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1.
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   

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This paper presents a contingency theory of approaches to teaching in Higher Education adopted by university academics who teach heterogeneous student cohorts within a changing university context. The study is located within the substantive context of academics within Australian universities who teach within the broad field of management studies. Orthodox grounded theory is employed to generate a contingency typology comprised of four separate teaching approaches: Distancing, Adapting, Clarifying, and Relating. The model demonstrates how academics utilise a variety of teaching approaches to address their ‘main concern’, namely maintaining their professional competence within the context of a rapidly changing university landscape and significantly heterogeneous groups of students. We have labelled this process ‘Maintaining Competence’. This model stresses the importance of the twin forces of structure and individual agency in determining teaching approaches. It emphasises the value of analysing what academics actually do in the classroom situation, rather than concentrating on normative assumptions of what they should do in terms of best practice.  相似文献   

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Aligned with recent changes to syllabuses in Australia is an assessment regime requiring teachers to identify what their students ‘know’ and ‘can do’ in terms of the quality of understanding demonstrated. This paper describes the experiences of 25 secondary science and mathematics teachers in rural schools in New South Wales as they explore the changing nature of assessment and its implications on their classroom practice. To help reconceptualise these changes, teachers were introduced to a cognitive structural model as a theoretical framework. Throughout the 2-year study, teachers attended a series of professional development sessions and received ongoing consultative support. Each session was taped and transcribed while interviews were conducted with each teacher at the end of both years. Analysis of these data using a grounded theory approach identified seven major components of teacher practice impacted by the study. The core component was questioning while the six contributing components were teachers’ pedagogical practices, attention to cognition, teaching strategies, assessment linked to pedagogy, classroom advantages for students, and classroom advantages for teachers. These findings represent a major shift in teachers’ perceptions of assessment from a focus on the accumulation of students’ marks to one of diagnosis as a means of directing teaching to enhance students’ scientific and mathematical understandings.  相似文献   

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This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.  相似文献   

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The professional literature in mathematics education is replete with calls to use tasks that are ‘authentic’, ‘relevant’ and related to ‘real life’ and the ‘real world’. Such activities are frequently advocated for their potential to motivate and engage students, but evidence of their ability to do so is rarely presented. This paper examines evidence in relation to the effectiveness of context problems in achieving their intended purposes and thereby contributing to enhanced student participation, engagement and achievement in mathematics education. It is argued that context problems are not a panacea and that categorising problems as contextualised or de-contextualised is less helpful than the consideration of more salient aspects of tasks that impact on their effectiveness. Such aspects also relate to the purposes for and affordances and limitations of particular tasks in relation to the purposes they are intended to serve, along with attention to the contexts in which students learn mathematics. Examples of theoretical and empirical programs built on these considerations are reviewed in terms of their potential to enhance participation, engagement and achievement in school mathematics.  相似文献   

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This paper is a response to Maria Andree’s paper. Andree tells in the paper how mistakes in practical lessons may be critical events to change students’ attitudes in regard science. While traditionally mistakes in practical lessons could obligate students to repeat the experiment in order to get the ‘right result’ in the paper we have a good example how we can use the incident to potentiate students’ participation. In my response I illustrate how transferable is what Andree speaks about but I put forward further reflections about the traditions that may act as impediment for students’ participation. I thus suggest that the critical paradigm should be a component in reflecting about science classroom practices in order to alter the traditions.  相似文献   

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In the article we compare the approaches of 3 in-service teachers and 3 student teachers when they tried to solve a verbal arithmetic problem in the classroom. Each interaction was studied using a System of Analysis that takes into account the cognitive processes involved in the solution of a mathematic problem and describes the interaction at different levels showing what is done and to what degree teachers and/or pupils are responsible for what is done. The results of the study suggest that both groups of teachers are different in how they direct the student’s attention toward the essential aspects implied in the resolution of word problem. On the one hand, the in-service teachers guaranteed students’ understanding of the problem before dealing with the solution, while students teachers only did so when pupils committed errors. On the other hand, the in-service teachers allowed a high level of student participation, while student teachers took a more prominent role so children’s participation was lower.  相似文献   

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Educational research has been criticised by governments and practitioners. For some politicians and policy makers, there is a tendency to look for direct links between research and successful, effective and efficient practice. Research is needed to inform their evidence-based practice as policy makers, and to provide the kind of research teachers need to base their practice on the best available evidence for doing ‘x rather than y’ (Hargreaves 1996) or predicting the ‘size of the effect of A on B’ (Blunkett 2000). There is no doubt that both teachers and policy makers do make decisions on a daily basis based on some form of evidence. This paper explores Hargreaves’ notion of evidence-based practice, providing a range of criticisms. It also examines Carr’s historical account of ‘praxis’ and ‘poiesis’ to suggest a notion of evidence-based praxis based partly on the historical notion of ‘phronesis’ — practical wisdom. The basis for this is the argument that wise and practical ethical and moral judgements are central to an understanding of teachers’ daily work. What to do in a specific educational situation cannot be determined solely by theoretical beliefs or by ‘techne’. However the ethical dimension is not the only consideration. The paper suggests that evidence-based praxis use Stenhouse’s notion of ‘actionable evidence’, which includes the ethical dimension, but also Thomson’s concept of ‘thisness’, which describes the unique contextual characteristics of a school. If disadvantaged schools can make some sort of difference to learning opportunities for students, it is argued that teachers might engage in evidence-based praxis which involves them in reflecting on, and theorising what is happening in classrooms, schools and neighbourhoods. This ‘praxis’ also involves them in modifying their theories, critically analysing ‘what works’, questioning how they know and developing ideas about how things might be done differently. There will be an element of developing knowledge about teaching and learning strategies (Hargreaves’ ‘body of knowledge’), but it will be in the context of the ethical and moral dilemmas associated with education. It will take up the question of local differences as well as a realistic approach to what constitutes actual school improvement. Evidence-based praxis is also essentially a collective activity not an individual approach. Future development of the notion of evidence-based praxis might also include involving students in a more reciprocal and open learning process like that highlighted by researchers who focus on student participation linked to school reform.  相似文献   

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A science teacher and her mentor reflect on their participation in the Learning Research Cycle, a professional learning model that bridges research and practice in both university and public school contexts. Teachers do scientific research in scientists’ laboratories, then bridge their scientific experiences with the design of new classroom learning environments and teacher-driven educational research projects. Science students do scientific research via their teachers’ lessons that bridge laboratory research with classroom learning. Scientists and educational researchers bridge their research interests to create new questions centered on teaching and learning in authentic science learning environments. The authors engaged in this qualitative inquiry present their perspectives on “what goes on,” “what we have learned,” and “what it means to the larger community.”  相似文献   

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Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.  相似文献   

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Previous research on science education has described various factors influencing students’ participation and produced categorizations of students based on e.g. cultural background. In this article it is argued, theoretically and empirically, that an understanding of students’ participation in science education needs to begin with an analysis of what activity students are engaged in. The aim is to explore how altering conditions of classroom work may open up opportunities for students mainly participating in an activity of education or schooling to engage in an activity of science learning. Activity is conceptualized in a Cultural-Historical Activity Theory perspective as object-oriented and transformative. Drawing on an ethnographic study in a Swedish compulsory school, a critical incident of the participation in science education of a 7th grade girl called Helena is analyzed. The results show that altered conditions of classroom practice may produce new possibilities for student participation, and point to the impossibility of determining students as ‘different kinds of students’ based on a priori categories e.g. sex, ethnicity, socio-economic background.  相似文献   

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In this case study, we examine a teacher’s journey, including reflections on teaching science, everyday classroom interaction, and their intertwined relationship. The teacher’s reflections include an awareness of being “a White middle-class born and raised teacher teaching other peoples’ children.” This awareness was enacted in the science classroom and emerges through approaches to inquiry. Our interest in Ms. Cook’s journey grew out of discussions, including both informal and semi-structured interviews, in two research projects over a three-year period. Our interest was further piqued as we analyzed videotaped classroom interaction during science lessons and discovered connections between Ms. Cook’s reflections and classroom interaction. In this article, we illustrate ways that her journey emerges as a conscientization. This, at least in part, shapes classroom interaction, which then again shapes her conscientization in a recursive, dynamic relationship. We examine her reflections on her “hegemonic (cultural and socio–economic) practices” and consider how these reflections help her reconsider such practices through analysis of classroom interaction. Analyses lead us to considering the importance of inquiry within this classroom community.
Jennifer GoldbergEmail:

Jennifer Goldberg   is an assistant professor in the Graduate School of Education and Allied Professions at Fairfield University. She received her PhD in educational research methodology from the University of California, Los Angeles. Her teaching and research focuses on the importance of teaching for social justice and the relationship between identity, talk, and interaction on student opportunities for learning. Kate Muir Welsh   is an associate professor in the University of Wyoming’s College of Education. She received her PhD in education from the University of California, Los Angeles. Kate teaches math and science methods courses to pre-service and in-service elementary teachers and graduate courses on Action Research. Her research focuses on social justice teaching. She is also Chair of the University of Wyoming’s Shepard Symposium on Social Justice.  相似文献   

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We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view. We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that ‘open boxes’, we ‘outsiders and boundary-crossers’ sought to expose contradictions between College and work, induce breakdowns and identify salient mathematics. Typically, we find that mathematical processes have been historically crystallised in ‘black boxes’ shaped by workplace cultures: its instruments, rules and divisions of labour tending to disguise or hide mathematics. These black boxes are of two kinds, signalling two key processes by which mathematics is put to work. The first involves automation, when the work of mathematics is crystallised in instruments, tools and routines: this process tends to distribute and hide mathematical work, but also evolves a distinct workplace ‘genre’ of mathematical practice. The second process involves sub-units of the community being protected from mathematics by a division of labour supported by communal rules, norms and expectations. These are often regulated by boundary objects that are the object of activity on one side of the boundary but serve as instruments of activity on the other side. We explain contradictions between workplace and College practices in analyses of the contrasting functions of the activity systems that structure them and that consequently provide for different genres and distributions of mathematics, and finally draw inferences for better alignment of College programmes with the needs of students.  相似文献   

18.
The influence of video clubs on teachers’ thinking and practice   总被引:1,自引:0,他引:1  
This article examines a model of professional development called “video clubs” in which teachers watch and discuss excerpts of videos from their classrooms. We investigate how participation in a video club influences teachers’ thinking and practice by exploring three related contexts: (a) teachers’ comments during video-club meetings, (b) teachers’ self-reports of the effects of the video club, and (c) teachers’ instruction across the year. Data analysis revealed changes in all three contexts. In the video-club meetings, teachers paid increased attention to student mathematical thinking over the course of the year. In interviews, teachers reported having learned about students’ mathematical thinking, about the importance of attending to student ideas during instruction, and about their school’s mathematics curriculum. Finally, shifts were also uncovered in the teachers’ instruction. By the end of the year, teachers increasingly made space for student thinking to emerge in the classroom, probed students’ underlying understandings, and learned from their students while teaching.  相似文献   

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The purpose of this paper is to contribute to the debate about how to tackle the issue of ‘the teacher in the teaching/learning process’, and to propose a methodology for analysing the teacher’s activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This methodology studies the mathematical activity the teacher organises for students during classroom sessions and the way he manages1 the relationship between students and mathematical tasks in two approaches: a didactical one [Robert, A., Recherches en Didactique des Mathématiques 21(1/2), 2001, 7–56] and a psychological one [Rogalski, J., Recherches en Didactique des Mathématiques 23(3), 2003, 343–388]. Articulating the two perspectives permits a twofold analysis of the classroom session dynamics: the “cognitive route” students are engaged in—through teacher’s decisions—and the mediation of the teacher for controlling students’ involvement in the process of acquiring the mathematical concepts being taught. The authors present an example of this cross-analysis of mathematics teachers’ activity, based on the observation of a lesson composed of exercises given to 10th grade students in a French ‘ordinary’ classroom. Each author made an analysis from her viewpoint, the results are confronted and two types of inferences are made: one on potential students’ learning and another on the freedom of action the teacher may have to modify his activity. The paper also places this study in the context of previous contributions made by others in the same field.  相似文献   

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