880 resultados para mathematical content knowledge


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Rezension von: Inge Hansen-Schaberg: Minna Specht - Eine Sozialistin in der Landerziehungsheimbewegung (1918 bis 1951). Untersuchung zur pädagogischen Biographie einer Reformpädagogin. (Studien zur Bildungsreform. Bd. 22). Frankfurt a.M./Bern: Lang 1992, 406 S.

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O estágio pedagógico é o culminar de todo um processo que teve início na formação inicial e no qual, o futuro professor pode pôr em prática as competências adquiridas ao longo dessa formação. Este compreende um conjunto de tarefas que proporcionam a organização, estruturação e realização do processo de ensino-aprendizagem. O presente relatório visa realizar de forma reflexiva e projetiva, a análise de todo o processo formativo decorrente do estágio pedagógico em Educação Física. Este momento de formação foi determinante para o desenvolvimento de conhecimentos e competências que me permitem resolver os problemas do processo de ensino-aprendizagem de modo mais eficaz e adequado, promovendo melhores condições para a aprendizagem dos alunos. Ao longo do estágio pedagógico destaco as dificuldades iniciais e a progressão percecionada em competências fundamentais para o desenvolvimento das funções de professor, como um superior conhecimento pedagógico do conteúdo, capacidade de planear conteúdos, e capacidade de realizar um real acompanhamento ativo das aprendizagens dos alunos, fomentando a avaliação formativa. Para o meu futuro profissional, considero necessário continuar a desenvolver esforços para apresentar capacidade de autocrítica, promover o trabalho colaborativo e cooperativo, e ainda manter uma procura incessante de superação e reflexão contínua. Estes são no meu entender fatores que têm um efeito muito importante no desempenho do professor e no processo de ensino-aprendizagem dos alunos.

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This report is a summary of the effects of the Michigan Teacher Excellence Program (MITEP) on me as a science educator. The first chapter is a report of an action research project jointly authored with two other science teachers participating in the MITEP program titled “Station Activities and Misconceptions in the Chemistry Classroom.” The second chapter is a reflective essay evaluating the impacts of the MITEP experience on my teaching skills and practice, knowledge of science education and science education research, and leadership skills. The most significant impacts were a dramatic increase in my earth science content knowledge, a deeper understanding of inquiry-based teaching methods, and an expanded professional network of science educators.

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In this article we present a critical description regarding some of the guidelines that we consider are needed within education at university level to guide and transform the educative system towards an education for sustainability. To speak about sustainability we need to consider restructuring the teaching programs at all educative levels. For this, we discuss the relevance in adapting the six dimensions of the content-based knowledge towards sustainability issues, as well as the implications that the concept of sustainability has for our views, attitudes and actions. Transformative learning theories and pedagogical strategies for teaching science which could be useful for educating for sustainability and which could encourage changes in the attitudes of those who will become future teachers, such as the 5 "E" model which promotes critical and reflexive thinking are also discussed. We propose an educative model for teaching about sustainability with four basic epistemological elements: a multicultural education, an education for the future, a holistic education, and, a participatory education.

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This paper identifies the ways in which the Productive Pedagogies framework has been refined as a research tool for evaluating classroom practice within a current study into issues of school reform in Queensland. Initially emerging from the landmark Queensland School Reform Longitudinal Study (1998–2001), the Productive Pedagogies has been taken up widely in Australia and internationally as both a research tool and metalanguage to support teachers to critically reflect on their practice. In this paper, following a brief description of the model’s four dimensions, we detail how we have addressed some methodological concerns in using and modifying the framework for the present study. In response to critiques by other researchers and debates within our own research team, we justify our use of the framework. To these ends, we present a refined methodology that addresses the importance of pedagogical process, substantiates the inclusion of particular items within the framework, supports a critical approach to issues of difference, includes students’ perspectives and recognises the significance of content knowledge in the assessment of quality pedagogy.

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In this thesis, the author presents a query language for an RDF (Resource Description Framework) database and discusses its applications in the context of the HELM project (the Hypertextual Electronic Library of Mathematics). This language aims at meeting the main requirements coming from the RDF community. in particular it includes: a human readable textual syntax and a machine-processable XML (Extensible Markup Language) syntax both for queries and for query results, a rigorously exposed formal semantics, a graph-oriented RDF data access model capable of exploring an entire RDF graph (including both RDF Models and RDF Schemata), a full set of Boolean operators to compose the query constraints, fully customizable and highly structured query results having a 4-dimensional geometry, some constructions taken from ordinary programming languages that simplify the formulation of complex queries. The HELM project aims at integrating the modern tools for the automation of formal reasoning with the most recent electronic publishing technologies, in order create and maintain a hypertextual, distributed virtual library of formal mathematical knowledge. In the spirit of the Semantic Web, the documents of this library include RDF metadata describing their structure and content in a machine-understandable form. Using the author's query engine, HELM exploits this information to implement some functionalities allowing the interactive and automatic retrieval of documents on the basis of content-aware requests that take into account the mathematical nature of these documents.

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In studies of media industries, too much attention has been paid to providers and firms, too little to consumers and markets. But with user-created content, the question first posed more than a generation ago by the uses & gratifications method and taken up by semiotics and the active audience tradition (‘what do audiences do with media?’), has resurfaced with renewed force. What’s new is that where this question (of what the media industries and audiences did with each other) used to be individualist and functionalist, now, with the advent of social networks using Web 2.0 affordances, it can be re-posed at the level of systems and populations as well.

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Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

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Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

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Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

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This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

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Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of ideas is presented which reflects the cognitive mechanisms that shape a learner’s understanding. This organisation of information may then be analysed, with the view to informing the design of mathematics instruction in face-to-face and/or computer-mediated learning environments. However, this analysis requires significant work to develop both theory and practice.

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This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.