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1.
An issue of particular concern in mathematics teacher education is the relationship between theory and practice, and the nature of university–school partnerships. We report here on results from a research project answering the call for a more systematic understanding of the practice learning context. The study focuses on the new Norwegian elementary teacher education programme and highlights the difficulties involved in connecting theory and practice and how prospective teachers may be supported in this respect. Focus group interviews involving 51 first-year prospective teachers and 25 teacher–mentors investigated early school placements, specifically prospective teachers’ positions in the classroom as teachers of mathematics, and the ways in which the mentoring relationship supported their developing role. Taking a communities of practice perspective, we found that the idea of movement across intersecting and sometimes conflicting communities of practice is helpful in aiding our understanding of the difficulty of connecting theory and practice. Additionally, variations in mentoring styles and perceptions of prospective teachers’ mathematics and pedagogic knowledge competencies play a part in some prospective teachers’ difficulties in taking up a role as legitimate peripheral participant in the school. We conclude by considering ways in which prospective teachers might be better supported to cope with school placement.  相似文献   

2.
Research on identity has been a growing domain in the contexts of teacher education and mathematics education; however, identity work has been explored to a much lesser extent, with a future orientation overlooked. In addition, earlier studies have not provided sufficient knowledge on how different elementary teacher education programs might facilitate pre-service teachers’ identity work. In this study, we compare future-oriented mathematical identity work through a narrative framework considering six pre-service teachers undergoing two different teacher education programs. All pre-service teachers reported having had negative experiences with mathematics during their school years. Based on the results we conclude that despite the striking similarities in pre-service teachers’ mathematical backgrounds, the ways in which these cases are conducting their identity work differ substantially. It seems that the main reasons for these differences are different emphases and pedagogical practices in mathematics education courses. Additionally, we further elaborate on our earlier conceptualisation of identity work.  相似文献   

3.
In this paper, we offer illustrations of a mathematics teacher’s difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher’s thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The paper is based on a sub-study that is part of a larger Colombian project, PROMESA (Creating Science and Mathematics Connected Learning Experiences that Open Opportunities for the Promotion of Algebraic Reasoning), which incorporated a Professional Learning Programme (PLP) seeking to integrate school science and mathematics teachers into working teams, in order to create science and mathematics connected learning experiences that considered the promotion of algebraic reasoning. The ‘challenging questions’ that emerged for this teacher, during the workshops of the induction stage of the PLP, became the driving force for her continued engagement in learning mathematics content in a connected way, as opposed to the compartmentalised content-item thinking that she had experienced as a school student. We provide illustrations of first steps in the development of a teacher’s mathematical understanding, which can support growth of mathematical knowledge for teaching.  相似文献   

4.
Abstract

This paper explores ways to bridge the separation that currently exists between the worlds of teacher research and academic research. Currently, many teachers feel that educational research conducted by those in the academy is largely irrelevant to their lives in schools. On the other hand, many academics dismiss the knowledge produced through teacher research as trivial and inconsequential to their work. In this paper, it is argued that our vision of educational research should include both teacher produced knowledge and knowledge produced by those in the academy, and take the position that the processes of teacher development, school reform, and teacher education can greatly benefit from occasions when academic and teacher knowledge cross the divide that currently separates teacher knowledge from academics and academic knowledge from teachers. Two specific examples are discussed that illustrate instances where academic knowledge and teacher knowledge have improved teaching, together with the assumptions regarding voice, power, ownership and status which make them successful cases. One case deals with the teaching of mathematics in the elementary school and the other is concerned with the teaching of language minority students. Also discussed are several ways in which knowledge produced by teachers and others who work in schools can potentially benefit academic research and teacher education programs in colleges and universities.  相似文献   

5.
In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.  相似文献   

6.
In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues’ mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers’ prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.  相似文献   

7.
教师专业发展必然需要教师专业知识的有力支撑。对高中数学教师专业知识进行的问卷调查和访谈发现：目前高中数学教师基本上较好地掌握了常用的教师专业知识,但也存在一些问题：对数学学科知识的关注范围过于狭窄;运用数学教学知识进行教学时偏向于被动;对数学课程标准的理解存在偏差。另外,研究还发现：数学教学知识的增长并非是持续的;不同层级的教师之间、不同类别学校中的教师之间,其差异主要体现在数学学科知识与数学教学知识。进而对数学教师教育提出相应建议：数学教师应适当拓展数学学科知识的关注范围;应依据调查数据加强数学教师教育培养计划的针对性;关于教师一般教育学知识的评价方式亟需改进等。  相似文献   

8.
In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.  相似文献   

9.
通过对初中数学青年骨干教师L老师的叙事研究．研究者认为初中数学学科教学知识对学科内容知识量的要求是有限的,但对教师理解内容知识的深刻性有较高要求;实践与反思是形成学科教学知识的关键。L老师学科教学知识的生成途径有其独特的地方,值得其他教师借鉴和学习,可以概括为“二研五专”,即：研究教材、研题磨题、专业阅读、专题研究、专业现场、专题写作、专家引领。  相似文献   

10.
Although research and policy suggest science and mathematics teachers should attend to their student's thinking during instruction, our field has inadequately defined what that means in relation to our ultimate goals for the practice. Here I present a theoretical argument that, in making their definitions, researchers should leverage the ways students understand such attention by characterizing teacher attention based on the epistemological messages it sends students about the nature of knowledge and learning in the classroom. Using data collected from high school science and mathematics teachers with a new video‐capture methodology, I present an analysis of variability in epistemological messages of teacher attention to illustrate work could unfold if we as researchers took up the theoretical claims made in this work. In doing so, I endeavor to draw the construct of epistemological messages into our collective conversations about teacher attention, and provide a starting point for our field to begin debating the most productive ways to study and unpack the epistemological messages we value in that teacher attention. I conclude by demonstrating the feasibility of using these messages to distinguish the types of teacher attention our field wants to develop and encourage in teacher education. © 2017 Wiley Periodicals, Inc. J Res Sci Teach 55: 94–120, 2018  相似文献   

11.
Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.  相似文献   

12.
Why are some teachers more effective than others? The importance of understanding the interplay between teacher preparation, pedagogy and student achievement has motivated a new line of research focusing on teacher knowledge. This study analyses the effects of teacher mathematics knowledge on student achievement using longitudinal data from rural Guatemalan primary schools. After presenting a conceptual framework for linking the work of the teacher with student learning in mathematics together with an overview of the different forms of teacher knowledge, the paper introduces the Guatemalan context and the analytical framework including the sample, data and methods. Overall, the results provide some empirical support for a widely held, if infrequently tested, belief in mathematics education: effective teachers have different kinds of mathematical knowledge. The results also suggest specific mechanisms by which effective teachers can make substantial impacts on student learning, even in extremely poor contexts.  相似文献   

13.
Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.  相似文献   

14.
In this paper, we argue that to prepare pre-service teachers for doing complex work of teaching like leading classroom mathematics discussions requires an implementation of different pedagogies of teacher education in deliberate ways. In supporting our argument, we use two frameworks: one curricular and one pedagogical. The curricular framework is based on the work of Hammerness et al. (Preparing teachers for a changing world. What teachers should learn and be able to do. San Francisco, Jossey-Bass Educational Series, pp 358–388, 2005) outlining four main goals of teacher learning: a vision of practice, knowledge of students and content, dispositions for using this knowledge, and a repertoire of practices and tools. The pedagogical framework is based on the work of Grossman et al. (Teach Teach Theory Pract 15(2):273–289, 2009a; Teach Coll Record 111(9):2055–2100, 2009b) outlining three pedagogies of practice: representations, decompositions, and approximations of practice. We use the curricular framework to examine the opportunities for teacher learning that were afforded by these three different pedagogies of practice in a unit on leading classroom mathematics discussion in a secondary mathematics methods course. We use evidence from our analysis to show how the coordination of those pedagogies of practice is better than any one of them in addressing important goals for teacher learning about classroom discussions.  相似文献   

15.
Previous research by the authors (Meade, McMeniman, Wilson, Kanes and Davey, 1991) indicated the effectiveness of the stimulated recall (SR) methodology for examining the knowledge bases underlying the classroom actions of effective teachers in secondary mathematics and science. This study investigates more fully the robustness of the SR technique with special reference to: (i) making explicit the implicit theories of teaching; and (ii) the ways in which teachers construe effective teaching and learning. It probes the teaching practices of one effective high school science teacher, and compares the findings to another such teacher from the 1991 study. The conclusions made are that despite its labour intensive and time consuming nature, SR is a useful methodology for gaining profound insight into the implicit theories and beliefs of teachers, and the relationship between beliefs and actions. In particular, these theories and beliefs mainly concentrate on general pedagogical knowledge and pedagogical content knowledge.  相似文献   

16.
Current reform-driven mathematics documents stress the need for teachers to provide learning environments in which students will be challenged to engage with mathematics concepts and extend their understandings in meaningful ways (e.g., National Council of Teachers of Mathematics, 2000, Curriculum and evaluation standards for school mathematics. Reston, VA: The Council). The type of rich learning contexts that are envisaged by such reforms are predicated on a number of factors, not the least of which is the quality of teachers’ experience and knowledge in the domain of mathematics. Although the study of teacher knowledge has received considerable attention, there is less information about the teachers’ content knowledge that impacts on classroom practice. Ball (2000, Journal of Teacher Education, 51(3), 241–247) suggested that teachers’ need to ‘deconstruct’ their content knowledge into more visible forms that would help children make connections with their previous understandings and experiences. The documenting of teachers’ content knowledge for teaching has received little attention in debates about teacher knowledge. In particular, there is limited information about how we might go about systematically characterising the key dimensions of quality of teachers’ mathematics knowledge for teaching and connections among these dimensions. In this paper we describe a framework for describing and analysing the quality of teachers’ content knowledge for teaching in one area within the domain of geometry. An example of use of this framework is then developed for the case of two teachers’ knowledge of the concept ‘square’.  相似文献   

17.
As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.  相似文献   

18.
Many mathematics educators have found thatprospective elementary school teachers' beliefsinterfere with their learning of mathematics.Often teacher educators consider these beliefsto be wrong or naïve and seek to challengethem so prospective teachers will reject themfor more generative beliefs. Because of theresilience of prospective teachers' beliefs inresponse to these challenges, teacher educatorscould consider alternative ways of thinkingabout and addressing beliefs, particularly thepotential of building on rather than tearingdown pre-existing beliefs. Data from anearly-field experience linked to amathematics-for-teachers course provideevidence that when prospective teachers workintimately with children, in this case tryingto teach 10-year-olds about fractions, theexperience has the intensity from which beliefscan grow. Most of the prospective teachers inthe study were surprised that mathematicsteaching was more difficult than they hadanticipated. They began to consider theimportance of providing children time to thinkwhen solving mathematical problems. The changedescribed in the study is incremental ratherthan monumental, suggesting that building uponprospective teachers' existing beliefs will bea gradual process.  相似文献   

19.
This article contributes to the discussion on mathematics teacher reflection. Reflection was included in a study of the didactisation practices of primary school mathematics teachers as one of nine didactisation practices. The study involved five volunteer primary school mathematics teachers. A qualitative design-research approach was designed which employed model-eliciting tasks to create new experiences for teachers. This article reports on the nature and development of mathematics teacher reflection. Teacher reflection was gauged at various times during the programme through written responses to open-ended reflective questionnaires. Teachers were involved in three types of sessions for a period of one year: 1) modelling sessions whereby they collaboratively solved a mathematical modelling task; 2) observing primary school students/learners solve the same problems; and 3) sessions discussing traditional and problem-centred teaching and learning. It was found that modelling tasks provided reflective platforms and a window to teacher resources, orientations and goals. It is recommended that further research into mathematics teacher reflection be conducted where teachers specifically implement modelling in their own classrooms.  相似文献   

20.
The preparation of teachers to teach mathematics to primary school children differs across nations and cultures. This study used mixed methods to examine the basic content knowledge of trainee teachers in Australia and China. A simple test (30 questions) of content based on an international comparative study in mathematics teacher training found that many of the Australian trainee teachers struggled with material that they might be expected to teach, while the Chinese teachers largely demonstrated mastery. The significance of this finding is examined in the context of the teacher preparation programs in two teacher training institutions. Cultural commentary is added by leading academics in each institution. It was found that in the Australian teacher training institution there was a focus on generic skills and relatively limited opportunity to develop trainee teachers’ content knowledge or specific pedagogy. The relevance of the findings is discussed through the framework of different beliefs in the nature of mathematics and mathematics teaching that have been reported to dominate the different educational systems in China and Australia.  相似文献   

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