766 resultados para Algebraic thinking


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The middle years of schooling has emerged as an important focus in Australian education. Student disengagement and alienation, the negative effects of non-completion of the senior years of schooling and underachievement have raised concerns about the quality of education during the middle years. For many schools, reshaping the middle years has involved incorporating Information and Communication Technologies (ICT) to motivate students. However, simultaneously there is a need to ensure that programs are academically rigorous. There is little doubt that there are potential benefits to integrating ICT into programs for middle years’ students. However, little is known about how middle years’ teachers perceive higher order thinking, which is a component of academic rigour. This paper investigates the question of What are teachers’ perceptions of higher order thinking in an ICT environment? The study is underpinned by socio-cultural theory which is based on the belief that learning occurs through social interaction and that individuals are shaped by the social and cultural tools and instruments they engage with. This investigation used a collective case study design. Two methods were used for data collection. These methods are semi-structured interviews with individual teachers and a class and a focus group discussion with teachers. Findings indicate that teachers hold various perceptions of higher order thinking that lead to productive approaches to integrating ICT in middle years’ classrooms. The paper highlights that there may be a continuum of perceptions of higher order thinking with ICT. This continuum may inform professional developers who are guiding and supporting teachers to integrate ICT into middle years’ classrooms.

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The arrival of substantial cohorts of English language learners from Africa with little, no or severely interrupted schooling is requiring new pedagogic responses from teachers in Australia and other Western countries of refugee re-settlement. If the students are to have optimal educational and life chances, it is crucial for them to acquire resources for conceptually deep and critical literacy tasks while still learning basic reading and writing skills. This requires teachers to extend their pedagogic repertoires: subject area teachers must teach language and literacy alongside content; high school teachers must teach what has been thought of as primary school curriculum. The aim of this article is to describe some teacher responses to these challenges. Data are drawn from a study involving an intensive language school and three high schools, and also from the author’s experience as a homework tutor for refugees. Stand-alone basic skills programs are described, as are modifications of long-established ESL programs. It is also argued that teachers need to find ways of linking with the conceptual knowledge of students who arrive with content area backgrounds different from others in their class. Everyday life experiences prior to, and after re-settlement in the West, are rich with potential in this regard.

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Malcolm Shepherd Knowles was a key writer and theorist in the field of adult education in the United States. He died in 1997 and left a large legacy of books and journal articles. This thesis traced the development of his thinking over the 46-year period from 1950 to 1995. It examined the 25 works authored, co-authored, edited, reissued and revised by him during that period. The writings were scrutinised using a literature research methodology to expose the theoretical content, and a history of thought lens to identify and account for the development of major ideas. The methodology enabled a gradual unfolding of the history. A broadly-consistent and sequential pattern of thought focusing on the notion of andragogy emerged. The study revealed that after the initial phases of exploratory thinking, Knowles developed a practical-theoretical framework he believed could function as a comprehensive theory of adult learning. As his thinking progressed, his theory developed into a unified framework for human resource development and, later, into a model for the development of self-directed lifelong learners. The study traced the development of Knowles’ thinking through the phases of thought, identified the writings that belonged within each phase and produced a series of diagrammatic representations showing the evolution of his conceptual framework. The production of a history of the development of Knowles’ thought is the major outcome of the study. In addition to plotting the narrative sequence of thought-events, the history helps to explicate the factors and conditions that influenced Knowles’ thinking and to show the interrelationships between ideas. The study should help practitioners in their use and appreciation of Knowles’ works.

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This article considers the distinctive ways in which the Special Broadcasting Service (SBS) has evolved over its history since 1980, and how it has managed competing claims to being a multicultural yet broad-appeal broadcaster, and a comprehensive yet low-cost media service. It draws attention to the challenges presented by a global rethinking of the nature of citizenship and its relationship to media, for which SBS is well placed as a leader, and the challenges of online media for traditional public service media models, where SBS has arguably been a laggard, particularly when compared with the Australian Broadcasting Corporation (ABC). It notes recent work that has been undertaken by the author with others into user-created content strategies at SBS and how its online news and current affairs services have been evolving in recent years.

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This naturalistic study investigated the mechanisms of change in measures of negative thinking and in 24-h urinary metabolites of noradrenaline (norepinephrine), dopamine and serotonin in a sample of 43 depressed hospital patients attending an eight-session group cognitive behavior therapy program. Most participants (91%) were taking antidepressant medication throughout the therapy period according to their treating Psychiatrists' prescriptions. The sample was divided into outcome categories (19 Responders and 24 Non-responders) on the basis of a clinically reliable change index [Jacobson, N.S., & Truax, P., 1991. Clinical significance: a statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12–19.] applied to the Beck Depression Inventory scores at the end of the therapy. Results of repeated measures analysis of variance [ANOVA] analyses of variance indicated that all measures of negative thinking improved significantly during therapy, and significantly more so in the Responders as expected. The treatment had a significant impact on urinary adrenaline and metadrenaline excretion however, these changes occurred in both Responders and Non-responders. Acute treatment did not significantly influence the six other monoamine metabolites. In summary, changes in urinary monoamine levels during combined treatment for depression were not associated with self-reported changes in mood symptoms.

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The global financial crisis, global pandemics, global warming and peak oil are indicative of a world facing major environmental, social and economic problems. At the same time, world population continues to rise and global inequalities deepen. Children are the most vulnerable to the impacts of unsustainable living with specific harms arising because of their physical and cognitive vulnerabilities. Nevertheless, children do not have to be victims in the face of these challenges. Education, including early childhood education, has an important role to in building resilience and capabilities in children that equip them as active and informed citizens now and in the future and who are capable of contributing to healthy and sustainable ways of living. Drawing on educational change literature, action research, education for sustainability, health promotion and systems theory, this paper outlines three strategies that can help reorient early childhood education towards sustainability. One strategy is the adoption of whole centre approaches to sustainability and education for sustainability. This means working across the whole of a centre’s operations – curriculum and pedagogy, physical and social environments, its partnerships and community connections. The second strategy – applied in conjunction with the first – is the use of action research to investigate the early childhood setting and to create the desired changes. The third strategy is the adoption of systems thinking as a way of leveraging support and momentum for change so that education for sustainability goes beyond the initiatives of individual teachers and centres, and becomes a systems-wide imperative.

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In their studies, Eley and Meyer (2004) and Meyer and Cleary (1998) found that there are sources of variation in the affective and process dimensions of learning in mathematics and clinical diagnosis specific to each of these disciplines. Meyer and Shanahan (2002) argue that: General purpose models of student learning that are transportable across different discipline contexts cannot, by definition, be sensitive to sources of variation that may be subject-specific (2002. p. 204). In other words, to explain the differences in learning approaches and outcomes in a particular discipline, there are discipline-specific factors, which cannot be uncovered in general educational research. Meyer and Shanahan (2002) argue for a need to "seek additional sources of variation that are perhaps conceptually unique ... within the discourse of particular disciplines" (p. 204). In this paper, the development of an economics-specific construct (called economic thinking ability) is reported. The construct aims to measure discipline-sited ability of students that has important influence on learning in economics. Using this construct, economic thinking abilities of introductory and intermediate level economics students were measured prior to the commencement, and at the end, of their study over one semester. This enabled factors associated with students' pre-course economic thinking ability and their development in economic thinking ability to be investigated. The empirical findings will address the 'nature' versus 'nurture' debate in economics education (Frank, et aI., 1993; Frey et al., 1993; Haucap and Tobias 2003). The implications for future research in economics education will also be discussed.

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In teaching introductory economics there has been a tendency to put a lot of emphasis on imparting abstract models and technical skills to students (Stilwell, 2005; Voss, Blais, Greens, & Ahwesh, 1986). This model building approach has the merit of preparing the grounding for students 10 pursue further studies in economics. However, in a business degree with only a small proportion of students majoring in economics, such an approach tend to alienate the majority of students transiting from high school in to university. Surveys in Europe and Australia found that students complained about the lack of relevance of economics courses to the real world and the over-reliance of abstract mathematical modelling (Kirman, 2001; Lewis and Norris, 1997; Siegfried & Round, 2000). BSB112 Economics 1 is one of the eight faculty core units in the Faculty of Business at QUT, with over 1000 students in each semester. In semester I 2008, a new approach to teaching this unit was designed aiming to achieve three inter-related objectives: (1) to provide business students with a first insight into economic thinking and language, (2) to integrate economic analysis with current Australian social, environmental and political issues, and (3) to cater for students with a wide range of academic needs. Strategies used to achieve these objectives included writing up a new text which departs from traditional economics textbooks in important ways, integrating students' cultures in teaching and learning activities, and devising a new assessment format to encourage development of research skills and applications rather than reproduction of factual knowledge. This paper will document the strategies used in this teaching innovation, present quantitative and qualitative evidence to evaluate this new approach and suggest ways of further improvement.

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The literature on critical thinking in higher education is constructed around the fundamental assumption that, while regarded as essential, is neither clearly or commonly understood. There is elsewhere evidence that academics and students have differing perceptions of what happens in university classrooms, particularly in regard to higher order thinking. This paper reports on a small-scale investigation in a Faculty of Education at an Australian University into academic and student definitions and understandings of critical thinking. Our particular interest lay in the consistencies and disconnections assumed to exist between academic staff and students. The presumption might therefore be that staff and students perceive critical thinking in different ways and that this may limit its achievement as a critical graduate attribute. The key finding from this study, contrary to extant findings, is that academics and students did share substantively similar definitions and understandings of critical thinking.

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This paper aims to describe the development of a critical thinking conceptual model which was constructed to guide the teaching and evaluation of critical thinking skills to Middle-Eastern nurses.

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The purpose of this paper is to present a framework to guide critical thinking through reflective journaling, and describe how a group of 20 Middle Eastern nurses used reflective journaling to enhance their practice. Journal documentation was used during clinical practicum to foster the development of critical thinking in order to assist nurses when analysing and evaluating their clinical experiences. The findings from this study demonstrated that nurses accepted the framework for journal documentation because it provided structure for reflection, speculation, synthesis and metacognition of events experienced during clinical practice. Journaling gave nurses the opportunity to transfer thoughts onto paper and write down subjective and objective data, and created dialogue between the nurse educators and nurses. They were engaged in productive and positive activity to enhance their nursing practice. Nurses also commented that writing helped to develop their confidence in writing English.

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This paper examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this paper, experiments were conducted to find solution of the equation system describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the author knows, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

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To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.