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1.
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.

Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research.

Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.

Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.

Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.  相似文献   

2.
ABSTRACT

This paper draws upon learning from three action research projects conducted as part of a Europe-wide project exploring young people’s social and political participation. Challenging dominant discourses about what ‘counts’ as participation and what does not, the paper explores how, through the action research projects, young people engaged in knowledge democracy in ‘new democratic arenas’. Building upon experiential knowing and creating knowledge and learning through practice, the young people explored their own democratic knowledge production, communication and engagement within a context of shifting discourses of participation, democratic engagement and active citizenship. The increasing preference of young people for more informal forms of participation as lived practice reflects a shift to young people constructing their own modes of participation and ‘remaking democracy’ in their own vision and according to their own needs. By working outside of the confines of normative assumptions of democratic practice and participation, young people exercised their own ‘political’ agency in response to their own priorities, interests and concerns and, in doing so, illustrated that new forms, understandings and practices of knowledge democracy can emerge that reflect the promise of inclusive democratic societies more meaningfully.  相似文献   

3.
ABSTRACT

This study employed the interview method to clarify the underlying dimensions of and relationships between students’ scientific ontological and epistemic beliefs. Forty Taiwanese high school students were invited to participate in this study. Through content analysis of the participants’ interview responses two ontological dimensions including ‘status of nature’ and ‘structure of nature’ were identified and found to be associated with each other. The two epistemic dimensions ‘knowledge’ and ‘knowing’ aligned with past literature were also categorised. Besides five pattern variations in terms of the aforementioned four dimensions were recognised based on the students’ philosophical stances on their scientific ontological and epistemic beliefs. According to the Chi-square test results both dimensions of scientific ontological beliefs were significantly related to the two dimensions of scientific epistemic beliefs respectively. In general the students who endorsed a more sophisticated ontological stance regarding the status and structure of nature tended to express a more mature epistemic stance toward scientific knowledge and ways of knowing. The results suggest that the maturation of students’ scientific epistemic beliefs may serve as a precursor and the fundamental step in promoting the sophistication of students’ scientific ontological beliefs.  相似文献   

4.
ABSTRACT

This article explores the close association between higher education and reading. I draw on the resources of literary studies to illuminate the phenomenon of educational ‘engagement’. I explore the accounts of reading offered in the phenomenological literary theory of Rita Felski and Marielle Macé and extend their ‘stylistics of existence’ into higher education to elaborate engagement’s ‘eventful’ character: it is not in the power of teacher or student to ‘bring about’ engagement. In place of pedagogical ‘method’, I demonstrate how Padraig Hogan’s treatment of education as the ‘courtship of sensibility’ is consistent with this phenomenological treatment of engagement. I am thus able to illustrate how engagement is in tension with instrumental approaches to teaching and learning. I conclude by offering an ethical relation of mutual belonging to subject matter as a corrective to the centrality of ‘knowledge’ in recent attempts to unify the different degrees and objects of engagement.  相似文献   

5.
Received conceptualizations of scientific literacy are grounded in (1) the notions of ‘knowledge’, ‘concepts’, and ‘skills’ that science students have to ‘acquire’, ‘appropriate’, or ‘construct’ or (2) the notion of ‘practices’ to which they have to be ‘enculturated’ so that they become part of a ‘community of practice’. All such notions articulate scientific literacy in a static form, which does not correspond to the dynamic nature of the literacies that can be observed in society. This study proposes a dialectical notion of scientific literacy, which makes thematic its nature as a situated, distributed, collective, emergent, indeterminate, and contingent process. It articulates the idea that knowing a (scientific) language is indistinguishable from knowing one's way around the world. As a consequence, the goal of science education can no longer be to make individual students exhibit particular forms of knowledge but to provide them with contexts in which it is more important to deal with, select, and negotiate different forms of expertise and knowledgeability. This leads one to think of science education as but a part of a democratic liberal education that allows students to become competent to participate in any conversation that includes others with different forms and levels of expertise than their own.  相似文献   

6.
Abstract

This paper explores LGBTIQ+ students’ experiences of knowing, performing and holding queerness in a tertiary educational environment. Through interviews conducted with LGBTIQ+ students at a large Australian metropolitan university, we examine the students’ engagement with other LGBTIQ+ students in the tertiary educational space. Although originally intending to explore LGBTIQ+ students’ experience of violence, harassment and abuse on campus, the study identified a number of themes concerning the normalisation of a set of beliefs, practices, presentations and performances. Drawing on frameworks of hetero/homo and trans-normativity, we explore how LGBTIQ+ students articulated concerns in knowing, performing and holding ‘authentic’ queerness. We find LGBTIQ students experienced barred access to knowledge, hostility and dismissal by other LGBTIQ+ students when they were either perceived as too queer, or not queer enough. Behind these interactions and at the heart of these tensions is the notion of an authentic queer identity in a post-gay era and the continuous challenges all LGBTIQ+ students face within a heteronormative society. New insights into how LGBTIQ+ students negotiate, manage and shape their interactions in a higher educational settings are provided, and the implications for tertiary educational institutions, in particular the need to support a diverse LGBTIQ+ community, are discussed.  相似文献   

7.
Abstract

This article examines the significance of Jacques Rancière’s work on pedagogy, and argues that to make sense of Rancière’s ‘lesson on the lesson’ one must do more but also less than merely explicate Rancière’s texts. It steadfastly refuses to draw out the lessons of Rancière’s writings in the manner of a series of morals, precepts or rules. Rather, it is committed to thinking through the ‘lessons’ of Rancière in another sense. Above all, Rancière wants to ‘teach’ his readers something absolutely crucial about teaching. In making this claim the article emphasizes the extent to which Rancière advocates an utterly radical pedagogy, one that completely reconceives all the central elements of ‘schooling’, including teacher, student, intelligence and knowledge. Rancière thinks it possible to teach without knowing; he believes that the best schoolmasters can operate not on the assumption of their expertise, but on the equality of intelligence; and this means ultimately that Rancière contends that we can ‘teach what we do not know’. The best schoolmasters are ignorant schoolmasters. Rancière’s radical pedagogy depends upon, just as it consistently advances, a thoroughgoing resistance to a certain form of epistemological and ontological mastery. The rejection of mastery—of schoolmasters who would know it all, and convey this knowing to their students—forms the very backbone of all of Rancière’s writings and critical investigations. This is the chief reason why Rancière is, in a way, always talking about pedagogy, even when his subject matter appears to be something else entirely.  相似文献   

8.
ABSTRACT

This article explores how a school’s decision to become co-operative affects its engagement relationships with students and parents. The findings stem from a wider study exploring approaches to engagement in a recently converted co-operative academy, a large secondary school in a northern English city. The article surfaces the possibilities and tensions that occur as the school seeks to reposition itself in the English education marketplace, with a co-operative model that explicitly sets out to promote mutualisation, not privatisation; ‘we’ rather than ‘me’. The process of becoming co-operative is examined by exploring the underlying purposes of the school’s engagement with students and parents and the relationships that emerge as a result. The study surfaces the issues faced as a co-operative school seeks to enact thicker, ‘collective forms’ of democratic engagement against a backdrop of English education policy based on individualistic notions of democracy as freedom of choice. The findings point to the need for a different policy understanding of school engagement, an understanding that suggests engagement is about the process of developing more equitable, collaborative relationships with stakeholders and rests on the repositioning of students, parents and community members – from ‘choosers’ and ‘consumers’ to a collective public in education.  相似文献   

9.
Abstract

STEM outreach programmes in secondary schools are mediated by STEM teachers who are responsible for organising, implementing and evaluating the activities with a view to promoting STEM subjects. However, research investigating teachers’ STEM roles and professional development through participation in outreach activities is limited. This paper explores teachers’ views of STEM activities, how they understand their role as primary facilitators and the impact of their STEM engagement on their professional development. STEM outreach provides distinct opportunities for situated and dialogic learning. STEM teachers’ effectiveness in engaging students by demonstrating the importance and relevance of STEM subjects in the real world and engaging captivating STEM outreach partners not only supports students learning but also enhances their opportunities to develop their knowledge and skills. Semi structured interviews were conducted with eleven teachers from six different schools in the West Midlands, United Kingdom. The data reveals STEM facilitators become the ‘face’ of STEM to their pupils. The expertise, knowledge and partnerships STEM facilitators develop, broadens their capacity to deliver teaching imbued with real world applications and improve students’ understanding of the range of new and upcoming careers available. Most importantly, participating in STEM outreach activities help teachers maintain and reinforce their own sense of identity as STEM professionals. Outreach activities provide opportunities for teachers to interact with leading scientists and obtain exposure to cutting-edge research.  相似文献   

10.
This article examines Anglo-western assumptions about the role of individual views and voices in constructing knowledge, and how these assumptions can disadvantage students from ‘Confucian-heritage’ cultures whose social values around education and authority constrain their self-expression in western classrooms. Lecturers may mistake their good manners for a lack of critical thinking or originality, and read their suggestive style as a failure to take responsibility for their ideas. A challenge for academic skills specialists promoting inclusive practices is to go beyond helping students to acculturate to local conventions, and help lecturers to recognise the varieties of writing that stem from different kinds of intellectual and social engagement with the world. This article advocates respect for students' reticence, together with explicit discussion of local expectations. It suggests a method by which lecturers, skills specialists and students could identify common goals of writers in different educational traditions, and see how these are achieved in the target discourse.  相似文献   

11.
This article explores why art education after modernism needs to engage with and assess two forms of knowledge. It distinguishes procedural knowledge or ‘knowing how’ from declarative knowledge or ‘knowing that’, and argues that current classroom practice and more general thinking in art education in the UK confuses evidence of procedural knowledge with evidence for declarative knowledge. A corollary is that assessment evidence for ‘knowing how’, which is shown or demonstrated, is confused with assessment evidence for ‘knowing that’, which requires spoken or written forms of reporting. This conceptual confusion is currently embedded in the national, flagship examination known as the General Certificate of Secondary Education, taken by students at the age of 16, resulting in that examination requiring evidence of understanding the meaning of art in its socio‐historical context while at the same time denying the necessity of written or spoken work to reveal such knowledge. The article advocates a Wittgensteinian, socio‐cultural solution to the confusions of current practice.  相似文献   

12.
ABSTRACT

The dynamics of knowledge in society have transformed the conditions of professional work and learning. Professional expertise has become increasingly specialised, and practitioners are challenged to keep up with rapid developments in their fields. At the same time, the complexity of professional work requires the integration of different forms of knowledge and knowing. Against this background, the knowledge settings in which learners engage and the practices and resources these offer are of vital importance. This article addresses professional education as embedded in profession-specific ‘machineries of knowledge construction’, that is, the set of practices and arrangements through which knowledge and ways of knowing in a profession are generated. It is argued that such machineries span settings in education and work. Examples from research in three professional programmes are used to discuss how students are introduced to epistemic practices and resources in selected knowledge settings. Analytical attention is given to the dynamic interplay between people, practices, knowledge resources and educational arrangements as well as to how connections to work and the epistemic machinery are made. Taking these linkages into account is important for our understanding of what learning entails in different areas of expertise and how this may change over time.  相似文献   

13.
Abstract

This paper considers the ‘knowledge economy’ as it is used in education rhetoric to establish social and educational consent for significant changes both to the spatial organisation of classrooms and their affective economies. We draw on ethnographic data from a study of ‘non-traditional classroom spaces’, where the spatial organisation of schooling emerged as a potential fulcrum through which the imaginary of the conventional primary classroom was being reconceptualised. Traditionally configured classroom spaces and the learning that takes place within them were being challenged and replaced by notions of twenty-first century learning in ‘agile’ learning environments. In the context of this reform agenda, these open-plan spaces were seen as offering new prospects for participation in a globally connected and competitive economic world that requires students to continuously adapt, innovate and respond creatively to a range of different problems. We consider how these everyday moments function as conceptual encounters between affective, embodied experiences and educational reform discourses that rationalise the implementation of non-traditional classroom spaces in ways that have very little to do with children and their futures. This cultural approach takes a step aside from numerous, and necessary, critiques of recent educational policies per se, in order to consider what might be learned from the uncanny spectres of child bodies that haunt them. The paper draws attention to examples of children’s affect in non-traditional classrooms and what that may tell us about current educational reform when sacrifice forms part of the missing account of educational reorganisation for the knowledge economy.  相似文献   

14.
Abstract

Assessment rubrics intend to make criteria explicit to students. However, an understanding of assessment criteria requires tacit knowledge about which students may not be aware. The lack of such knowledge is notable in undergraduate health science students taking a compulsory course in the social sciences. This study performed a content analysis of how 1st year health sciences students interpret a SOLO assessment rubric for a sociology ‘reflection piece’ essay. The findings suggest that empiricism, standardisation and lack of tacit knowledge limit students’ ways of reasoning about the rubric. These limitations manifest in a methodical difference between students’ expectations and lecturers’ intentions of using a rubric. This difference is illustrated by the students’ need for procedural knowledge and the lecturer’s expectation of conceptual knowledge. These differences have implications for teaching, learning and assessment in health sciences undergraduate education. The findings also justify a dialogical approach to assessments through facilitating students’ epistemological development.  相似文献   

15.
ABSTRACT

School students demonstrate a lack of interest in choosing science studies and science-related careers. To better understand the underlying reasons, this study aims to examine secondary school students’ perceptions of working life skills and how these perceptions relate to the skills of the twenty-first century. The participants in this study were 144 Finnish 7th graders (aged 13–14 years). Using a questionnaire and qualitative content analysis, we examined their perceptions of working life skills in ‘careers in science’ and ‘careers with science’. Results reveal that although students have a great deal of knowledge about working life skills, it is often just stereotyped. Sector-specific knowledge and skills were highlighted in particular but skills related to society, organisation, time and higher order thinking, were often omitted. Results also indicate that students do not associate ‘careers in science’ with creativity, innovation, collaboration or technology and ICT skills. Conversely, according to the students, these careers demand more sector-specific knowledge and responsibility than ‘careers with science’. We conclude that students need more wide-ranging information about scientific careers and the competencies demanded; such information can be acquired by e.g. interacting with professionals and their real working life problems.  相似文献   

16.
This article presents the results of an exploratory study of students’ knowledge about scientists and countries’ contributions to science, aiming at answering two research questions: “In which ways are students aware of the history of scientific development carried out by different people in different places of the world? What can be influencing and shaping their awareness?” Thus, this study aimed at depicting students’ knowledge about History of Science (HOS), focusing on what they know about science being done by people and communities from different parts of the world and on how this knowledge is constructed through their engagement with school science. An exploratory research was carried out at two multicultural state secondary schools in London, UK, involving 200 students aged 12–15 (58.5% girls, 41.5% boys) and five science teachers. The method involved an initial exploration of students’ knowledge about HOS through an open-ended survey, followed by classroom-based observations and semi-structured interviews with the participants. Results showed a disconnection between remembering scientists and knowing about their work and background, hinting at an emphasis on illustrative and decontextualised approaches towards HOS. Additionally, there was a lack of diversity in these students’ answers in terms of gender and ethnicity when talking about scientists and countries in science. These findings were further analysed in relation to their implications for school science and for the fields of HOS, science education and public perception of science.  相似文献   

17.
《Africa Education Review》2013,10(2):263-282
Abstract

Throughout the world, education curriculum are determined and guided by knowledge perceived as being critical for the advancement of humanity. Often such progress is indicated and determined by curriculum shaped by the ways of knowing of the dominant cultural group or languages that have achieved hegemonic status in such communities, in the process marginalizing any ‘indigenous’ ways of knowing as embedded in the language of other cultures. Sometimes such curriculum have little or no connection with contemporary reality. In this article I therefore argue that inclusive curricular knowledge types are critical in education in order to enable all people, individually and collectively, to progress without being inhibited by the hegemony of so-called ‘scientific’ knowledge. I also argue that knowledge as embedded in a language is power, and should therefore be connected to reality. Using critical social theory, I propose an alternative, inclusive treatment of knowledge types in education curriculum – open-ended inquiry – in order to level the learning field for all learners, and, in so doing, to adequately prepare tomorrow's world citizenry.  相似文献   

18.
This article explores and attempts to rectify current conceptual confusion found in secondary art education in the UK between procedural knowledge or ‘knowing how’ and declarative knowledge or ‘knowing that’. The paper argues that current practice confuses procedural knowledge with declarative knowledge. A corollary is that assessment evidence for ‘knowing how’, which is shown or demonstrated, is confused with assessment evidence for ‘knowing that’, which requires spoken or written forms of reporting. The confusion is replicated in the national examination, the General Certificate of Secondary Education, taken by students at the age of 16. The article traces this confusion to three dualisms: the Cartesian dualisms of mind and body, an individual mind and the distributed mind of culture, and the more recent mind‐in‐brain hemisphere dualism. The article advocates a Wittgensteinian embodied, socio‐cultural view of mind as a way of solving the current conceptual confusion that prevails in art education in the UK.  相似文献   

19.
This article provides a critical commentary on the concepts of representation and digital artefacts in Morgan and Kynigos’s article of this Special Issue. To set the context, in the first part, I examine some of the tensions that arose during discussions through the 1980s and 1990s about representation in mathematics education research. Then, I comment on the conceptual differences between Morgan’s and Kynigos’s approaches. These differences point to different epistemological assumptions that lead to different conceptualizations of artefacts in learning processes. In the last part, I argue that Morgan’s and Kynigos’s approaches have the merit of moving the discussion about representations to new theoretical horizons. I suggest, however, that a discussion about representations and digital artefacts requires a thematized account of the manner in which the phenomenological artefact- and representation-mediated knowledge produced by students in the classroom relates to the target cultural mathematical knowledge. Such an account, I contend, requires an explicit ontological conception of knowing and knowledge. I conclude the article with an example in which knowledge is considered as codified movement and knowing as the event of its enactment in concrete practice. Within this Hegelian materialist viewpoint, representations are neither predicated in terms of an adequacy between ideas and their representations nor as heuristic devices in meaning making processes. Representations are rather an integral part of the activity of knowledge presentation.  相似文献   

20.
How can higher education educate graduates who know more than ‘just knowledge’? Such an education includes developing in students an awareness of the limits of their knowledge, an ability to discern what kinds of knowledge are appropriate in a given situation and a sensitivity to different forms of knowing. When is scientific rigour appropriate and when is another type of knowing appropriate? When should one set aside own preferences in favour of the needs of others? This paper rethinks ‘bildung’ as a source of ideas on aims for teaching students. Making the arguably ephemeral ideal of bildung work in practice can be an obstacle. This paper, however, takes it as a positive challenge, exploring ways in which bildung might be appropriate in professional education. If bildung can be helpful even within this most applied part of higher education, implications in terms of the development of more readily applicable and fully inclusive notions of bildung would benefit not only professional education but also higher education more generally. Drawing on work by Wolfgang Klafki, the authors argue the value of updated notions of bildung. Klafki's three-part conception of bildung as self-determination, co-determination and solidarity helps reconnect the importance of personal development with that of peer communities (e.g., professional bodies) and action for others. Klafki's framework facilitates working with ethical-epistemological questions such as these.  相似文献   

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