815 resultados para Mathematical thinking


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The play Epic Sea Battle at Night was originally staged in 1967, to commemorate two of China’s People’s Liberation Army’s military triumphs over the Taiwanese navy two years previously. Produced at the height of the Chinese Cultural Revolution, the play is an example of the exploitation of the arts as an ideological instrument, celebrating military heroism and political conviction. Stills from the play were included in, China Pictorial 11, an English language propaganda pamphlet that was distributed to Western Imperialists in order to educate them in Maoist policy. Today, these images are clear representations of ideology. More than forty years after the Cultural Revolution, the ideology under which we live, neo-liberal late-capitalism, deliberately shirks from such blatant displays of propaganda. We have supposedly the freedom to believe whatever we like in a post-ideological age, and yet core beliefs about meritocracy, individualism and competitiveness frequently go unchallenged. By juxtaposing the visual language of ideology with the text of the capitalist manifesto, the re-enactment of a scene from Epic Sea Battle at Night harnesses the aesthetics of the past so as to allow us to reconsider the alleged neutrality of the present. The design of the stage, the positioning of the actors, costumes and props of the current production closely resembled those documented in China Pictorial 11, yet the actors’ monologues belong to a completely different context. No less heroic and utopian in tone than the speech given by the political instructor of gunboat 874 in the original play, the capitalist manifesto was an attempt to give a concrete language to the shapeless ideology of the present, and to force the invisible currents that govern life today, in China as in the West, to the surface. Neither a lecture on neo-liberal economics, nor a theatrical performance of a narrative, the piece appropriated the format of the propaganda play to re-evaluate the relationship between art and politics now.

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From its roots in strategic management theory, stakeholder management has been adopted by the construction management academic community and applied as a valid paradigm around which research work has been generated aiming to improve project effi ciencies and effectiveness. However, academics have argued that stakeholder management should move away from purely theoretical discussions and engage more with the realities of construction project work. This paper re-appraises the stakeholder management concept for the construction domain by re-thinking some of the fundamental principles and ideals present within the more general stakeholder theory literature. It engages with issues which researchers have arguably failed to acknowledge and calls for a re-evaluation of construction stakeholder management research by presenting a review around four distinctive themes: the moral obligations of engaging with stakeholders against the business and efficiency driven imperatives of construction organisations; the contrast between theoretical abstractions and empirically grounded research; the tensions between theoretical convergence versus calls for multiple and divergent perspectives on stakeholder management and the practicalities of conducting stakeholder management in the construction domain. Such a critical re-appraisal of stakeholder management thinking both generates new lines of enquiry and promises to help inform and shape current and future industry practice.

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This article evaluates how the different papers in this special issue fill a gap in our understanding of cognitive processes that are being activated when second language learners or bilinguals prepare to speak. All papers are framed in Slobin’s (1987) Thinking for Speaking theory, and aim to test whether the conceptualisation patterns that were learned in early childhood can be relearned or restructured in L2 acquisition. In many papers the focus is on identifying constraints on this restructuring process. Among these constraints, the role of typological differences between languages is investigated in great depth. The studies involve different types of learners, language combinations and tasks. As all informants were given verbal rather than non-verbal tasks, the focus is here on the effects of conceptual transfer from one language on another, and not on the effects of language on non-linguistic cognition. The paper also sketches different avenues for further research in this field and proposes that researchers working in this field might want to take up the challenge of investigating whether speakers of different languages perceive motion outside explicitly verbal contexts differently, as this will enable us to gain an understanding of linguistic relativity effects in this domain. Studying which teaching methods can help learners to restructure their conceptualisation patterns may also shed new light on the aspects of discourse organization and motion event construal that are most difficult for learners.

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Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.

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Straightforward mathematical techniques are used innovatively to form a coherent theoretical system to deal with chemical equilibrium problems. For a systematic theory it is necessary to establish a system to connect different concepts. This paper shows the usefulness and consistence of the system by applications of the theorems introduced previously. Some theorems are shown somewhat unexpectedly to be mathematically correlated and relationships are obtained in a coherent manner. It has been shown that theorem 1 plays an important part in interconnecting most of the theorems. The usefulness of theorem 2 is illustrated by proving it to be consistent with theorem 3. A set of uniform mathematical expressions are associated with theorem 3. A variety of mathematical techniques based on theorems 1–3 are shown to establish the direction of equilibrium shift. The equilibrium properties expressed in initial and equilibrium conditions are shown to be connected via theorem 5. Theorem 6 is connected with theorem 4 through the mathematical representation of theorem 1.

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Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

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This paper addresses how secondary history teachers view the nature and purposes of their subject and how they think these views impact on their practice. Data were collected through individual qualitative interviews with eleven UK history teachers at the start of their careers. Their views on the nature of history are broadly empiricist with postmodern perspectives having been less influential. Their rationales for the subject emphasise broader educational purposes. The case for further emphasis on subject understandings in teacher education is made through a consideration of the implications of a lack of emphasis of more postmodern perspectives on classroom practice.

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According to the thinking-for-speaking (TFS) hypothesis, speakers of different languages think differently while in the process of mentally preparing content for speech. The aim of the present paper is to critically discuss the research carried out within the TFS paradigm, against the background of the basic tenets laid out by the proponents of this framework. We will show that despite substantial progress in the investigation of crosslinguistic differences in the organisation of information in discourse, the studies that actually examine the cognitive aspects of speech production are, to date, vanishingly few. This state of affairs creates a gap in our knowledge about the thought processes that co-occur with speech production during language use and acquisition. We will argue that in order to reach a more comprehensive picture of the cognitive processes and outcomes of speech production, methodologies additional to the analysis of information organisation must be used.

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In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

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Since the Dearing Report .1 there has been an increased emphasis on the development of employability and transferable (‘soft’) skills in undergraduate programmes. Within STEM subject areas, recent reports concluded that universities should offer ‘greater and more sustainable variety in modes of study to meet the changing demands of industry and students’.2 At the same time, higher education (HE) institutions are increasingly conscious of the sensitivity of league table positions on employment statistics and graduate destinations. Modules that are either credit or non-credit bearing are finding their way into the core curriculum at HE. While the UK government and other educational bodies argue the way forward over A-level reform, universities must also meet the needs of their first year cohorts in terms of the secondary to tertiary transition and developing independence in learning.

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A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.