The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Children's Fiction About 9/11: Ethnic, Heroic and National Identities

In this study, Lampert examines how cultural identities are constructed within fictional texts for young people written about the attacks on the Twin Towers. It identifi es three significant identity categories encoded in 9/11 books for children:ethnic identities, national identities, and heroic identities,arguing that the identities formed within the selected children’s texts are in flux, privileging performances of identities that are contingent on post-9/11 politics. Looking at texts including picture books, young adult fiction, and a selection of DC Comics, Lampert finds in post-9/11 children’s literature a co-mingling of xenophobia and tolerance; a binaried competition between good and evil and global harmony and national insularity; and a lauding of both the commonplace hero and the super-human. The shifting identities evident in texts that are being produced for children about 9/11 offer implicit and explicit accounts of what constitutes good citizenship, loyalty to nation and community, and desirable attributes in a Western post-9/11 context. This book makes an original contribution to the field of children’s literature by providing a focused and sustained analysis of how texts for children about 9/11 contribute to formations of identity in these complex times of cultural unease and global unrest.

Regulating roles of the use of the balanced scorecard in shaping corporate identities

The literature on corporate identity management suggests that managing corporate identity is a strategically complex task embracing the shaping of a range of dimensions of organisational life. The performance measurement literature and its applications likewise now also emphasise organisational ability to incorporate various dimensions considering both financial and non-financial performance measures when assessing success. The inclusion of these soft non-financial measures challenges organisations to quantify intangible aspects of performance such as corporate identity, transforming unmeasurables into measurables. This paper explores the regulatory roles of the use of the balanced scorecard in shaping key dimensions of corporate identities in a public sector shared service provider in Australia. This case study employs qualitative interviews of senior managers and employees, secondary data and participant observation. The findings suggest that the use of the balanced scorecard has potential to support identity construction, as an organisational symbol, a communication tool of vision, and as strategy, through creating conversations that self-regulate behaviour. The development of an integrated performance measurement system, the balanced scorecard, becomes an expression of a desired corporate identity, and the performance measures and continuous process provide the resource for interpreting actual corporate identities. Through this process of understanding and mobilising the interaction, it may be possible to create a less obtrusive and more subtle way to control “what an organisation is”. This case study also suggests that the theoretical and practical fusion of the disciplinary knowledge around corporate identities and performance measurement systems could make a contribution to understanding and shaping corporate identities.

Negotiating multiple identities between school and the outside world : A critical discourse analysis

This article examines interview talk of three students in an Australian high school to show how they negotiate their young adult identities between school and the outside world. It draws on Bakhtin’s concepts of dialogism and heteroglossia to argue that identities are linguistically and corporeally constituted. A critical discourse analysis of segments of transcribed interviews and student-related public documents finds a mismatch between a social justice curriculum at school and its transfer into students’ accounts of outside school lived realities. The article concludes that a productive social justice pedagogy must use its key principles of (con)textual interrogation to engage students in reflexive practice about their positioning within and against discourses of social justice in their student and civic lives. An impending national curriculum must decide whether or not it negotiates the discursive divide any better.

Certainties and uncertainties : ethics and professional identities of early childhood educators

This study is an inquiry into the professional identity constructions of early childhood educators, where identity is conceptualised as social and contextual. Through a genealogical analysis of narratives of four Queensland early childhood teachers, the thesis renders as problematic universal and fixed notions of what it is to be an early childhood professional. The data are the four teachers’ professional life history narratives recounted through a series of conversational interviews with each participant. As they spoke about professionalism and ethics, these teachers struggled to locate themselves as professionals, as they drew on a number of dominant discourses available to them. These dominant discourses were located and mapped through analysis of the participants’ talk about relationships with parents, colleagues and authorities. Genealogical analysis enabled multiple readings of the ways in which the participants’ talk held together certainties and uncertainties, as they recounted their experiences and spoke of early childhood expertise, relational engagement and ethics. The thesis concludes with suggestions for ways to support early childhood teachers and pre-service teachers to both engage with and resist normative processes and expectations of professional identity construction. In so doing, multiple and contextual opportunities can be made available when it comes to being professional and ‘doing’ ethics. The thesis makes an argument for new possibilities for thinking and speaking professional identities that include both certainty and uncertainty, comfort and discomfort, and these seemingly oppositional terms are held together in tension, with an insistence that both are necessary and true. The use of provocations offers tools through which pre-service teachers, teachers and teacher educators can access new positions associated with certainties and uncertainties in professional identities. These new positions call for work that supports experiences of ‘de-comfort’ – that is, experiences that encourage early childhood educators to step away from the comfort zones that can become part of expertise, professional relationships and ethics embedded within normative representations of what it is to be an early childhood professional.

“I am a secondary teacher and I teach history and SOSE” : negotiating pre-service teacher identities in times of curriculum change

Secondary social education in Australia is set to change with the new national history curriculum but integrated social education will continue in the middle years of schooling. Competing discourses of disciplinary and integrated social education approaches create new challenges for pre-service teachers as identification with a teaching area is an important aspect of developing a broader teacher identity. Feedback on a compulsory, final year curriculum studies unit revealed the majority of secondary pre-service teachers identified with at least one social science discipline. However, only a small number listed the integrated social education curriculum of Studies of Society and Environment (SOSE), even though SOSE was an essential part of their brief. More complex identities were revealed in post-teaching practice interviews. In times of curriculum change, attention to pre-service teachers’ disciplinary knowledge is critical in developing a stable subject identity.

Looking for Daisy : constructing teacher identities

Research on teacher identities is both important and increasing. In this forum contribution I re-interpret assertions about an African American science teacher’s identities in terms of Jonathon Turner’s (2002) constructs of role identity and sub-identity. I contest the notion of renegotiation of identities, suggesting that particular role identities can be brought to the foreground and then backgrounded depending on the situation and the need to confirm a sub-identity. Finally, I recommend the inclusion of teachers’ voices in identity research through greater use of co-authoring roles for teachers.