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1.
Nesrin Cengiz Kate Kline Theresa J. Grant 《Journal of Mathematics Teacher Education》2011,14(5):355-374
Studies show that extending students’ mathematical thinking during whole-group discussions is a challenging undertaking. To
better understand what extending student thinking looks like and how teachers’ mathematical knowledge for teaching (MKT) supports
teachers in their efforts to extend student thinking, the teaching of six experienced elementary school teachers was explored.
During group discussions, all six teachers created opportunities for extending student thinking about important mathematical
ideas and solution methods. Findings on the nature of these episodes include identification of individual instructional actions
and the ways in which teachers’ MKT was connected to these actions. 相似文献
2.
Amy E. Ryken 《Journal of Mathematics Teacher Education》2009,12(5):347-364
This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in
relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning
skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation
task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial
tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures
created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving
beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings
suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices
by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking
and curriculum materials. 相似文献
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Erik Jacobson Joanne Lobato Chandra H. Orrill 《International Journal of Science and Mathematics Education》2018,16(8):1541-1559
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
5.
Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding. 相似文献
6.
The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a transformation of participation perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group. 相似文献
7.
The challenges facing those who seek to prepare mathematics teachers are well established in the literature. Most of the research to date has focused on the perceptions and understandings of pre-service teachers, but not on the perceptions and understandings of teacher educators. In this study, we explore how four teacher educators understand their pre-service secondary teachers as the pre-service teachers attempt to make sense of teaching through the investigation of a multimedia case study of practice. We found that the teacher educators adopted two different implementation strategies: one strategy tended to be open-ended and exploratory; the other was more focused on the teacher educators' goals of anticipating student understanding and developing mathematical content knowledge for teaching. We also found that, in using the case study, teacher educators elicited pre-service teachers' thinking about the complexities of the teacher's role in small group work, about the value of explicitly revealing the teacher's reflections on the lessons, about the role of planning and preparation, and about the limits of pre-service teachers' abilities to understand and appreciate students' thinking and to extend lesson ideas. Both teacher educators and their pre-service teachers gained perspectives on the role of a teacher's mathematical content knowledge. These results imply that multimedia case studies of practice can serve as vehicles for revealing the knowledge and practice of teacher educators, as they engage in supporting the professional development of pre-service teachers. 相似文献
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This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, Human Development 52:109–128, 2009) to understand students’ mathematical thinking. This study challenged teachers’ pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students’ knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students’ ideas and connect informal or invented strategies with classroom mathematics. 相似文献
10.
Dawn Teuscher Kevin C. Moore Marilyn P. Carlson 《Journal of Mathematics Teacher Education》2016,19(5):433-456
Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus. Specifically, we extend previous work in this area by utilizing Piaget’s construct of decentering (The language and thought of the child. Meridian Books, Cleveland, 1955) to explain teachers’ actions relative to both their thinking and their students’ thinking. In characterizing decentering with respect to a teacher’s focus on student thinking, we use two illustrations that highlight the importance of decentering in making in-the-moment decisions that are based on student thinking. We also discuss the influence of teacher decentering actions on the quality of student–teacher interactions and their influence on student learning. We close by discussing various implications of decentering, including how decentering is related to other research constructs including teachers’ development and enactment of mathematical knowledge for teaching. 相似文献
11.
Kooloos Chris Oolbekkink-Marchand Helma van Boven Saskia Kaenders Rainer Heckman Gert 《Journal of Mathematics Teacher Education》2022,25(4):453-477
Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.
相似文献12.
Frank Rosenkränzer Christian Hörsch Stephan Schuler Werner Riess 《International Journal of Science Education》2013,35(14):1932-1951
ABSTRACTSystems’ thinking has become increasingly relevant not only in education for sustainable development but also in everyday life. Even if teachers know the dynamics and complexity of living systems in biology and geography, they might not be able to effectively explain it to students. Teachers need an understanding of systems and their behaviour (content knowledge), and they also need to know how systems thinking can be fostered in students (pedagogical content knowledge (PCK)). But the effective development of teachers’ professional knowledge in teaching systems thinking is empirically uncertain. From a larger study (SysThema) that investigated teaching systems thinking, this article reports the effects of the three different interventions (technical course, didactic course and mixed course) in student teachers’ PCK for teaching systems thinking. The results show that student teachers’ PCK for teaching systems thinking can be promoted in teacher education. The conclusion to be drawn from our findings is that a technically orientated course without didactical aspects seems to be less effective in fostering student teachers’ PCK for teaching systems thinking. The results inform educators in enhancing curricula of future academic track and non-academic track teacher education. 相似文献
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This paper considers the kind of pedagogical knowledge and principles involved in the operationalisation of knowledge of children's mathematical thinking as a process of dynamic assessment. Using a case study of a particular child, this paper explores planning and instruction for a child determined by a detailed and informed interpretation of the child's conceptual understanding through a dynamic process. It presents as a case study the observations of a teacher who had undertaken professional development in children's mathematical thinking, theoretically informed by Cognitively Guided Instruction and Maths Recovery. The observations revealed the child's mathematical understanding and how the teacher used this knowledge dynamically to inform teaching. The paper outlines the kind of knowledge required of teachers to enact this dynamic process in mathematics teaching and argues for the centrality of this to the development of inclusive practice. 相似文献
14.
In chemical education, many secondary school students experience difficulties in understanding three mutual related meanings of topics, that is, the macroscopic meaning, the microscopic meaning, and the symbolic meaning. As a consequence, student teachers should be prepared carefully to learn how to teach this difficult issue. This article presents a naturalistic case study of the development of eight student teachers pedagogical content knowledge (PCK) of the multiple meanings of chemistry topics. The student teachers (all M.Sc.) participated in a teacher education program of which the initial phase focused on learning from teaching instead of learning of teaching. They were asked individually to choose and teach a chemistry curriculum topic with a focus on the macro-micro-symbolic issue. Research data were obtained by interviewing the student teachers individually before and after the lessons. The outcomes indicated a development of student teachers knowledge of teaching difficulties, for instance, too fast and mainly implicit reasoning between macro- and micro-meaning, and a dominant orientation towards the micro-meaning of topics. A development of knowledge of students difficulties was also indicated, for instance, difficulties in understanding the macro- and micro-meaning of reaction equations. Implications for the follow-up phases of the program are presented. 相似文献
15.
Primary special school teachers' knowledge and beliefs about supporting learning in numeracy 
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下载免费PDF全文 Lio Moscardini 《Journal of Research in Special Educational Needs》2015,15(1):37-47
This paper presents findings from a qualitative study of a group of 12 teachers in primary special schools in Scotland for children with moderate learning difficulties. It sets out an analysis of classroom observations and interviews that explored teachers' knowledge and beliefs about teaching and learning in mathematics with children with moderate learning difficulties. The teachers were interviewed pre‐ and post‐intervention; this was a research‐based professional development programme in children's mathematical thinking (Cognitively Guided Instruction) which teachers then developed in their classrooms. The findings showed that prior to the professional development, the teachers had a limited knowledge of children's mathematical development with teaching frequently informed by intuitive beliefs and dated and sometimes discredited practices. Most teachers had low expectations of children with learning difficulties. Post‐intervention, the teachers reviewed this stance and affirmed that a deeper understanding of children's mathematical thinking provided a more secure knowledge base for instruction. They also recognised the extent to which learners were constrained by existing classroom practices. The paper argues for the commonality of this knowledge base and considers the problematic nature of viewing such knowledge as sector specific. 相似文献
16.
Robin Jacob Heather Hill Doug Corey 《Journal of research on educational effectiveness》2017,10(2):379-407
In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during mathematics lessons. Specifically, it focused on helping teachers (a) learn more mathematics, (b) understand how children learn math, (c) use formative assessment to develop insight into what specific students know and do not know, and (d) develop effective classroom instructional strategies that enable student problem solving. Participants included 105 fourth- and fifth-grade teachers teaching in 19 low-income schools within a single district. Teachers were randomly assigned within schools either to a “business as usual” control group or to receive the professional development. The training consisted of a week-long summer institute and four to six in-service days during the school year. The training was run by full-time trained associates. We find some limited evidence of positive impacts on teachers' mathematical knowledge for teaching, but no effects on instructional practice or student outcomes. 相似文献
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Rebecca Mitchell Charalambos Y. Charalambous Heather C. Hill 《Journal of Mathematics Teacher Education》2014,17(1):37-60
Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is theoretical. In this study, we examine the task and knowledge demands for teaching integer operations with representations by analyzing teaching practice. Teaching integer operations is used as an intensity case, as integer operations are challenging for students, and teachers are often required to employ several representations to teach this topic. Following a practice-based approach while also taking prior literature into consideration, we first generate a list of tasks entailed in teaching with representations and then discuss the knowledge demands imposed on teachers to successfully undertake this work. We highlight these tasks and knowledge demands by analyzing and discussing an integer addition and an integer subtraction episode for each of two teachers, Bonita and Karen. Based on our analysis, we organize the generated knowledge components using the Mathematical Knowledge for Teaching framework. We conclude by drawing implications for teacher educators and curriculum developers. 相似文献
19.
Jeffery H. Marshall M. Alejandra Sorto 《International Review of Education/Internationale Zeitschrift für Erziehungswissenschaft/Revue internationale l'éducation》2012,58(2):173-197
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
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The purpose of this cross-national study is to understand teachers’ views about the meaning of instructional coherence and the ways to achieve instructional coherence. With respect to the meaning of instructional coherence, whereas the majority of U.S. teachers paid attention to connections between teaching activities, lessons, or topics, the majority of Chinese teachers emphasized the interconnected nature of mathematical knowledge beyond the teaching flow. U.S. teachers expressed their views about ways to achieve instructional coherence through managing a complete lesson structure. In contrast, Chinese teachers emphasized pre-design of teaching sequences, transitional language and questioning based on the study of textbooks and students beforehand. Moreover, they emphasized addressing student thinking and dealing with emerging events in order to achieve “real” coherence. The findings of the study contribute to our understanding about the meaning of instructional coherence and ways to achieve instructional coherence in different cultural contexts. 相似文献