159 resultados para Mathematical knowledge for teaching


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An enormous amount of research in the conceptual change tradition has shown the difficulty of learning fundamental science concepts, yet conceptual change schemes have failed to convincingly demonstrate improvements in supporting significant student learning. Recent work in cognitive science has challenged this purely conceptual view of learning, emphasising the role of languages, and the importance of personal and contextual aspects of  understanding science. The research described in this paper is designed around the notion that learning involves the recognition and development of students’ representational resources. In particular, we argue that difficulties with the concept of force are fundamentally representational in nature. The paper describes the planning and implementation of a classroom sequence in force that focuses on representations and their negotiation, and reports on the effectiveness of this perspective in guiding teaching and learning. Classroom sequences involving three teachers 158 2008 NARST Annual International Conference were videotaped using a combined focus on the teacher and groups of students. Video analysis software was used to code the variety of representations used, and sequences of representational negotiation. Stimulated recall interviews were conducted with teachers and students. The paper will report on the effect of this approach on teacher knowledge and pedagogy, and on student learning of force.

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Astronomy is one of the recurrent contemporary issues in the mass media where news related to comets, new stars, satellites, space tests, etc., frequently appear. Through this media presence students develop an interest in learning about aspects of astronomy. However, the information students gain from various sources, both inside and outside the classroom, doesn't often increase their knowledge about the most basic and common aspects of astronomy (Martinez Pena & Gil Quilez, 2001). Studies that have explored students' and teachers' understandings of astronomical concepts (Kalkan et al, 2007; Trumper, 2001) have found many alternative conceptions relating to basic astronomical processes such as day and night, the seasons, gravity and the relative distances between celestial objects.

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Universities have focused on teaching and learning at a time when quality has become the marker of distinction in international higher education markets. Education markets have meant pedagogical relations have become contractualised with a focus on student satisfaction, exemplified in consumer-oriented generic evaluations of teaching. This article argues, by analysing one example, that generic evaluations are more about accountability and marketing than about improvement of teaching and learning. Furthermore, what students want is not the only criterion for judging teaching. Rather, professionals require, as do academics, a capacity for critical judgement about what constitutes valued knowledge in the pedagogical relationship between teacher and student.

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Previously, we indicated that we wanted to address the dialogue pertaining to education and teaching approaches to increase the use of specific types of evidence that exist to guide and inform practice, and began this by focusing on Clinical Practice Guidelines (CPG). This column builds on that knowledge to highlight how educators can use CPGs in practice and change situations whilst also raising awareness of the limitations of these tools in terms of their impact on practice.

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In this paper images are used to support the conceptualisation and recognition of embodied pedagogy. Analysis of data gathered during an arts-based teaching project in pre-service teacher education revealed the presence of an embodied pedagogy and supports the further deployment of embodied teaching and learning in teacher education. Embodied pedagogy includes embodied teaching and embodied learning but is conceptualised through ‘pedagogy as relational’ – between teaching and learning and between teacher and learner. Through image this paper presents traces of embodied pedagogy from the classroom. These tracings of embodied pedagogy in classrooms defy baseline certainty and instead assert Benjamin’s thesis that knowledge can only ‘stand up’ through multiplicity, through all acts of knowing.

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Today’s workforce is characterised by an increasing mix of people with varying career aspirations, work motivators and job satisfiers. This paper discusses the intergenerational nature of today’s workforce, which is currently dominated by the age groups commonly referred to as Baby Boomers and Generation X. The Baby Boomers defined and redefined work during the last quarter of the twentieth century, but as they track towards retirement, GenXers’ valued work patterns and their career and life aspirations are increasingly dominating. This paper draws on a body of literature about a younger generation of workers and the current world of work in today’s knowledge society, and discusses possible implications for the teaching profession, particularly for attracting and retaining young people as teachers.

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Sustainability is a critical aim of Malaysian public policy and an important aim in education. Nonetheless, what sustainability means as it relates to education and the relationship between education and a sustainable future is unclear. In this paper I shall investigate the role that Universities in Malaysia play in shifting the practice and culture of innovation and creativity towards more sustainable values and outcomes. Sustainable education is based on ensuring that the capacities of students and the broader society are reengaged and empowered through connecting education to the needs and aspirations of civil society and moving away from neoliberal ideas of education as a practice of consumption towards, sustainable values of advancing human dignity.

Creativity and innovation within such an educational framework are goals and practices deeply connected and embedded within sustainable commitments to social justice, the public good, as well as individual growth and development which provide a critical legitimizing principle for university research and teaching. One of the key theoretical influences in making this argument will draw from the arguments of Amartya Sen whose theorization of capability may provide us with a way of thinking about social growth and development that is not possessively individualistic but rather socially concerned. I will discuss this in reference to the approach of University Sains Malaysia which provides an example of a public University seeking to engage sustainability and tie educational creativity and innovation back to the common good and a sustainable future.

The philosophical aim of this paper is to show how universities can pursue creativity and innovation as socially useful practices for advancing humane and sustainable values throughout Malaysian society and avoid the fusion of creativity with possessive individualism, consummerization and social irresponsibility. In this respect this paper addresses directly the theme of the conference: ‘Thinking Minds: Nurturing the Design of a Better Future'. '

To realise our national aspirations, a concerted effort is needed to increase our nation’s competitiveness, productivity and innovativeness. Attributes such as desire for knowledge, innovative thinking, creativity and competitiveness must be imbued within our people. The inculcation of moral values, progressiveness and performance-based cultures must also be instilled if we are to nurture successful individuals of the highest quality. This will determine our success as a knowledge-based economy.’ (Badawi 2007)

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As Australia becomes increasingly multicultural, there are many that would argue that the teaching and learning of music at educational settings can be carried out in a number of ways where cultural context and authenticity is imperative. This paper discusses the main arguments of teaching and learning in music education and provides some theoretical perspectives of teaching African music as groundwork for the discussion and findings. This paper is part of a wider study called 'Smaller steps in longer journeys' and. provides insight into the teaching of South African music in Melbourne. Three South African voices (my own as tertiary music educator, an artist in schools and a primary music specialist) through reflection and interview data considers 'how' and 'why' African music is taught The discussion presents an openmindedness of music when it travels to a new country where the pedagogy is the process of production and exchange, a social-discursive practice whereby process and understanding is more important than just product. As music requires no visa it will continue to travel and be shared in different context where pedagogical practice considers teacher, learner and knowledge.

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The thesis is a culmination of my research which drew on tyangi wedi tjan Rak Mak Mak Marranunggu and Marrithiel knowledge systems. These awa mirr spiritual knowledge systems have guided our Pilu for millennium and have powerful spiritual affiliation to the land and our continued presences. The understandings of the spiritual connectedness and our practices of relatedness have drawn on Pulitj, our deep awa mirr spiritual philosophy that nourishes us on our country. This philosophy gave us our voice and our presence to act in our own ways of knowing and being on the landscapes created by the Western bureaucratic systems of higher education in Australia to bring forth our Tyikim knowledge systems to serve our own educational interests. From this spiritual ‘Puliyana kunun’ philosophical position the thesis examines colonising constructions of Tyikim peoples, Tyikim knowledge systems in education, Tyikim research and access to higher education for Tyikim students. From the research, it is argued that the paradigm, within which the enclave-derived approach to Indigenous higher education is located, is compatible with the normalising imperialistic ideology of higher education. The analysis of the Mirrwana/Wurrkama participatory action research project, central to the research, supported an argument for the Mirrwana/Wurrkama model of Indigenous higher education. Further analysis identified five key pedagogical principles embedded within this new model as metaphorically equivalent to wilan~bu of the pelangu. The thesis identifies the elements of the spirituality of the narrative exposed in the research-in-action through the “Marri kubin mi thit wa!”. This is a new paradigm for Tyikim participation in higher education within which the Mirrwana/Wurrkama model is located. Finally, the thesis identifies the scope for Tyikim knowledge use in the construction of contemporary ‘bureaucratic and institutionalised’ higher education ngun nimbil thit thit teaching and learning experiences of Tyikim for the advancement of Tyikim interests. Here the tyangi yigin tjan spiritual concepts of narrative and landscape are drawn upon both awa mirr metaphorically and in marri kubin mi thit wa Tyikim pedagogical practice.

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An extensive literature documents teachers’ failure to include ideas about the 'nature of science' (NOS) in their classroom programmes, despite widespread advocacy for this as an essential component of more inclusive science teaching. This thesis frames much of the existing NOS literature as a deficit literature that focuses on epistemology, while largely ignoring the ontological realities of the classroom and overestimating individual teacher’s agency to change their enacted curriculum. Epistemologically-focused NOS reforms are positioned as curriculum 'add-ons', which teachers are likely to ignore. A NOS focus on ontology would entail curriculum restructuring, attending first to the contexts in which scientific knowledge is produced, and the ways it acts in the world. In any case, science itself has changed in recent years. Drawing from the sociology of science, in particular the work of Bruno Latour, the thesis compares traditional philosophical thinking about the ontology of science with more recent 'networked' views. Brent Davis explains the educational implications of key ideas from complexity science. Political philosopher Stephen White adds an ethical dimension. His ideas are used to argue for replacing 'strong' ontologies of realist science with more nuanced and actively tended 'weak' ontologies, as appropriate to the rapid sociological changes of the twenty-first century. The thesis argues that epistemological uncertainties that could lead to the suspicion of relativism are potentially threatening in the classroom because of hegemonic pressures towards consensus and a certain, safe status for the knowledge taught. Seeking an alternative pathway to change, Daniel Liston’s conceptualisation of teaching as a passionate act informs the analysis of the empirical component of the thesis. Eight recipients of New Zealand Royal Society Science Teacher Fellowships were interviewed on four occasions over two years. They discussed their personal learning during a year-long sabbatical to carry out an extended science investigation and their thoughts and actions on returning to the classroom. Narrative methodology is used to explore the teachers’ stories, revealing both passion for their personal learning and an ethical concern for their students’ learning to care for both the natural world and science as a means of its investigation. The thesis argues for the use of ontological approaches to the initial introduction of NOS ideas in school science, with epistemological concepts added only once a topic has been grounded in what Latour calls 'matters of concern'.Two potential teaching strategies—the production of network diagrams and the use of Davis's 'bifurcations'as a critical inquiry tool—are the focus of hypothetical experimentation. First in the context of global warming, and then addressing the challenges posed to teaching evolution by the proponents of 'intelligent design', these strategies are shown to have the potential to address some of science education’ s thornier issues, not just the NOS question. However, when conflicting expectations create tensions for teachers in the classroom moment, it is difficult for them to introduce reflective, deeply philosophical changes to their representation of science. Their working realities need to be acknowledged, and the tensions ameliorated, if we expect substantive change in their current practice.

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This thesis examines the professional knowledge of new secondary school teachers in New Zealand, their negotiation of multiple discourses encountered in policy and practice, and their processes of professional identity formation. It is also a study of policy reform. In New Zealand, as elsewhere, recent educational and social reforms have brought about major changes to the way education is managed and implemented. These reforms emphasise market ideologies promoting consumer choice and responsibility, while measuring and monitoring quality and effectiveness. At the same time, the reforms attempt to alleviate social inequality. Teachers' negotiation of an accountability culture and the dominant equity policies is a major focus of this study. The study draws upon group interviews held with nine new teachers during the first two years of their teaching careers. The group interviews were designed to elicit extended narratives from individual teachers, as well as promote more interactive dialogue and reflections within the groups. Because the interviews were conducted at different points in their early careers, the study also has a longitudinal element, allowing insight into how teachers' views are formed or changed during an intense period of professional learning. Analysis of the teachers' narratives is informed by poststructural and feminist understandings of identity and knowledge and by a methodological orientation to writing as a method of enquiry. The thesis develops three main types of discussion and sets of arguments. The first examines new teachers' negotiation of the 'macro' context of teacher knowledge formation that is, their negotiation of an educational policy environment that juxtaposes an equity agenda with accountability controls. In order to historically situate these dilemmas, the particular political, social and educational context of New Zealand is examined. It is argued that teachers negotiate competing political and conceptual debates about social justice, equity and difference, and that this negotiation is central to the formation of professional knowledge. The analysis illustrates ways in which teachers make sense of equity discourses in educational policy and practice, and the apparent contradictions that arise from placing tight accountability standards on schools and teachers to achieve associated equity goals. The second type of discussion focuses on teachers' negotiation of the 'micro' dimension of professional knowledge, looking closely at the processes and practices that form professional identity. Against stage or developmental models of teacher identity, it is argued that professional identity is formed in an ongoing, uneven and fluid manner and is socially and discursively situated/embedded. It is further argued that professional knowledge and identity are entwined and that this relationship is most usefully understood through analysis of the discursive practices that frame teachers' working lives and through which teachers work out who they are or should become and what and how they (should) think. This analysis contributes new perspectives to debates in teacher education about teacher preparation and the knowledge required of teachers in current 'new times'. The final cluster of arguments brings together these macro and micro aspects of professional knowledge and identity with a case study of how new teachers negotiated a recent educational reform of senior secondary school qualifications in New Zealand. This reform has had a significant impact on secondary schools and on the way teachers, and New Zealanders in general, think about education, achievement and success. It was found that this reform significantly challenged new teachers to question their beliefs about assessment and justice in education, and what counts as success. This case study draws attention to the tensions between equity, academic excellence and standards-based assessment, and contributes to understanding how teacher professional knowledge forms both in the context of a specific educational policy reform and in relation to educational reform in general. This study contributes new knowledge to the formation of teacher professional knowledge and identity in an educational climate of change in New Zealand. The findings offer new insights for teacher educators, policymakers and schools into how teachers build, shape and sustain professional knowledge; how they juggle contradictions between a desire for justice, policy imperatives and teacher education rhetoric; the self-constructed, but contingent nature of professional knowledge and identity; and the urgency to address identity formation as part of teacher education and to take account of the dynamic ways in which identities form. These matters need to be articulated in teacher education both pre-service and in-service in order to address teacher retention and satisfaction, and teachers' commitment to equity reform in education.

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This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

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The high infant mortality in Zambia is largely attributable to malnutrition. It is exacerbated by the inability of mothers to recognise threats to nutritional status and take corrective action. Advice in ‘Health Centres’ is often inaccessible to mothers. The Traditional Birth Attendants (TBAs) work with pregnant women in local communities, and the purpose of this study was to develop and implement an educationprogram in growth monitoring and nutrition for the TBAs and then to evaluate its effects. Twenty five TBAs from two peri-urban areas of Kitwe were enrolled in this pilot study and eighteen completed the program. The researcher developed and taught a program to the TBAs over ten days. A pretest was given before the teaching program to enable the researcher to obtain information about the knowledge and skills of the TBAs. Following the teaching program the TBAs were re-tested, with the same questionnaire. Focus groups were conducted to enable the TBA to provide information on the teaching materials and the education program. The TBAs then returned to their communities and put into practice the skills and knowledge they had learned for six months. Their practice was monitored by a trained Public Health Nurse. The researcher also surveyed 38 pregnant women about their knowledge of growth monitoring and nutrition before the TBAs went into the field to work with their local communities. The same questionnaire used with the pregnant women was administered to 38 new mothers with children aged 0 to 6 months to gain information of their knowledge and skills following the work of the TBAs. The program was evaluated by assessing the extent to which TBAs knowledge and skills were increased, the knowledge and understanding of a selection of their clients and the rates of malnutrition of infants in the area under study. The results from the research clearly indicated that the teaching program on growth monitoring and nutrition given to the selected group of TBAs had a positive effect on their knowledge and skills. It was found that the teaching developed their knowledge, practical skills, evaluative skills. That they were able to give infants’ mothers sound advice regarding their children’s nutrition was revealed by the mother’s increased knowledge and the decrease in numbers of malnourished children in the study areas at the conclusion of the research. The major outcomes from the study are: that Zambian TBAs can be taught to carry out an expanded role; field experience is a key factor in the teaching program; making advice available in local communities is important; and preliminary data on the Zambian experience were generated. Recommendations are: The pilot program should be expanded with continuing support from the Health Department. Similar educational programs should be introduced into other areas of Zambia with support from the Ministry of Health. That in administering a teaching program: Sufficient time must be allocated to practical work to allow poorly educated women to attain the basic skills needed to master the complex skills required to competently reduce faltering in their communities. The teaching materials to illustrate nutritional principles for feeding programs must be developed to suite locally available foods and conditions. Methods of teaching should suit the local area, for example, using what facilities are locally available. The timing of the teaching program should be suitable for the TBAs to attend. This may vary from area to area, for example it may be necessary to avoid times traditionally given to fetching water or working in the fields. For similar reasons, the venue for the teaching program should be suitable to the TBAs. The teachers should go into the TBAs’ community rather than causing disruption of the TBAs’ day by expecting them to go to the teacher. Data should be collected from a larger group of TBAs and clients to enable sophisticated statistical analysis to complement data from this pilot program. The TBAs should be given recognition for their work and achievement. This is something which they asked for. They do not ask for payment, rather acknowledgment through regular follow up and approbation.

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Human development has occurred against a timeline that has seen the creation of and diffusion of one innovation after another. These innovations range from language to complex computing and information technologies. The latter are assisting with the distribution of information, and extend to the distribution of the human species beyond the planet Earth. From early times, information has been published and mostly for a fee to the publisher. The absorption and use of information has had a high priority in most societies from early times, and has become institutionalised in universities and institutes of technical learning. For most in Western societies, education is now a matter of ‘lifelong learning’. Today, we see higher education institutions, worldwide, adapting their organisational structures and operating procedures and forming strategic alliances with communications content providers and carriers as well as with information technology companies. Modern educational institutes seek productivity and efficiency. Many also seek to differentiate themselves from competitors. Technological convergence is often seen by management to be a saviour in many educational organisations. It is hoped that lower capital and recurrent costs can be achieved, and that competitors in an increasingly globalised industry can be held at bay by strategic use of knowledge media (Eisenstadt, 1995) commonly associated with distance education in the campus setting. Knowledge media set up costs, intellectual property costs and training costs for staff and students are often so high as to make their use not viable for Australian institutes of higher education. Against this backdrop, one might expect greater educator and student use of publisher produced textbooks and digital enhancements to the textbook, particularly those involved in distance education. A major issue is whether or not the timing of instructor adoption of converging information technology and communications technologies aligns with the wishes of both higher education management and government, and with those who seek commercial gain from the diffusion and adoption of such technologies. Also at issue is whether or not it is possible to explain variance in stated intentions to recommend adoption of new learning technologies in higher education and implementation. Will there occur educator recommendation for adoption of individual knowledge media such as World Wide Web access to study materials by students? And what will be the form of this tool and others used in higher education? This thesis reports on more recent changes in the technological environment and seeks to contribute to an understanding of the factors that lead to a willingness, or unwillingness, on the part of higher education instructors, as influencers and content providers, to utilise these technologies. As such, it is a diffusion study which seeks to fill a gap in the literature. Diffusion studies typically focus on predicting adoption based on characteristics of the potential adopter. Few studies examine the relationship between characteristics of the innovation and adoption. Nearly all diffusion studies involve what is termed discontinuous innovation (Robertson, 1971). That is, the innovation involves adoptees in a major departure from previous practice. This study seeks to examine the relationship between previous experience of related technologies and adoption or rejection of dynamically continuous innovation. Continuous and dynamically continuous innovations are the most numerous in the real world, yet they are numerically the least scrutinised by way of academic research. Moreover, the three-year longitudinal study of educators in Australian and New Zealand meets important criteria laid down by researchers Tornatzky and Klein (1982) and Rogers (1995), that are often not met by similar studies. In particular the study examines diffusion as it is unfolding, rather than selectively examining a single innovation and after the fact, thus avoiding a possible pro-innovation bias. The study examines the situation for both ‘all educators’ and ‘marketing / management educators’ alone in seeking to meet the following aim: Establish if intended adopters of specific knowledge media have had more experience of other computer-based technologies than have those not intending to adopt said knowledge media. The analytical phase entails use of factor analysis and discriminant analysis to conclude that it is possible to discriminate adopters of selected knowledge media based on previous use of related technologies. The study does not find any generalised factor that enables such discrimination among educators. Thus the study supports the literature in part, but fails to find generalised factors that enable unambiguous prediction of knowledge media adoption or otherwise among each grouping of educators examined. The implications are that even in the case of related products and services (continuous or dynamically continuous innovation), there is not statistical certainty that prior usage of related products or technologies is related to intentions to use knowledge media in the future. In this regard, the present study might be said to confirm the view that Rogers and Shoemaker's (1971) conceptualisation of perceived innovation characteristics may only apply to discontinuous innovations (Stratton, Lumpkin & Vitell, 1997). The implications for stakeholders such as higher education management is that when seeking to appoint new educators or existing staff to knowledge media project teams, there is some support for the notion that those who already use World Wide Web based technologies are likely to take these technologies into teaching situations. The same claim cannot be made for computer software use in general, nor Internet use in general.