Teaching English as an additional language in senior high school : critical discourses in critical times

This paper presents a Critical Discourse Analysis (CDA) of four policy documents currently offering ‘sets of possibilities’ for the teaching of English as an additional or second language (hereafter EAL/ESL) in senior classrooms in Queensland, Australia. The aim is to identify the ways in which each document re-presents the notion of critical literacy. Leximancer software, and Fairclough’s textually-oriented discourse analysis method (2001, 2003) are used to interrogate the relevant sections of the documents for the ways in which they re-present (sic) and construct the discourses around critical language study. This paper presents the description, interpretation and explanation of the discourses in these documents which constitute part of a larger project in which teacher interviews and classroom teaching are also investigated for the ways in which ‘the critical’ is constructed and contested in knowledge and practice.

The politics of literacy in David Almond and Dave McKean’s "The Savage" (2008)

Competency in language and literacy are central to contemporary debates about education in Anglophone nations around the world. This paper suggests that such debates are informing not just educational policy but children’s literature itself as can be seen in Almond and McKean’s The Savage. This hybrid text combines prose and graphic narrative and narration in order to tell the story of Blue, a young British boy negotiating his identity in the aftermath of his father's death. While foregrounding a narrative of ideal masculinity, The Savage enacts and privileges a formal and thematic ideal of literacy as index of individual agency and development. Almond and McKean produce a politicised understanding of language and literacy that simultaneously positions The Savage in a textual tradition of socio-culturally disenfranchised youth, and intervenes in that tradition to (perhaps ironically) affirm the very conditions previously critiqued by that very tradition. Where earlier authors such as Barry Hines sought to challenge normative accounts of language and literacy in order to indict educational policy and praxes, Almond and McKean work to naturalise the very logics of education and agency by which their protagonist has been disenfranchised. In doing so, The Savage exemplifies current approaches to education which claim to value social and cultural diversity while imposing national standardised testing predicated on assumptions about the legitimacy of uniform standards and definitions of literacy.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

The impact of outcomes-driven curriculum reform on teacher perspectives of professional practice

This thesis is the result of an investigation of a Queensland example of curriculum reform based on outcomes, a type of reform common to many parts of the world during the last decade. The purpose of the investigation was to determine the impact of outcomes on teacher perspectives of professional practice. The focus was chosen to permit investigation not only of changes in behaviour resulting from the reform but also of teachers' attitudes and beliefs developed during implementation. The study is based on qualitative methodology, chosen because of its suitability for the investigation of attitudes and perspectives. The study exploits the researcher's opportunities for prolonged, direct contact with groups of teachers through the selection of an over-arching ethnography approach, an approach designed to capture the holistic nature of the reform and to contextualise the data within a broad perspective. The selection of grounded theory as a basis for data analysis reflects the open nature of this inquiry and demonstrates the study's constructivist assumptions about the production of knowledge. The study also constitutes a multi-site case study by virtue of the choice of three individual school sites as objects to be studied and to form the basis of the report. Three primary school sites administered by Brisbane Catholic Education were chosen as the focus of data collection. Data were collected from three school sites as teachers engaged in the first year of implementation of Student Performance Standards, the Queensland version of English outcomes based on the current English syllabus. Teachers' experience of outcomes-driven curriculum reform was studied by means of group interviews conducted at individual school sites over a period of fourteen months, researcher observations and the collection of artefacts such as report cards. Analysis of data followed grounded theory guidelines based on a system of coding. Though classification systems were not generated prior to data analysis, the labelling of categories called on standard, non-idiosyncratic terminology and analytic frames and concepts from existing literature wherever practicable in order to permit possible comparisons with other related research. Data from school sites were examined individually and then combined to determine teacher understandings of the reform, changes that have been made to practice and teacher responses to these changes in terms of their perspectives of professionalism. Teachers in the study understood the reform as primarily an accountability mechanism. Though teachers demonstrated some acceptance of the intentions of the reform, their responses to its conceptualisation, supporting documentation and implications for changing work practices were generally characterised by reduced confidence, anger and frustration. Though the impact of outcomes-based curriculum reform must be interpreted through the inter-relationships of a broad range of elements which comprise teachers' work and their attitudes towards their work, it is proposed that the substantive findings of the study can be understood in terms of four broad themes. First, when the conceptual design of outcomes did not serve teachers' accountability requirements and outcomes were perceived to be expressed in unfamiliar technical language, most teachers in the study lost faith in the value of the reform and lost confidence in their own abilities to understand or implement it. Second, this reduction of confidence was intensified when the scope of outcomes was outside the scope of the teachers' existing curriculum and assessment planning and teachers were confronted with the necessity to include aspects of syllabuses or school programs which they had previously omitted because of a lack of understanding or appreciation. The corollary was that outcomes promoted greater syllabus fidelity when frameworks were closely aligned. Third, other benefits the teachers associated with outcomes included the development of whole school curriculum resources and greater opportunity for teacher collaboration, particularly among schools. The teachers, however, considered a wide range of factors when determining the overall impact of the reform, and perceived a number of them in terms of the costs of implementation. These included the emergence of ethical dilemmas concerning relationships with students, colleagues and parents, reduced individual autonomy, particularly with regard to the selection of valued curriculum content and intensification of workload with the capacity to erode the relationships with students which teachers strongly associated with the rewards of their profession. Finally, in banding together at the school level to resist aspects of implementation, some teachers showed growing awareness of a collective authority capable of being exercised in response to top-down reform. These findings imply that Student Performance Standards require review and, additional implementation resourcing to support teachers through times of reduced confidence in their own abilities. Outcomes prove an effective means of high-fidelity syllabus implementation, and, provided they are expressed in an accessible way and aligned with syllabus frameworks and terminology, should be considered for inclusion in future syllabuses across a range of learning areas. The study also identifies a range of unintended consequences of outcomes-based curriculum and acknowledges the complexity of relationships among all the aspects of teachers' work. It also notes that the impact of reform on teacher perspectives of professional practice may alter teacher-teacher and school-system relationships in ways that have the potential to influence the effectiveness of future curriculum reform.

Learning power and language expressiveness

The topic of the present work is to study the relationship between the power of the learning algorithms on the one hand, and the expressive power of the logical language which is used to represent the problems to be learned on the other hand. The central question is whether enriching the language results in more learning power. In order to make the question relevant and nontrivial, it is required that both texts (sequences of data) and hypotheses (guesses) be translatable from the “rich” language into the “poor” one. The issue is considered for several logical languages suitable to describe structures whose domain is the set of natural numbers. It is shown that enriching the language does not give any advantage for those languages which define a monadic second-order language being decidable in the following sense: there is a fixed interpretation in the structure of natural numbers such that the set of sentences of this extended language true in that structure is decidable. But enriching the original language even by only one constant gives an advantage if this language contains a binary function symbol (which will be interpreted as addition). Furthermore, it is shown that behaviourally correct learning has exactly the same power as learning in the limit for those languages which define a monadic second-order language with the property given above, but has more power in case of languages containing a binary function symbol. Adding the natural requirement that the set of all structures to be learned is recursively enumerable, it is shown that it pays o6 to enrich the language of arithmetics for both finite learning and learning in the limit, but it does not pay off to enrich the language for behaviourally correct learning.