268 resultados para Mathematical thinking


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The nature and characteristics of how learners learn today are changing. As technology use in learning and teaching continues to grow, its integration to facilitate deep learning and critical thinking becomes a primary consideration. The implications for learner use, implementation strategies, design of integration frameworks and evaluation of their effectiveness in learning environments cannot be overlooked. This study specifically looked at the impact that technology-enhanced learning environments have on different learners’ critical thinking in relation to eductive ability, technological self-efficacy, and approaches to learning and motivation in collaborative groups. These were explored within an instructional design framework called CoLeCTTE (collaborative learning and critical thinking in technology-enhanced environments) which was proposed, revised and used across three cases. The field of investigation was restricted to three key questions: 1) Do learner skill bases (learning approach and eductive ability) influence critical thinking within the proposed CoLeCTTE framework? If so, how?; 2) Do learning technologies influence the facilitation of deep learning and critical thinking within the proposed CoLeCTTE framework? If so, how?; and 3) How might learning be designed to facilitate the acquisition of deep learning and critical thinking within a technology-enabled collaborative environment? The rationale, assumptions and method of research for using a mixed method and naturalistic case study approach are discussed; and three cases are explored and analysed. The study was conducted at the tertiary level (undergraduate and postgraduate) where participants were engaged in critical technical discourse within their own disciplines. Group behaviour was observed and coded, attributes or skill bases were measured, and participants interviewed to acquire deeper insights into their experiences. A progressive case study approach was used, allowing case investigation to be implemented in a "ladder-like" manner. Cases 1 and 2 used the proposed CoLeCTTE framework with more in-depth analysis conducted for Case 2 resulting in a revision of the CoLeCTTE framework. Case 3 used the revised CoLeCTTE framework and in-depth analysis was conducted. The findings led to the final version of the framework. In Cases 1, 2 and 3, content analysis of group work was conducted to determine critical thinking performance. Thus, the researcher used three small groups where learner skill bases of eductive ability, technological self-efficacy, and approaches to learning and motivation were measured. Cases 2 and 3 participants were interviewed and observations provided more in-depth analysis. The main outcome of this study is analysis of the nature of critical thinking within collaborative groups and technology-enhanced environments positioned in a theoretical instructional design framework called CoLeCTTE. The findings of the study revealed the importance of the Achieving Motive dimension of a student’s learning approach and how direct intervention and strategies can positively influence critical thinking performance. The findings also identified factors that can adversely affect critical thinking performance and include poor learning skills, frustration, stress and poor self-confidence, prioritisations over learning; and inadequate appropriation of group role and tasks. These findings are set out as instructional design guidelines for the judicious integration of learning technologies into learning and teaching practice for higher education that will support deep learning and critical thinking in collaborative groups. These guidelines are presented in two key areas: technology and tools; and activity design, monitoring, control and feedback.

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Keeping exotic plant pests out of our country relies on good border control or quarantine. However with increasing globalization and mobilization some things slip through. Then the back up systems become important. This can include an expensive form of surveillance that purposively targets particular pests. A much wider net is provided by general surveillance, which is assimilated into everyday activities, like farmers checking the health of their crops. In fact farmers and even home gardeners have provided a front line warning system for some pests (eg European wasp) that could otherwise have wreaked havoc. Mathematics is used to model how surveillance works in various situations. Within this virtual world we can play with various surveillance and management strategies to "see" how they would work, or how to make them work better. One of our greatest challenges is estimating some of the input parameters : because the pest hasn't been here before, it's hard to predict how well it might behave: establishing, spreading, and what types of symptoms it might express. So we rely on experts to help us with this. This talk will look at the mathematical, psychological and logical challenges of helping experts to quantify what they think. We show how the subjective Bayesian approach is useful for capturing expert uncertainty, ultimately providing a more complete picture of what they think... And what they don't!

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Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

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This paper provides a contextual reflection for understanding best practice teaching to first year design students. The outcome (job) focused approach to higher education has lead to some unanticipated collateral damage for students, and in the case we discuss, has altered the students’ expectations of course delivery with specific implications and challenges for design educators. This tendency in educational delivery systems is further compounded by the distinct characteristics of Generation Y students within a classroom context. It is our belief that foundational design education must focus more on process than outcomes, and through this research with first year design students we analyse and raise questions relative to the curriculum for a Design and Creative Thinking course—in which students not only benefit from learning the theories and processes of design thinking, conceptualisation and creativity, but also are encouraged to see it as an essential tool for their education and development as designers. This study considers the challenges within a design environment; specifically, we address the need for process based learning in contrast to the outcome-focused approach taken by most students. The authors base their reflections on teaching design students at a university in Queensland, Australia.

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Double-pass counter flow v-grove collector is considered one of the most efficient solar air-collectors. In this design of the collector, the inlet air initially flows at the top part of the collector and changes direction once it reaches the end of the collector and flows below the collector to the outlet. A mathematical model is developed for this type of collector and simulation is carried out using MATLAB programme. The simulation results were verified with three distinguished research results and it was found that the simulation has the ability to predict the performance of the air collector accurately as proven by the comparison of experimental data with simulation. The difference between the predicted and experimental results is, at maximum, approximately 7% which is within the acceptable limit considering some uncertainties in the input parameter values to allow comparison. A parametric study was performed and it was found that solar radiation, inlet air temperature, flow rate and length has a significant effect on the efficiency of the air collector. Additionally, the results are compared with single flow V-groove collector.

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The use of immobilised TiO2 for the purification of polluted water streams introduces the necessity to evaluate the effect of mechanisms such as the transport of pollutants from the bulk of the liquid to the catalyst surface and the transport phenomena inside the porous film. Experimental results of the effects of film thickness on the observed reaction rate for both liquid-side and support-side illumination are here compared with the predictions of a one-dimensional mathematical model of the porous photocatalytic slab. Good agreement was observed between the experimentally obtained photodegradation of phenol and its by-products, and the corresponding model predictions. The results have confirmed that an optimal catalyst thickness exists and, for the films employed here, is 5 μm. Furthermore, the modelling results have highlighted the fact that porosity, together with the intrinsic reaction kinetics are the parameters controlling the photocatalytic activity of the film. The former by influencing transport phenomena and light absorption characteristics, the latter by naturally dictating the rate of reaction.

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This paper aims to address the knowledge gap in regards to the potential intermediary role tertiary institutions can play in developing generic design thinking/design led innovation capabilities in non-designers. Specifically, it investigates the value derived from the contribution of postgraduate design students as facilitators/educators for undergraduate non-design student cohorts. It examines a design immersion workshop designed to encourage the use of design thinking capabilities for project brief development for undergraduate multi-disciplinary student teams involved in a community service learning project for a social enterprise. The workshop was facilitated by design led innovation masters students embedded in industry organisations to research the integration of design led innovation capabilities in business. Data was collected from participating non-design students and postgraduate facilitators’ in the form of reflective journals and semi-structured interviews. The thematic analysis provided insight into the value of design thinking/design led innovation immersion programs for both the postgraduate facilitators and the undergraduate non-design students. The research results will inform a tentative foundation prototype framework to allow for ongoing program developments and research in design thinking/design led innovation integration in higher education, facilitating the development of generic capabilities required to empower future generations for business innovation and active citizenship in the 21st century knowledge economy.

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This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

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This study investigated the practices of two teachers in a school that was successful in enabling the mathematical learning of students in Years 1 and 2, including those from backgrounds associated with low mathematical achievement. The study explained how the practices of the teachers constituted a radical visible pedagogy that enabled equitable outcomes. The study also showed that teachers’ practices have collective power to shape students’ mathematical identities. The role of the principal in the school was pivotal because she structured curriculum delivery so that students experienced the distinct practices of both teachers.

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Fracture healing is a complicated coupling of many processes. Yet despite the apparent complexity, fracture repair is usually effective. There is, however, no comprehensive mathematical model addressing the multiple interactions of cells, cytokines and oxygen that includes extra-cellular matrix production and that results in the formation of the early stage soft callus. This thesis develops a one dimensional continuum transport model in the context of early fracture healing. Although fracture healing is a complex interplay of many local factors, critical components are identified and used to construct an hypothesis about regulation of the evolution of early callus formation. Multiple cell lines, cellular differentiation, oxygen levels and cytokine concentrations are examined as factors affecting this model of early bone repair. The model presumes diffusive and chemotactic cell migration mechanisms. It is proposed that the initial signalling regime and oxygen availability arising as consequences of bone fracture, are sufficient to determine the quantity and quality of early soft callus formation. Readily available software and purpose written algorithms have been used to obtain numerical solutions representative of various initial conditions. These numerical distributions of cellular populations reflect available histology obtained from murine osteotomies. The behaviour of the numerical system in response to differing initial conditions can be described by alternative in vivo healing pathways. An experimental basis, as illustrated in murine fracture histology, has been utilised to validate the mathematical model outcomes. The model developed in this thesis has potential for future extension, to incorporate processes leading to woven bone deposition, while maintaining the characteristics that regulate early callus formation.

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This research investigated the sustained use of process drama in a middle school foreign language classroom. The experience led to widespread learner engagement, a deeper contextualisation of the language as a socio-cultural practice, and a willingness to use the spoken and written language, regardless of limited proficiency. The drama required that language use be context and culture specific, contingent and multi-modal, which encouraged the beginner students to "mushfake" or improvise spoken and written text. Particularly important was the way the body was used through drama to express emotion, remember language and to illustrate the sociocultural context of its use.

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This thesis explored the current state of knowledge management in policing. A psychometric instrument was created and validated for use within police agencies as a means of facilitating the capture and transferral of critical investigative knowledge. The aim is to ensure that investigative expertise is not lost when detectives retire or leave the service. Improved knowledge management strategies that rely on this psychometric instrument can lead to greater efficiency and effectiveness in criminal investigation.

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Purpose The social marketing literature tends to focus on upstream marketing (policy) and downstream (individual behaviour change) and has a limited view on midstream (working with partners and community groups) social marketing. The paper proposes midstream social marketing should also include an understanding of how services and service employees influence and support individual behaviour change goals. The paper presents four key services marketing principles - derived from services theory and thinking - which the paper believes to be essential for implementing effective midstream social marketing. Design/methodology/approach This is a conceptual paper that uses service theory and case-examples to show how service thinking can be used as a midstream social marketing approach. Findings For effective uptake and impact of social marketing services amongst people and populations, social marketers need to design programs that consider the service experience, the service employee, service quality/customer value and the active role of the customer in value creation. Research limitations/implications Services marketing is a well-established sub-discipline of marketing which, until recently, has not interacted with social marketing. The extension and application of services theory for social marketing can enrich and propel the social marketing discipline forward. Further research is recommended to evaluate how service principles can be applied in practice. Social implications Given that social marketing services tend not to be accessed in sufficient numbers by the people who most need them, social marketers need to think beyond the technical, cognitive, and organisational-focused goals when designing social services. Originality/value This paper identifies key service theories that social marketers should understand and use and is thus a source of fresh ideas for theory and practice.

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The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual. With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to signifi cant changes in the forms of mathematical and scientifi c thinking required beyond the classroom. Modelling, in its various forms, can develop and broaden students’ mathematical and scientific thinking beyond the standard curriculum. This chapter first considers future competencies in the mathematical sciences within an increasingly complex world. Consideration is then given to interdisciplinary problem solving and models and modelling, as one means of addressing these competencies. Illustrative case studies involving complex, interdisciplinary modelling activities in Years 1 and 7 are presented.