, pointing out to the “modern spirit” underlying both the aforementioned novels’ and contemporary education’s relation to knowledge. Then, with the help of J. Rancière’s take on education, I will try and make educational sense of Calvino’s account of Bouvard and Pécuchet failed quest to know everything there is to be known, and relate it to the particular model of knowledge at work in education, one that needs to be questioned. Finally, I will draw on Calvino’s praise of “the contemporary novel as (…) a method of knowledge” (SM, p. 105), and particularly on his analysis of Perec’s masterpiece La Vie mode d’emploi, and his rehabilitation of the idea of arbitrariness, to outline some reflections about how an educational multiplicity, where “everything is in everything” could come to life (Rancière, 1991, p. 26). (shrink)

The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...) TPA - of the relation algebra reducts of $$\mathsf{TPA}$$ TPA ’s, as well. We prove that the equational theory of $$\mathsf{TPA}^-$$ TPA - is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)