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1.
In this paper I address the question: How is it that people come to choose mathematics and in what ways is this process gendered? I draw on the findings of a qualitative research study involving interviews with 43 young people all studying mathematics in post‐compulsory education in England. Working within a post‐structuralist framework, I argue that gender is a project and one that is achieved in interaction with others. Through a detailed reading of Toni and Claudia’s stories I explore the tensions for young women who are engaging in mathematics, something that is discursively inscribed as masculine, while (understandably) being invested in producing themselves as female. I conclude by arguing that seeing ‘doing mathematics’ as ‘doing masculinity’ is a productive way of understanding why mathematics is so male dominated and by looking at the implications of this understanding for gender and mathematics reform work.  相似文献   

2.
Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the classroom. Teachers and curriculum designers have developed an extensive vocabulary for describing tasks, using adjectives such as ‘rich’, ‘open’, ‘real-life’, ‘engaging’ and so on. But do teachers have a shared understanding of what these adjectives mean when they are applied to mathematics tasks? In study 1, we investigated teachers’ appraisals of adjectives used to describe mathematics tasks, finding that task appraisals vary on seven dimensions, which we termed engagement, demand, routineness, strangeness, inquiry, context and interactivity. In study 2, focusing on the five most prominent dimensions, we investigated whether teachers have a shared understanding of the meaning of adjectives when applied to mathematics tasks. We found that there was some agreement about inquiry and context, some disagreement about routineness and clear disagreement about engagement and demand. We conclude that at least some adjectives commonly used to describe tasks are interpreted very differently by different teachers. Implications for how tasks might be discussed meaningfully by teachers, teacher educators and curriculum designers are highlighted.  相似文献   

3.
A beautiful myth? The gendering of being/doing ‘good at maths’   总被引：2，自引：1，他引：2  
This paper draws on a research study into why more boys than girls choose to study mathematics. My starting point is that only four of the 43 young participants, and all of them male, self‐identified as ‘good at maths’. By reading these interviews as narratives of self, I explore the ‘identity work’ accomplished within their talk and within the talk of those who produced themselves/are produced as ‘not good at maths’. I argue that central to this are the ways that young people locate themselves in a series of inter‐related gendered binary oppositions including: fast/slow, competitive/collaborative, independent/dependent, active/passive, naturally able/hardworking, real understanding/rote learning and reason/calculation. I then explore the socio‐cultural context that makes such imaginings a central feature of young people’s relationships with mathematics, discussing the role of the gendered discourses of rationality evident in western enlightenment thinking and in popular culture’s stereotypes of mathematical ‘nerds’ and ‘geniuses’.  相似文献   

4.
Trends in curriculum reform recognise the need to develop skills and competencies in addition to specifying what knowledge should be taught and when. However, a balance between skills and knowledge is sometimes difficult to achieve. In this paper which takes mathematics as the focus, we consider reform currently underway in Wales, from the perspective of a ‘knowledge approach’ and from the perspective of the Successful Futures report which is, we argue, driven more by a skills approach at the heart of which are ‘four purposes’: developing young people as ambitious, capable learners; enterprising, creative contributors; ethical, informed citizens; and healthy, confident individuals. Our interest is in the contribution that mathematics makes to the four purposes; and contribution that the four purposes make (or do not make) to the development of a school mathematics curriculum. After outlining the background and context, the paper consults literature and experts to consider what mathematics is and how the learning of mathematics can be seen to fulfil the four purposes. The study contributes to understanding the difficulties of re-contextualising school subjects from the academic disciplines and proposes that operating with a curriculum driven by big ideas or overarching statements places higher demands on teacher knowledge.  相似文献   

5.
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6.
Phenomenology has been with us for many years, and yet grasping phenomenology remains a difficult task. Heidegger, too, experienced this difficulty and devoted much of his teaching to the challenge of working phenomenologically. This article draws on aspects of Heidegger’s commentary in progressing the teaching and learning of phenomenology, especially as this pertains to research in fields such as education. Central to this task is elucidation of what I believe to be the most important feature of phenomenology—what Heidegger referred to as the ‘starting point’ of phenomenology. I have written this article in the manner of a phenomenological workshop with the intention of inviting the reader to engage experientially with this starting point.  相似文献   

7.
In this paper I address the challenge of developing theory in relation to the practices of mathematics teaching and its development. I do this by exploring a notion of ‘teaching as learning in practice’ through overt use of ‘inquiry’ in mathematics learning, mathematics teaching and the development of practices of teaching in communities involving teachers and educators. The roles and goals of mathematics teachers and educators in such communities are both distinct and deeply intertwined. I see an aim of inquiry in teaching to be the ‘critical alignment’ (Wenger, 1998) of teaching within the communities in which teaching takes place. Inquiry ‘as a tool’ and inquiry ‘as a way of being’ are important concepts in reflexive developmental processes in which inquiry practice leads to better understandings and development of theory.  相似文献   

8.
In this article, I argue that poetic inquiry is a valuable method for producing knowledge that complements current research into ‘what works’ in reintegrating young people into secondary education. Researching ‘what works’ and ‘finding effects’ leads to insight into which interventions and tools are the focus of the research, and effectiveness is the goal. In contrast, poetic inquiry shifts the focus from the tools and interventions to the young people and their experience of their situation, the system, and opportunities. The goal is a more general understanding, rather than an assessment of effectiveness. I argue that as a qualitative research method, poetic inquiry can evoke emotion and illuminate the polyvocality of experience, which is important when understanding these young people. By use of poetic examples, the article demonstrates how the young people have pronounced experiences of deficiency, uncertainty, failure, but also of hope, certainty, and belonging.  相似文献   

9.
The paper outlines the dilemmas and paradoxes faced by lecturers and student teachers as they interact in a mathematics education subject that deals with both mathematics as a discipline and as a language, and with appropriate pedagogies for the teaching and learning of mathematics in primary schools. For the lecturer there is a tension between comforting and challenging the students. Are they to be wooed into a more positive attitude to mathematics, at the cost of avoiding the complexity of the discipline; or are they to be challenged by the unique character of mathematics, at the risk of alienation and exclusion? The latter often returns students to their original perception of maths as a harsh and unforgiving subject which is beyond their capabilities as they struggle with unfamiliar concepts and the discomfort of ‘not knowing’. For student teachers there is, paradoxically, a desire to ‘instil understanding’ when they themselves may not fully understand. They often idealise what is good practice but deny it in their own learning.  相似文献   

10.
A common move in the study of creativity and performativity is to present the former as an antidote to the latter. Might we, therefore, see work on creativity in education as heralding an era of post-performativity? In this paper I argue that the portrayal of performativity in the literature on creativity presents an overly simplistic (vulgar?) understanding of what the former involves. In this literature, performativity is used to represent the tightening control over curriculum and pedagogy to meet externally imposed targets. Though this represents a ‘manifestation’ of performativity, it is not constitutive of it. During this paper, I contend that a vulgar or partial understanding of performativity is what leads writers to view creativity as its antidote. To demonstrate what is at stake here, I draw on Lyotard’s understanding of performativity. For Lyotard, performativity is a narrative in which effectiveness has usurped Enlightenment narratives of truth and justice and ultimately comes to shape our understanding of the world. During the paper, I try to show that the literature on creativity in education focuses on effectiveness, jettisons concerns with ‘truth’ and partakes in the nihilism of performativity.  相似文献   

11.
The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both as an object with which to communicate (like a word is used) and as an object on which to focus and to organise her or his mathematical ideas (again as a word is used) even before she or he fully comprehends the meaning of this sign. Through this sign usage, I claim that the mathematical concept evolves for that learner so that it eventually has personal meaning, like the meaning of a new word does for a child; furthermore, because the usage is socially regulated, I claim that the concept evolves for the learner so that its usage concurs with its usage in the mathematical community. In line with Vygotsky, I call this usage of the mathematical sign before mature understanding, ‘functional use’. I demonstrate ‘functional use’ of signs (manipulations, imitations, template-matching and associations) through an analysis of an interview in which a mathematics university student engages with a ‘new’ mathematical sign, the improper integral, using pedagogically designed tasks and a standard Calculus textbook as resources.  相似文献   

12.
Futures Literacy is the capacity to design and implement processes that make use of anticipation, generally with the purpose of trying to understand and act in a complex emergent context. This article examines the potential of Futures Literacy to contribute to the realisation of a better balance between learning that is shaped by the supposition that what needs to be learned is knowable in advance, what I will label ‘push’ education, and ‘pull’ learning, that starts from the discovery of not knowing something, initiating the search for hypotheses, experiments, and evidence that eventually lead to understanding. Insufficient Futures Literacy impedes the expansion our anticipatory activities beyond preparation and planning, with the result that at both the individual and institutional levels it is difficult to find the motivation and capability to undertake and organise learning that goes beyond ‘push’ education, or what people ‘need’ to know now in order to get: a ‘good job’, be ‘good citizens’, etc., in the future. As a result humanity may be less able to embrace complexity or pursue a diversification approach to resilience.  相似文献   

13.
Since it was first published in 2011, ‘A Manifesto for Education’ by Gert Biesta and Karl Anders Säfström has received numerous enthusiastic reviews and been hailed as providing ‘an alternative vision for education’. Such enthusiasm, however, is perhaps not purely attributable to the substance of the text but also to the form that it adopts. In this regard, I attempt to explore what the authors refer to as the ironic usage of this genre of writing in relation to its message. The authors diagnose a problem in education related to the modern understanding of time, and they suggest an alternative ‘non‐temporality’ in which we ‘stay in the tension between “what is” and “what is not” ’. While I appreciate the Manifesto's attempt to offer criticism based on the link between freedom and temporality in education, I take issue with aspects of their analysis. I discuss temporality and freedom through a reading of Martin Heidegger in which the concept of time in education is understood in terms of human freedom as possibility.  相似文献   

14.
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   

15.
Metacognition can be described as an internal conversation that seeks to answer the questions, ‘how much do I really know about what I am learning’ and, ‘how am I monitoring what I am learning?’ Metacognitive regulation skills are critical to meaningful learning because they facilitate the abilities to recognize the times when one's current level of understanding is insufficient and to identify the needs for closing the gap in understanding. This research explored how using the Science Writing Heuristic (SWH) as an instructional approach in a laboratory classroom affected students’ practice of metacognitive skills while solving open-ended laboratory problems. Within our qualitative research design, results demonstrate that students in the SWH environment, compared to non-SWH students, used metacognitive strategies to a different degree and to a different depth when solving open-ended laboratory problems. As students engaged in higher levels of metacognitive regulation, peer collaboration became a prominent path for supporting the use of metacognitive strategies. Students claimed that the structure of the SWH weekly laboratory experiments improved their ability to solve open-ended lab problems. Results from this study suggest that using instruction that encourages practice of metacognitive strategies can improve students’ use of these strategies.  相似文献   

16.
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17.
This paper examines the history, rationale, uses and abuses of writing journals in primary classrooms. We argue that writing journals form part of a pedagogy derived from an understanding of how children can be motivated to express themselves, independently of teachers. Moreover, they demonstrate the power of welcoming children's home cultures into the classroom. However, we also wish to argue that the use of writing journals is part of the teaching profession's ‘creative compliance’ that can still contribute to the marginalisation of effective educational practice. We document how, in some schools in England, writing journals have been reduced to token gestures towards creativity and independence and in effect collude with and support what is increasingly becoming a pedagogical hegemony.  相似文献   

18.
This paper examines David Bakhurst's attempt to provide a picture of ‘the kinds of beings we are’ that is ‘more realistic’ than rationalism. I argue that there is much that is rich and compelling in Bakhurst's account. Yet I also question whether there are ways in which it could be taken further. I introduce the discussion by exploring Bakhurst's engagement with phenomenology and, more specifically, Hubert Dreyfus—who enters Bakhurst's horizon on account of his inheritance of the philosophy of John McDowell. Whilst I recognise that Bakhurst's encounter with Dreyfus demonstrates his achievements—over rationalism and over Dreyfus—I also suggest that it opens up certain questions that remain to be asked of his position on account of its conceptualism. These questions originate, not from a Dreyfusian phenomenological perspective, but from the post‐phenomenological perspective of Jacques Derrida. Through appealing to key Derridean tropes, I aim to show why the conceptual idiom Bakhurst retains may hold us back from understanding the open nature of human thought. I end by considering what therefore needs to come—and what needs to be let go—in order to best do justice to the ‘kinds of beings we are’.  相似文献   

19.
This article addresses two questions. The first question is this: ‘when ought teachers to encourage or discourage students’ belief of a given proposition on the one hand (call this ‘directive teaching’), and when ought teachers to simply facilitate students’ understanding of that proposition, on the other (call this ‘non‐directive teaching’) (cf. the work of Michael Hand)? The second question is this: ‘which propositional content should curricula address?’ An answer to these questions would amount to what I will call a ‘theory of propositional curricula content’, by providing both a means for choosing content, and a directive for teaching that content. While the answer that I give to the second question is unlikely to prove exhaustive, I still consider that it would form an important part of the answer, hence the title a ‘towards a theory of propositional curricula content’.  相似文献   

20.
There has been a recent push to reframe curriculum and pedagogy in ways that make school more meaningful and relevant to students’ lives and perceived needs. This ‘relevance imperative’ is evident in contemporary rhetoric surrounding quality education, and particularly in relation to the junior secondary years where student disengagement with schooling continues to abate. This paper explores how teachers translate this imperative into their mathematics and science teaching. Interview data and critical incidents from classroom practice are used to explore how six teachers attempted to make the subject matter meaningful for their students. Four ‘Categories of Meaning Making’ emerged, highlighting key differences in how the nature of science and mathematics content constrained or enabled linkages between content and students’ lifeworlds. While the teachers demonstrated a commitment to humanising the subject at some level, this analysis has shown that expecting teachers to make the curriculum relevant is not unproblematic because the meaning of relevance as a construct is complex, subject-specific, and embedded in understanding the human dimensions of learning, using, and identifying with, content. Through an examination of the construct of relevance and a humanistic turn in mathematics and science literature I argue for an expanded notion of relevance.  相似文献   

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