There is a growing recognition in society that more needs to be done to support LGBTQ youth in schools. In particular, school climate reports reveal that this need is particularly pressing for transgender individuals who are little understood and often rendered invisible or made to conform to gender-normative social standards. This mixed methods study surveyed and interviewed preservice teachers at three Catholic institutions. In particular, we focus on the shifting landscape of Catholic education in Canada as it relates to the (...) support of transgender youth. The content of the study is framed by a common first grade social studies theme: family diversity, and takes its lead from the recent papal urging to pursue topics of discomfort at the peripheries of Catholic thinking. We explore how Catholic preservice teachers respond to the idea of teaching about transgender-parent families. The findings show there is dissonance between the personal and professional beliefs of new Catholic teachers. This dissonance is reflective of the beliefs held by North American Catholics at large, thus further illuminating the challenges and opportunities that are present in the emerging discussion about how to best support transgender students in Catholic school contexts. (shrink)

We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an (...) extra condition such as continuity. (shrink)

The concept of school inclusion applied to disabled children knows an international distribution and is more or less used in national contexts, but with wide variations in interpretation. The concept of disability tends to be supplanted by other terms such as «special needs». These notional transformations are at the heart of the tensions that exist within the education system and also perform in their relations with various external partners, including experts of disability and parents. The major issues are those (...) of the educational finalities of the institutions and practices for these children: separate or common socialization, people development or acquisition of knowledge, perspectives of skilled labor or not etc. Among the possible approaches to the current problem, the first step is the analysis of the regulatory and institutional legislative, established in France for so-called «disabled» children. The second step is favored by the approach of ethnographic field which has the advantage of showing the representations and practices of actors in everyday life. The example developed is that of an elementary school in the city of Paris, which seeks to meet the challenge of hosting the difference while maintaining the goal of «academic excellence.» In this tension, how are teachers, specialists, parents, children with disabilities among their peers? What finally are the evolutions outlook? (shrink)

This article compares case studies to better understand how third grade teachers, serving low-income (including Title I) schools, adapted their instruction in the midst of a global pandemic to better support their students’ learning about locally-relevant civic issues. Civic perspective-taking components were embedded in the unit design with the aim of building deliberative, inclusive classrooms. The team designed lessons drawing from theories of culturally sustaining pedagogy. Using semi-structured interview data, we examined teachers’ reported thinking and perceptions about students’ needs and (...) their own struggles to deliver purposeful, equitable instruction. Findings indicate that as teachers collaboratively designed the lessons they discussed how to balance relevance and sensitivity in relation to content that mirrored students lived realities. This study advances our understanding of what challenges teachers overcome to integrate culturally-sustaining practices in their social studies instruction. (shrink)

A notation for an ordinal using patterns of resemblance is based on choosing an isominimal set of ordinals containing the given ordinal. There are many choices for this set meaning that notations are far from unique. We establish that among all such isominimal sets there is one which is smallest under inclusion thus providing an appropriate notion of normal form notation in this context. In addition, we calculate the elements of this isominimal set using standard notations based on collapsing (...) functions. This provides a capstone to the results in [2, 6, 8, 9, 7], using further refinement of ordinal arithmetic developed in [8] which then both allows for a simple characterization of normal forms for patterns of order one and will play a key role in the arithmetical analysis of pure patterns of order two, [5]. (shrink)

This report summarises a study examining preservice elementary teachers? geometry content knowledge with a focus on parallelogram. It was a descriptive study examining 45 preservice teachers? reasoning in the process of determining which quadrilateral can be classified as a parallelogram. Findings have revealed that these elementary teachers do not possess sound understanding of parallelogram and class inclusion between parallelogram and trapezoid at the expected level.

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show (...) that the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo—Fraenkel set theory (IZF). (shrink)

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions . As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show (...) that the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo-Fraenkel set theory. (shrink)

This article is based on a five-year action-research project implemented in elementary school in Mauritius, which mobilized members of the educational community as well as various partners, and which revealed the challenges and stakes of a pedagogical experimentation that promotes well-being in the perspective of an inclusive educational community. The qualitative and quantitative survey that mobilized the different actors made it possible to measure the impacts of the experimentation, particularly on the school environment, the well-being of the children and (...) that of the teachers. It also showed that the successful implementation of such an educational innovation was correlated to the consideration and support of all school stakeholders: students and their families, teachers and their supervisors, and outside contributors. (shrink)

This study aims to explore the level of information and knowledge 150 Spanish kindergarten and elementary school teachers in pre-service training have about human rights. We compared two groups of students: students with no specific training and students with specific training (the students with specific training study with the new training teaching programme that includes a compulsory subject related to citizenship education). The contents are organized around three thematic areas. Human rights are included in the first area ‘Basic concepts (...) to promote equality and participation in Elementary Education’; the other two areas are: ‘Learning to participate at Elementary School’ and ‘Building a civil school that promotes equality and participation at Elementary School’. It is a one semester subject with 3 h of teaching per week. The main hypothesis is that a specific training on human rights will lead to an important improvement not only in student’s level of knowledge but also in the way they categorize this specific content. We have administered a questionnaire designed for the study. In general, our results show that students of both groups have a basic and limited knowledge about human rights. The group with specific training shows a higher level of knowledge than the other group and a different way of organizing it. This would go in the direction of other studies of supporting and reinforcing the inclusion of specific training on human rights during the initial teacher training programmes at the university. (shrink)

We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and (...) prove that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k. (shrink)

C. U. Jensen suggested the following construction, starting from a field $K: K_0 = K, K_{\alpha + 1} = K_\alpha ((X_\alpha)), K_\alpha = \bigcup K_\beta$ if $\alpha$ is limit and asked when two fields $k_\alpha$ and $K_\beta$ are equivalent. We give a complete answer in the case of a field $K$ of characteristic 0.

Foucault’s sodomite’: Damian’s Liber gomorrhianus (1049) reopened. Taking Michel Foucault’s famous statement about the difference between the ‘Medieval sodomite’ and the heteronormative ‘19th century homosexual’ as its cue, this article surveys the discursive source of that statement in the work of Peter Damian (1007–1072) with regard to his obscure, yet consequential text, Liber gomorrhianus (presented in 1049 to Pope Leo IX, preceding the Council of Reims). Drawing on the recent research by Ranft and because Damian is such an understated figure (...) in the corpus of Medieval philosophy, an overview of Damian’s life and work is presented, especially in terms of Damian’s 11th century reforming labour ethics. Only then the article proceeds to reopen Damian’s text, indicating that the ‘Medieval sodomite’ is far removed from an elementary precursor to the modern scientia sexualis homosexual, but is indeed presented by Damian as a complex and gender-inclusive licentious person, within the context of the disintegration of sexual morality (especially within the domains of celibacy and confession) in the middle to late 11th century church and monasteries. Cross-referencing the own translation of the Latin text with the translation of Payer, the article disseminates and critiques the key concepts in Damian’s argument for the summarily deposition of lapsi [fallen priests] and the expulsion of promiscuous monks (and nuns) from the orders, especially with regard to Damian’s concepts of contra-natural and irrational fornication. Pope Leo’s deeply pastoral and insightful answer to Damian ( Ad splendidum nitentis ) is presented in the last part of the article, including his sanctioning of Damian’s complex concept of sodomy, which on that ground, became the conceptual source for the council of Reims (1049), and subsequent Medieval councils dealing with the ‘problem of sodomy’ in the church and monasteries. The canons of those councils were indeed the source of Foucault’s analysis of Medieval sexuality – yet the more fundamental source was Damian’s obscure text. (shrink)

Like Kant at his time, Jürgen Habermas wants to encourage the reader to use his „reasonable liberty“. There is no doubt, that the philosophical positions of Kant on the one hand and of Hegel on the other hand hold, until today, a key role in the development of the „discourse of modern age“. In order to oppose a short-circuited synthesis of both systems, which are obliged to the idea of liberty quite differently, this essay demonstrates the substantial differences regarding to (...) elementary concepts like peculiarity of the individual will, law and legislation, people and sovereignty of the people. That both philosophers differ in their interest of questioning becomes quite clear regarding to the citizen/state relation. While Hegel tries to describe the reality of the state as a „moral universe“ and therefore as „reality of reason“, Kant is interested in knowing about the potential state togetherness of individuals which have experienced in them the „radical evil“. The differences concerning the estimation of the „subjective“ individual will in its relationship to the „objective“ will of „generality“, concerning also the (Rousseauian) concept of contract and the citizens as „co-legislators“ are culminating in the relationship between „law“ and „morality“. Whereas Kant (wrongly) ignores ethos and history, Hegel is lacking the concept of „intersubjective communication“ (so Habermas states). From both insufficiencies conclusions are resulting which are important for coping with the actual difficulties with „inclusion“ and „integration“. (shrink)

Purpose: According to literature, students' attitudes towards peers with disabilities are crucial for the social inclusion of students with disabilities.Therefore, knowledge about students' behavioral intention to interact with peers with intellectual disability can help improve the social inclusion of students with ID. This study aimed to examine the psychometric properties of the Arabic version of the Behavioral Intention to Interact with Peers with Intellectual Disability Scale.Data were collected from 887 elementary school students (591 female and 296 male) (...) from third to sixth grades in Saudi Arabia.Psychometric properties of the BIS were examined with a confirmatory factor analysis, measurement invariance analysis (across gender), and reliability scales (internal consistency).The results supported the two-dimensional structure of the BIS. The internal consistency of the BIS and each of its subscales was good.Furthermore, no measurement variance was found for male and female students.The Arabic version of the scale showed good psychometric properties and therefore can be recommended to measure students' behavioral intention to interact with peers with intellectual disability. (shrink)

Where do we come from? Are we merely a cluster of elementary particles in a gigantic world receptacle? And what does it all mean? In this highly original new book, the philosopher Markus Gabriel challenges our notion of what exists and what it means to exist. He questions the idea that there is a world that encompasses everything like a container life, the universe, and everything else. This all-inclusive being does not exist and cannot exist. For the world itself (...) is not found in the world. And even when we think about the world, the world about which we think is obviously not identical with the world in which we think. For, as we are thinking about the world, this is only a very small event in the world. Besides this, there are still innumerable other objects and events: rain showers, toothaches and the World Cup. Drawing on the recent history of philosophy, Gabriel asserts that the world cannot exist at all, because it is not found in the world. Yet with the exception of the world, everything else exists; even unicorns on the far side of the moon wearing police uniforms. Revelling in witty thought experiments, word play, and the courage of provocation, Markus Gabriel demonstrates the necessity of a questioning mind and the role that humour can play in coming to terms with the abyss of human existence. (shrink)

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest (...) modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. (shrink)

This paper investigates what choices teachers made and what rationales they offered related to the inclusion and exclusion of primary source photographs for a hypothetical unit about the U.S. Civil Rights Movement in order to better understand teachers’ curricular decision-making as it relates to representing the histories of oppressed people. Elementary and secondary social studies/history teachers from three different in-service and pre-service cohorts ( n=62) selected and discarded images from a bank of 25 famous and lesser-known photographs. Their (...) decisions and explanations were coded for emergent themes. Findings reveal that these teachers tended to be guided by criteria both technical (how they might teach using a particular photograph) and philosophical (why they might teach about a particular photograph), with narrow definitions of what they deemed relevant and appropriate for their students. Their choices constructed a sanitized narrative of the Civil Rights Movement that largely avoided a discussion of racism. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such (...) is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object . Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such (...) is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object. Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

In this fascinating new book, Affrica Taylor encourages an exciting paradigmatic shift in the ways in which childhood and nature are conceived and pedagogically deployed, and invites readers to critically reassess the naturalist childhood discourses that are rife within popular culture and early years education.Through adopting a common worlds framework, Reconfiguring the Natures of Childhood generates a number of complex and inclusive ways of seeing and representing the early years. It recasts childhood as:messy and implicated rather than pure and innocent; (...) situated and differentiated rather than decontextualized and universal; entangled within real world relations rather than protected in a separate space.Throughout the book, the author follows an intelligent and innovative line of thought which challenges many pre-existing ideas about childhood. Drawing upon cross-disciplinary perspectives, and with international relevance, this book makes an important contribution to the field of childhood studies and early childhood education, and will be a valuable resource for scholars, postgraduate students and higher education teachers. (shrink)

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest (...) modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. (shrink)

Relations of belonging are at the heart of biopolitical analysis. They determine, at the biological level, who is included in the polis and who is excluded from it. More abstractly, belonging is the conceptual mechanism of classification. By examining the specific relations of belonging within the biopolitical paradigms of four key works – Durkheim’s Elementary Forms of Religious Life, Girard’s Violence and the Sacred, Agamben’s Homo Sacer, and Esposito’s Bios – this article will highlight the dynamic of classification at (...) the heart of each. Doing so will make the question of belonging explicit and render the dialectic of inclusion/exclusion visible. More than simply emphasizing the centrality of belonging to biopolitical analysis, this article will demonstrate that any politic over life must ignore and deny an originary politic of life. Returning biopolitics to the question of belonging thus entails the affirmation of relation and the positive association of life itself. (shrink)

We show, for any ordinal γ ≥ 3, that the class RaCAγ is pseudo-elementary and has a recursively enumerable elementary theory. ScK denotes the class of strong subalgebras of members of the class K. We devise games, Fⁿ (3 ≤ n ≤ ω), G, H, and show, for an atomic relation algebra A with countably many atoms, that Ǝ has a winning strategy in Fω(At(A)) ⇔ A ∈ ScRaCAω, Ǝ has a winning strategy in Fⁿ(At(A)) ⇐ A ∈ (...) ScRaCAn, Ǝ has a winning strategy in G(At(A)) ⇐ A ∈ RaCAω, Ǝ has a winning strategy in H(At(A)) ⇒ A ∈ RaRCAω for 3 ≤ n < ω. We use these games to show, for γ ≥ 5 and any class K of relation algebras satisfying RaRCAγ ⊆ K ⊆ ScRaCA₅, that K is not closed under subalgebras and is not elementary. For infinite γ, the inclusion RaCAγ ⊂ ScRaCAγ is strict. For infinite γ and for a countable relation algebra A we show that A has a complete representation if and only if A is atomic and Ǝ has a winning strategy in F(At(A)) if and only if A is atomic and A ∈ ScRaCAγ. (shrink)

We investigate a certain system of intuitionistic set theory from three points of view: an elementary set theory with bounded separation, a topos with distinguished inclusions, and a category of classes with a system of small maps. The three presentations are shown to be equivalent in a strong sense.

This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control (...) theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples.This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists. (shrink)

Despite changes in their representation and visibility, there are still serious concerns about the inclusion and day-to-day workplace challenges various groups face (e.g., women, ethnic and cultural minorities, LGBTQ+, people as they age, and those dealing with physical or mental disabilities). Men are also underrepresented in specific work fields, in particular those in HEED (Health care, Elementary Education and the Domestic sphere). Previous literature has shown that group stereotypes play an important role in maintaining these inequalities. We outline (...) how insights from research on stigma, social-identity, and self-regulation together increase our understanding of how targets are affected by and regulate negative stereotypes in the workplace. This approach starts from the basis that members of negatively-stereotyped groups are not just passive recipients of negative attitudes, stereotypes, and behaviors, but are active individuals pursuing multiple goals, such as goals for belonging and achievement. We argue that it is only by understanding stigma from the target’s perspective (e.g., how targets are affected and respond) that we can successfully address workplace inequality. Key in this understanding is that stereotypes, prejudice and discrimination have taken on much more subtle forms, with consequences for the way members of stigmatized-groups cope. These insights lead us to propose an approach to understanding barriers to workplace equality that highlights four key aspects: a) the different (often subtle) potential triggers of identity-threat in the workplace for members of stigmatized-groups, b) the ways in which members of stigmatized-groups cope with these threats, c) the role of supportive factors that mitigate potential threats and affect self-regulation, and d) potential hidden costs for the self or others of what appears at first to be effective self-regulation. The focus on threats, coping, support, and potential hidden costs helps us understand why current diversity efforts are not always successful in increasing and maintaining members of stigmatized-groups in organizations, and provides insight into how we can aid efforts to effectively lower barriers to workplace equality. (shrink)

Although there is broad support in the current Brazilian legislation and many curricular documents published in the last three decades, we still face the challenge of the inclusive education in our classrooms. This is a qualitative research in which we investigate the perception of three school pedagogical coordinators about the inclusion of disabled children in regular classes of Elementary and High School of the schools that self-declared favorable to the Inclusive Education. The results suggest perceptions of Inclusive Education (...) with specific goal to comply with current legislation, which aims exclusively at the socialization of the disabled as a target of charity, without great teaching learning goals that allow equal access to school knowledge and continuity of study in the educational system. (shrink)

ArgumentA Catoptrica attributed to Euclid appears in manuscripts amongst treatises dealing with elementary astronomy. Despite this textual background, the treatise has always been read literally as a theory of mirrors, and its astronomical significance has gone unnoticed. However, optics, catoptrics, and astronomy appear strongly intermingled in sources such as, amongst others, Geminus, Theon of Smyrna, Plutarch and Cleomedes. If one compares the optical reasoning put forward in these sources to account for the formation of moonlight with arguments of Catoptrica, (...) one is able to shed new light on several principles and propositions of Catoptrica, some of which had been deemed corrupt, meaningless, and obscure. Moreover, the present analysis offers a glimpse at the context of a specific stage in the evolution of ancient catoptrics: Whether literally or by analogy, several of its results appear to have been set against a wider astronomical background, which explains the inclusion of Catoptrica in the group of texts loosely defined as “little astronomy.”. (shrink)

In truth-functional analysis we need not worry about the purported ambiguity of the English ‘or,’ for we can assign different symbols and define each by means of a truth table. However, at least in classes in elementary logic, we often try to indicate that there is some rationale to the assignation of truth values by marshaling English disjunctive sentences which will clearly render an inclusive or an exclusive reading, without the explicit addition of one of the qualifying phrases, “or (...) both” or “but not both.” At this point one discovers people writing on logic saying quite different things about the English ‘or.’ In his Methods of Logic Quine takes the inclusive sense to be the more naturally intended and claims that “indisputable instances of the exclusive use” are rare. Yet in The Principles of Logic Bradley says that no one ever really intends to use ‘or’ in any other than an exclusive sense; and Bosanquet followed him in this. In this paper I am interested in attempting to discover why the British Idealists held that ‘or’ is always exclusive, especially in the face of various examples which, prima facie, establish both uses in English. Why would Bradley feel compelled to deny “any possible instance in which alternatives are not exclusive”? As it turns out, the position held by Bradley and Bosanquet is stronger and more interesting than one initially expects. (shrink)

Leibniz propôs que demonstrações fossem reformuladas como deduções a partir de identidades, e que proposições do tipo A = A fossem a fonte única de verdade. Neste artigo, procuro explicar essa teoria da prova (e do conhecimento), assim como seus conceitos elementares, ou seja, os conceitos de identidade, verdade (ou possibilidade) e proposição (inclusive a teoria leibniziana da redutibilidade a proposições sujeito-predicado). Leibniz proposed that demonstrations be reformulated as deductions from identities, and that propositions of the type A = A (...) be the only source of truth. In this article, I aim to explain this theory of proof (and knowledge), as well as its elementary concepts, such as identity, truth (or possibility) and proposition (including Leibniz's theory of reducibility of propositions to subject-predicate form). (shrink)

Ludwik Borkowski has constructed a quantifier-less calculus of names (BRN1), which is regarded as a base system here. The system can be extended with the use of the deductive power of rules of introduction and omission of functors π and σ (BRN2), which serve here as the substitutes of quantifiers. If we adopt the extensionality rule for the functor of singular inclusion (REε), we obtain yet another extending of the system (BRN3) accompanied by simultaneous considerable reduction of the primary (...) rules. The interpretation of the last system in elementary ontology is included. (shrink)

Considerable evidence supports that preschool education is a milestone stage for children. Nonetheless, systematic preschool gifted education programs rarely exist in public elementary schools. The current study explored the perceptions of 16 preschool teachers from seven public schools in Abu Dhabi, United Arab Emirates regarding their views about various components of gifted education for preschool children. Qualitative analyses, using the inductive data analysis method, revealed several themes such as the concept and identification of giftedness, characteristics of gifted preschoolers, preschoolers’ (...) problem-solving skills, the communication and social skills of gifted preschoolers, resources/services offered by the school to serve gifted preschoolers, enrichment programs available for gifted preschoolers, inclusive education for gifted preschoolers, twice-exceptional preschoolers, and governmental support. The results of this study may help advocate for infusing more services and programs related to the identification and education of gifted preschoolers in public schools. The findings identified the need to have an abundance of assessment tools and enrichment programs that can empower preschool teachers to cater for giftedness. (shrink)

During the second half of the 20th century education has been recognized as a human right in several international conventions, and the UN also holds that “Education shall be free” and that “Elementary education shall be compulsory” (UN, 1948, Article 26). The education-as-a-human right-project could be viewed as a good intention of global inclusion in recognizing that all individuals have a right to education in virtue of being humans, and the idea of education as a human right thus (...) has a tremendous global significance. However, if we look at this more critically, the education-as-a-human right-project, may not only be grounded in altruistic good intensions for the disadvantaged. The term “elementary education”, or sometimes “primary education”, which is used in several human rights-documents seems to suggest that it is some sort of formalized education. It would be useful however to make a distinction between formal and informal education, as well as between teaching, learning, education and schooling, in the discussion of the right to education and specifically in the discussion concerning education as a “human right”. There is obviously a difference between the right to teach, the right to learn, the right to education and the right to schooling. And how are these rights related to compulsory schooling, compulsory education and the supposed duty to teach and duty to learn? A further concern is what makes this a human right rather than for example a juridical right as a citizen. By addressing these questions within a theoretical framework of social ontology and ameliorative conceptual analysis I believe that we can find new ways of dealing with fundamental problems within philosophy of education such as the nature, purpose and aims of education as well as the right to education. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 21.1 (2001) 63-67 [Access article in PDF] A Buddhist Reflects (Practices Reflection) on Some Christians' Reflections on Buddhist Practices Grace Burford Prescott College A tourist lost in New York City asks of a passerby, "How do I get to Carnegie Hall?"The musically inclined informant replies, "Practice, practice, practice!" Often people who have just heard I am a college professor with a specialty in Buddhism ask me "Are (...) you a practicing Buddhist?" This question has always stumped me. My most common retort (it's not really an answer), "I keep practicing; maybe someday I'll get it right," both evades and critiques the question. As we use the term in everyday conversation, "practice" generally means disciplined repetition of an activity, usually in preparation for a performance of some kind. In relation to a religious path, "practice" usually refers to the integration of certain prescribed actions (practices) in one's life. My retort derives from the mixing of these two meanings of the word "practice," and the assumption that--for one reason or another--religious practice does not lead to a perfect performance in the spiritual equivalent of Carnegie Hall.The form of the question puzzles me. Why do they ask about my practice? Why not just ask me "Are you a Buddhist?" I think they expect to discover that I engage in a Buddhist equivalent of going to church. Maybe the inclusion of practice in the question indicates anticipation of some level of earnestness, of application of my self/energy/time in service of my religion--some outward, observable manifestation of my religious orientation, above and beyond just teaching college students about this religion. Perhaps they expect me to confess to being a vegetarian, or meditating, or chanting, or attending Buddhist services of some kind. Although I find the question somewhat intrusive, I understand that most often it arises from well-meaning curiosity, if not genuine interest, and I try to follow my retort with something more pedagogically effective.For most of my life, practice has been about music. I sang before I talked; I began to study piano at an early age; in elementary school I took up guitar and clarinet; in high school I started voice lessons. Learning to play all of these instruments required [End Page 63] practice. Recently, I took up the electric bass guitar, and I'm back to daily practicing. Practice does produce something; it is linearly causal. If I practice my instrument, I get better at producing the sounds I want to produce. Only a nonmusician would say this does not amount to a real accomplishment. At the same time, the activity one practices is the same activity one hopes to perform: I play the bass when I practice, in order to be able to play the bass. Still, I must practice--to get where I want to go, to improve the quality of my playing. After all, I first heard the Carnegie Hall joke from my guitar teacher, who told it both to amuse me and to inspire me to practice, practice, practice. At about the same time, author Catherine Drinker Bowen advised a group of us high school students that--based on her experiences growing up in a family full of musicians--the most effective way to learn an instrument is to fall in love with one's music teacher. In other words, desire serves the crucial function of inspiring one to practice. Yet I know that the same desire that motivates me to practice so that I can play more skillfully (as in "practice makes perfect") can hold me back if I focus on that future desired skillful playing (the "perfection") instead of the present moment of my playing. Further, I can practice to the point of technical expertise--I can accomplish that skill level I am aiming for in practice--and still not produce the musical quality I aspire to play. Practice does produce something necessary, but that something does not suffice. Musicians are no better at naming that other necessary ingredient than are... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 21.1 (2001) 63-67 [Access article in PDF] A Buddhist Reflects (Practices Reflection) on Some Christians' Reflections on Buddhist Practices Grace Burford Prescott College A tourist lost in New York City asks of a passerby, "How do I get to Carnegie Hall?"The musically inclined informant replies, "Practice, practice, practice!" Often people who have just heard I am a college professor with a specialty in Buddhism ask me "Are (...) you a practicing Buddhist?" This question has always stumped me. My most common retort (it's not really an answer), "I keep practicing; maybe someday I'll get it right," both evades and critiques the question. As we use the term in everyday conversation, "practice" generally means disciplined repetition of an activity, usually in preparation for a performance of some kind. In relation to a religious path, "practice" usually refers to the integration of certain prescribed actions (practices) in one's life. My retort derives from the mixing of these two meanings of the word "practice," and the assumption that--for one reason or another--religious practice does not lead to a perfect performance in the spiritual equivalent of Carnegie Hall.The form of the question puzzles me. Why do they ask about my practice? Why not just ask me "Are you a Buddhist?" I think they expect to discover that I engage in a Buddhist equivalent of going to church. Maybe the inclusion of practice in the question indicates anticipation of some level of earnestness, of application of my self/energy/time in service of my religion--some outward, observable manifestation of my religious orientation, above and beyond just teaching college students about this religion. Perhaps they expect me to confess to being a vegetarian, or meditating, or chanting, or attending Buddhist services of some kind. Although I find the question somewhat intrusive, I understand that most often it arises from well-meaning curiosity, if not genuine interest, and I try to follow my retort with something more pedagogically effective.For most of my life, practice has been about music. I sang before I talked; I began to study piano at an early age; in elementary school I took up guitar and clarinet; in high school I started voice lessons. Learning to play all of these instruments required [End Page 63] practice. Recently, I took up the electric bass guitar, and I'm back to daily practicing. Practice does produce something; it is linearly causal. If I practice my instrument, I get better at producing the sounds I want to produce. Only a nonmusician would say this does not amount to a real accomplishment. At the same time, the activity one practices is the same activity one hopes to perform: I play the bass when I practice, in order to be able to play the bass. Still, I must practice--to get where I want to go, to improve the quality of my playing. After all, I first heard the Carnegie Hall joke from my guitar teacher, who told it both to amuse me and to inspire me to practice, practice, practice. At about the same time, author Catherine Drinker Bowen advised a group of us high school students that--based on her experiences growing up in a family full of musicians--the most effective way to learn an instrument is to fall in love with one's music teacher. In other words, desire serves the crucial function of inspiring one to practice. Yet I know that the same desire that motivates me to practice so that I can play more skillfully (as in "practice makes perfect") can hold me back if I focus on that future desired skillful playing (the "perfection") instead of the present moment of my playing. Further, I can practice to the point of technical expertise--I can accomplish that skill level I am aiming for in practice--and still not produce the musical quality I aspire to play. Practice does produce something necessary, but that something does not suffice. Musicians are no better at naming that other necessary ingredient than are... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 21.1 (2001) 63-67 [Access article in PDF] A Buddhist Reflects (Practices Reflection) on Some Christians' Reflections on Buddhist Practices Grace Burford Prescott College A tourist lost in New York City asks of a passerby, "How do I get to Carnegie Hall?"The musically inclined informant replies, "Practice, practice, practice!" Often people who have just heard I am a college professor with a specialty in Buddhism ask me "Are (...) you a practicing Buddhist?" This question has always stumped me. My most common retort (it's not really an answer), "I keep practicing; maybe someday I'll get it right," both evades and critiques the question. As we use the term in everyday conversation, "practice" generally means disciplined repetition of an activity, usually in preparation for a performance of some kind. In relation to a religious path, "practice" usually refers to the integration of certain prescribed actions (practices) in one's life. My retort derives from the mixing of these two meanings of the word "practice," and the assumption that--for one reason or another--religious practice does not lead to a perfect performance in the spiritual equivalent of Carnegie Hall.The form of the question puzzles me. Why do they ask about my practice? Why not just ask me "Are you a Buddhist?" I think they expect to discover that I engage in a Buddhist equivalent of going to church. Maybe the inclusion of practice in the question indicates anticipation of some level of earnestness, of application of my self/energy/time in service of my religion--some outward, observable manifestation of my religious orientation, above and beyond just teaching college students about this religion. Perhaps they expect me to confess to being a vegetarian, or meditating, or chanting, or attending Buddhist services of some kind. Although I find the question somewhat intrusive, I understand that most often it arises from well-meaning curiosity, if not genuine interest, and I try to follow my retort with something more pedagogically effective.For most of my life, practice has been about music. I sang before I talked; I began to study piano at an early age; in elementary school I took up guitar and clarinet; in high school I started voice lessons. Learning to play all of these instruments required [End Page 63] practice. Recently, I took up the electric bass guitar, and I'm back to daily practicing. Practice does produce something; it is linearly causal. If I practice my instrument, I get better at producing the sounds I want to produce. Only a nonmusician would say this does not amount to a real accomplishment. At the same time, the activity one practices is the same activity one hopes to perform: I play the bass when I practice, in order to be able to play the bass. Still, I must practice--to get where I want to go, to improve the quality of my playing. After all, I first heard the Carnegie Hall joke from my guitar teacher, who told it both to amuse me and to inspire me to practice, practice, practice. At about the same time, author Catherine Drinker Bowen advised a group of us high school students that--based on her experiences growing up in a family full of musicians--the most effective way to learn an instrument is to fall in love with one's music teacher. In other words, desire serves the crucial function of inspiring one to practice. Yet I know that the same desire that motivates me to practice so that I can play more skillfully (as in "practice makes perfect") can hold me back if I focus on that future desired skillful playing (the "perfection") instead of the present moment of my playing. Further, I can practice to the point of technical expertise--I can accomplish that skill level I am aiming for in practice--and still not produce the musical quality I aspire to play. Practice does produce something necessary, but that something does not suffice. Musicians are no better at naming that other necessary ingredient than are... (shrink)

Human rights have increasingly come to the center of political and social philosophy since 1945. The have been widely discussed in publications on topical human rights issues, in the work of some of the most notable philosophers of the time like Jürgen Habermas and John Rawls, and in volumes on global justice. But, despite Habermas work in Diskurs Ethik, discussion ethics has never clearly been presented as a normative ethical theory in competition with the classical rivals such as utilitarianism and (...) Kantian ethics. This paper makes a clear, concise case recognition of human rights ethics as a contemporary normative ethical theory, and for its inclusion in future elementary textbooks. Universal legal human rights protect the central ethical human right to freedom of expression. Human Rights Ethics supersedes classical theories based on evident first principles because these principles are either merely asserted without justification or are justified by being superseded by the final self-justifying standard of definable ethical discussion. The very refutation of human rights ethics could be sound only through ethical discussion, with all parties exercising the ethical, but not yet universally legal, right to freedom of expression. Hence the refutation of the ethical right to freedom of expression cannot be sound. (shrink)

The purpose of our article is to investigate and report on a document analysis study of social studies education in Argentina. In particular, our focus is on the progression of citizenship education and the inclusion of global perspectives in social studies education within Argentina's elementary schools. Like many other countries in the world, Argentina has followed a growing trend to include global perspectives in their national curricula. We investigate the contours of what this entails for Argentina's elementary (...) schools. We begin the article by situating our purpose in the larger field of global citizenship education. Next, we review the literature and describe Argentina's socio-historical context and report on how that context informs Argentina's education system. We then move to the study's methodology, which is grounded in the following research questions: (1) How is social studies organized in Argentina and how has the purpose of social studies evolved over time? (2) To what degree, if any, are global perspectives represented in Argentina's elementary social studies curricula? To address these questions, we employ document analysis research design (Bowen, 2009). In this analysis, we review Argentina's education policy documents and social studies curricular documents. We follow Fereday and Muir-Cochrane's (2006) three-prong approach for data analysis of documents. We share the findings of the research based on the aforementioned questions. We conclude the article with a discussion of how environmental awareness, human rights, and global competencies are included in the initiative to increase global citizenship education within Argentina's social studies curricula. (shrink)

Abstract:This essay explores performance-driven aspects of U.S. bands in the contexts of Pierre Hadot’s Philosophy as a Way of Life, Lewis Carroll’s Alice’s Adventures in Wonderland, Jacques Derrida’s Aporias, and the author’s experience teaching both elementary general music and beginning band. The author wonders what band education might look like when the profession’s fixation on futuristic performances and allegiances to past traditions are laid aside; the article proposes that the profession of band might benefit from a more present-focused, process-oriented (...) approach to making music, akin to that of the general music classroom setting. The author advocates for a deeper engagement in critical dialogue around the role tradition plays in current band education practices in ways that reach toward inclusive, present-focused music making. (shrink)

In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the φ4 model and (...) demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ4 and φ6 cases since they provide the most realistic models of elementary particles. (shrink)

For successful application of educational inclusive concept, next to the material and technical requirements, of high importance is also the quality and improvement of educational practice, education and competence of all participants in the educational process. Teachers are crucial part of the educational process so their acquired knowledge and skills are of great importance for the success of the inclusive education. Aim of this paper was to determine geography teacher’s attitudes towards working with pupils with developmental difficulties. For the purpose (...) of the research survey was conducted including geography teachers in elementary and secondary schools in Croatia. Research results indicate that teachers do not consider themselves educated enough neither competent for everyday work with pupils with developmental difficulties and they express the need for additional education. In their school work they try to adopt teaching materials and methods according to children’s difficulties. Cooperation with school professional and pedagogical service and parents is one of the main preconditions for successful teaching. There are significant differences in teacher’s attitudes in elementary in relation to ones in secondary schools. (shrink)

In a fluent, easy-to-read style, Frondizi presents a useful, elementary analysis of the nature of value; the basic problems of value theory; an historical survey of the various solutions to these problems; and finally, his own theory concerning the answers to these issues. The basic problem of axiology is exposed by the author as the dilemma between subjectivism and objectivism. It is in this frame of reference that the views of R. B. Perry, Wittgenstein, Carnap, Ayer, and Russell are (...) briefly outlined as examples of subjectivist doctrines. The material apriorism of Max Scheler is described in detail as illustrative of objectivism. Because the theories of Scheler are not too well-known among English-speaking philosophers, the exposition of his doctrines by Frondizi in this text are particularly useful and interesting. Between the Scylla of 'de gustibus non est disputandum' and the Charybdis of absolute standards of value Frondizi asserts the theory that "value is a Gestalt quality, the synthesis of objective and subjective contribution, and which exists and has meaning only in concrete human situations." Value is viewed as open-ended--able to be "furthered by the constant exercise of man's imagination, intelligence and action." Although it may be an open question as to whether the notion of Gestalt somehow resolves basic problems in axiology, it is, nevertheless, interesting to consider Frondizi's account. The book is also useful for its inclusion of a bibliography at the end of each chapter.--S. C. (shrink)