327 resultados para mathematical content knowledge


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How do you identify "good" teaching practice in the complexity of a real classroom? How do you know that beginning teachers can recognise effective digital pedagogy when they see it? How can teacher educators see through their students’ eyes? The study in this paper has arisen from our interest in what pre-service teachers “see” when observing effective classroom practice and how this might reveal their own technological, pedagogical and content knowledge. We asked 104 pre-service teachers from Early Years, Primary and Secondary cohorts to watch and comment upon selected exemplary videos of teachers using ICT (information and communication technologies) in Science. The pre-service teachers recorded their observations using a simple PMI (plus, minus, interesting) matrix which were then coded using the SOLO Taxonomy to look for evidence of their familiarity with and judgements of digital pedagogies. From this, we determined that the majority of preservice teachers we surveyed were using a descriptive rather than a reflective strategy, that is, not extending beyond what was demonstrated in the teaching exemplar or differentiating between action and purpose. We also determined that this method warrants wider trialling as a means of evaluating students’ understandings of the complexity of the digital classroom.

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This paper reports on the initial phase of a Professional Learning Program (PLP) undertaken by 100 primary school teachers in China that aimed to facilitate the development of adaptive expertise in using technology to facilitate innovative science teaching and learning such as that envisaged by the Chinese Ministry of Education’s (2010-2020) education reforms. Key principles derived from literature about professional learning and scaffolding of learning informed the design of the PLP. The analysis of data revealed that the participants had made substantial progress towards the development of adaptive expertise. This was manifested not only by advances in the participants’ repertoires of Subject Matter Knowledge and Pedagogical Content Knowledge but also in changes to their levels of confidence and identities as teachers. By the end of the initial phase of the PLP, the participants had coalesced into a professional learning community that readily engaged in the sharing, peer review, reuse and adaption, and collaborative design of innovative science learning and assessment activities. The findings from the study indicate that those engaged in the development of PLPs for teachers in China need to take cognizance of certain cultural factors and traditions idiosyncratic to the Chinese educational system. A set of revised principles is then presented to inform the future design and implementation of PLPs for teachers in China.

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Universities no longer equip graduates solely with the content knowledge of their discipline, but also with prospective employment skills. Professions also seek graduates who can ‘collaborate, share skills and knowledge, and communicate their ideas effectively’ (Kruck and Reif, 2001, p 37). However, as admission to university does not always guarantee that one is well equipped for the task, first year students also need guidance in the development of academic skills. This session describes two models of peer assisted learning embedded within the Torts and Legal Foundations B units at the Faculty of Law, Queensland University of Technology, and how they are used to supplement student understanding of substantive law with the development of academic and work-related skills. Student perceptions of the programs developed are considered, together with the challenges faced. Session participants will be asked to contribute to a discussion of these challenges and to offer ideas on their redress.

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There is increased accountability of initial teacher education (ITE) programs in Australia to develop Graduate teachers who are better prepared. Most ITE programs have been designed using Pedagogical Content Knowledge. Informed by the growing Technological Pedagogical Content Knowledge (TPACK) research, this journal article suggests that ITE programs need to develop Graduate teachers who have the TPACK capabilities to use technologies to support teaching and student learning. Insights from the research and evaluation of the Teaching Teachers for the Future (TTF) Project, which was guided by the TPACK conceptualisation, are provided. The TTF Project, which involved all Higher Education Institutions providing ITE programs in Australia, drew upon the TPACK conceptualisation. The TTF Project research and evaluation included the development and administration of a TTF TPACK Survey and the implementation of the Most Significant Change Methodology. Key findings resulting from the employment of these methodologies are summarised to provide guidance to inform the improvement of ITE programs to develop Graduate TPACK capabilities.

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Universities provide preservice teachers (mentees) with directions on how to engage within their school placements, yet mentees have ongoing concerns about how to interact with their mentors. What are desirable attributes and practices for preservice teachers in their roles as mentees? This qualitative study gathers data from primary and secondary Australian teachers (n=25) through extended response questionnaire and audio-recorded focus group discussions, and preservice teachers (n=10) using audio-recorded interviews at the conclusion of their four-week practicum. Findings indicated that mentors had clear views on desirable attributes (e.g., enthusiasm, commitment, resilience) and practices (e.g., planning, preparation, building a teaching repertoire) for mentees; whereas mentees had varying views on identifying such attributes and practices and did not refer to: content knowledge, differentiation, and knowing school and university policies. This showed that mentees need more guidance for focusing on specific attributes and practices to benefit the mentoring relationship and their teaching development.

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This qualitative study investigates English as Foreign Language (EFL) teachers' perceptions and practices of blended learning in a Vietnamese university and influencing factors. Findings revealed that teachers have limited understandings and use of blended learning due to three primary influential factors: (i) the traditional teacher-centred pedagogy, (ii) institutional management and leadership styles, and (iii) fragmented knowledge of technological, pedagogical, and content knowledge (TPACK) for blended learning. To improve the take up and potential benefits of blended learning in EFL education in Vietnamese universities, this study proposes (i) a systematic understanding of blended learning concepts, (ii) a localised TPACK framework, and (iii) a model of teacher professional development program.

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Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

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This volume captures the innovative, theory-based, and grounded work being done by established scholars who are interrogating how teacher education can prepare teachers to work in challenging and diverse high-poverty settings. It offers articles from the US, Australia, Canada, the UK and Chile by some of the most significant scholars in the field. Internationally, research suggests that effective teachers for high poverty schools require deep theoretical understanding as well as the capacity to function across three well-substantiated areas: deep content knowledge, well-tuned pedagogical skills, and demonstrated attributes that prove their understanding and commitment to social justice. Schools in low socioeconomic communities need quality teachers most, however, they are often staffed by the least experienced and least prepared teachers. The chapters in this volume examine how pre-service teachers are taught to understand the social contexts of education. Drawing on the individual expertise of the authors, the topics covered include unpacking poverty for pre-service teachers, issues related to urban schooling as well as remote and regional area schooling.

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Purpose The purpose of this paper is to highlight the importance of enterprise educators working collectively to develop a unique scholarship of teaching. The authors argue that the time is right for educators in this domain to secure the future of enterprise education. Acknowledging the debate between "entrepreneurship education" and "enterprise education," the authors set out to develop a unification model through which educators can act collectively to demonstrate the leadership required to secure the autonomy of the domain. Design/methodology/approach The authors bring several pertinent ideas (pedagogical content knowledge, heutagogy and academagogy) to the attention of academics/researchers involved in the design, development and delivery of enterprise education. The innovative approach to combine these ideas with prevailing thinking in this domain has facilitated a model for collective action. Findings It is at the level of the shared philosophical positions that the authors can best cooperate to shape the future direction of enterprise education. The authors argue against dwelling upon how the authors differ in terms of context and process issues. Such matters can only fragment the theory and practice of enterprise education. The authors need to develop greater appreciation of shared philosophical positions and leverage this understanding into a unique scholarship of teaching, specific to enterprise education. Practical implications – As enterprise education becomes more global, it is also likely to become more attractive to business schools that long for a new positioning tool in the increasingly overcrowded markets that they compete in. Originality/value This paper encourages enterprise educators to reflect upon the knowledge they hold of their own practice, and that of other enterprise educators.

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Teaching with digital technologies is essential to the development of 21st century students’ graduate capabilities. However, relatively little is known about the extent to which Queensland VET teachers engage with digitally-enhanced teaching, or have the capacity to do so. Using a mixed methods approach, this thesis investigated the current digital teaching capacities of VET teachers and how current professional development opportunities are helping to address their learning needs.

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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.