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1.
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
2.
抛锚式教学模式在英美文学选读中的应用 总被引：1，自引：0，他引：1
“抛锚”式教学是建构主义教学的一部分,在英美文学教学中具有很好的效果。通过教师的“抛锚”,学生可以更好地理解、消化作品,并在作品的情境中把握作者意图,促进课堂的互动,从而有利于教师和学生更好地完成教学和学习任务。 相似文献
3.
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical modeling is treated more as a venue for learning other mathematics than as an instructional goal in its own right. From this perspective, we are compelled to ask how learning of mathematics beyond modeling may occur as students generate and validate mathematical models. We consider a diagrammatic model of mathematical modeling as a process that allows us to identify how mathematical understandings may develop or surface while learners engage in modeling tasks. Through examples from prospective teachers' mathematical modeling work, we illustrate how our diagrammatic model serves as a tool to unpack the intricacies of students’ mathematical experience while engaging in modeling tasks. 相似文献
4.
Helen M. Doerr 《Educational Studies in Mathematics》2006,62(1):3-24
Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this paper, I present the results of a study in which teachers had extensive opportunities to examine the development of students' conceptual models of exponential growth in the context of their own classrooms. I describe two related aspects of the practice of one teacher: (a) how she listened to students' alternative solution strategies and (b) how she responded to these strategies in her practice. The results of the analysis suggest that as the teacher listened to her students, she developed a sophisticated schema for understanding the diversity of student thinking. The actions of the teacher supported extensive student engagement with the task and led the students to revise and refine their own mathematical thinking. This latter action reflects a significant shift in classroom practice from the role of the teacher as evaluator of student ideas to the role of students as self-evaluators of their emerging ideas. 相似文献
5.
M. Kathleen Heid Glendon W. Blume Rose Mary Zbiek Barbara S. Edwards 《Educational Studies in Mathematics》1998,37(3):223-249
Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are
one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics
teachers to use interviews to understand their students' mathematical understandings as well as to prepare teachers to use
technology-intensive curricula. This study examined the influences on three high school mathematics teachers as they learned
to use task-based interviews to understand students' mathematical understandings. The areas of teacher knowledge and conceptions
that influenced the teachers we studied were: teachers' mathematical understandings and knowledge of technology and the perceived
importance of curriculum topics; teachers' views of knowing mathematics; teachers' perceptions of students' characteristics
and needs; and teachers' perceptions of interviewing and the role of questioning in interviews.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
6.
This article presents findings from an ongoing study of urban teachers' efforts to embrace mathematics reform with student populations that are culturally, linguistically, and socioeconomically diverse (CLSD). We investigate the teacher's role in providing accessible and valuable mathematical learning opportunities to diverse students. Through narrative vignettes of practice and analyses of the personal and intellectual resources teachers draw on in CLSD contexts, we examine the challenges and possibilities two third-grade teachers face as they attempt such reform. One teacher's strengths were in making cultural connections with her students; the other's strengths were in pursuing complex and meaningful mathematics with her students. Building on our analysis, we offer a framework for examining the work of attending to mathematical and cultural issues simultaneously. Our findings suggest that such work is complex; however, teachers are seldom supported in their efforts to integrate these two perspectives. Our aim is to examine the dimensions of culturally relevant mathematics teaching and explore where the fields of mathematics and bilingual-bicultural education need to speak to one another. 相似文献
7.
本结合课程改革的实际，分析了课程改革进程中影响教师教学观念转变的五个因素：传统教育教学观念；新概念的理解程度；培训机制；评价机制；物质利益。并在此基础上提出了三个对策：建立适当的培训机制；尽快启动新的配套评价机制；继续改变教师的物质待遇，提高教师的社会地位。 相似文献
8.
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics.
In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research
on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate
the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests
that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms
where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional
approaches that support the learning of mathematics through the process of guided reinvention. 相似文献
9.
学习模式的变革取向与预期特点 总被引：2，自引：0，他引：2
根据学习模式类型的性质和价值,论述了当前我国学习模式变革的基本取向,并在此基础上,结合国内外教育教学改革的发展走势,分别从目标取向、学习理念、学习任务、评价倾向、教学方式、学习情境、学习分组、教师角色、学习者角色和信息技术支持等方面,描述了学习模式变革的十大预期特点,以期为认识和探索学习模式的变革提供一个具有可操作意义的思维框架。 相似文献
10.
本研究采用定性与定量相结合的方法,通过问卷调查英语专业二年级和四年级学生并收集数据,运用频率分布统计和因子分析对统计结果进行分析,以期考察不同年级学生对<跨文化交际>课程教与学的认知及其对相应课程标准的认同程度.研究结果表明两个年级的学生对<跨文化交际>课程标准呈现出较高的认同度,但他们的认识角度有所不同,认同的程度也有差异,二年级对课程的理解方式与课程标准更趋一致. 相似文献
11.
基于问题的学习与我国的教育现实 总被引：79，自引：0，他引：79
基于问题的学习是将学习"抛锚"于具体问题之中的一种情境化了的、以学生为中心的教学方法.它主张问题是学习的起点,注重学生的已有知识、小组合作和教师的指导或促进在学习活动中的作用.PBL与我国新课程改革中倡导的教育观念具有基本的一致性,但要全面实施这种模式,还必须要面对我国的教育现实,处理好教师角色转换与师资培训模式不协调的问题和学生自主学习与教育资源不足的矛盾. 相似文献
12.
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
13.
Erna Yackel Michelle Stephan Chris Rasmussen Diana Underwood 《Educational Studies in Mathematics》2003,54(1):101-126
In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of
using already established principles to design instruction, and vertical didactising the activity of developing new tools
and principles for instructional design. The first case illustrates horizontal didactising by elaborating how the constructs
chains of signification and models were used to design an instructional sequence involving linear growth. The second and third
cases illustrate vertical didactising by developing argumentation analyses and generative listening, respectively, as instructional
design tools. In the second case, argumentation analyses emerge as a tool that other designers can use to anticipate the quality
of conversations that can occur as students engage in tasks prior to implementing the instructional sequence. The third case
develops the notion of generative listening as a conceptual tool within the context of designing differential equations instruction
to gain insights into what are, for students, experientially-real starting points that are mathematical in nature and to provide
inspirations for revisions to instructional sequences.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a “real-world” scenario. Even though the school values students’ ideas, the reaction of the teacher to one student’s alternative modelling of the problem suggests that he was expecting a particular answer to be provided using routine mathematical models and thinking while not being interested in exploring the student’s unexpected alternative. We place his reasoning for doing so within broad pedagogical discourses that we think define the “allowable” responses of teachers and students in ways that inhibit meaning-making for both. These broad discourses are defined as the progressive constructivist approach, the scaffolding discursive approach, the situation modelling approach and the dialogic approach. We consider the advantages and the potential consequences each might bring to the case. We suggest that extensive consideration of pedagogical discourses in mathematics classes must be reconsidered both for how we understand students’ mathematical meaning-making and how we construct student agency in relationship to culture, whether as apprentices or authors. 相似文献
15.
In this study, we examined the instructional coherence in a Chinese mathematics classroom by analyzing a sequence of four
videotaped lessons on the topic of fraction division. Our analysis focused on the characteristics of instructional coherence
both within and across individual lessons. A framework was developed to focus on lesson instruction in terms of its content
and process and the teacher's use of classroom discourse. The analyses of lesson instruction were further supplemented with
the analyses of teaching materials and interviews with the teacher. The findings go beyond previous studies that mainly focused
on a single lesson to provide further evidence about Chinese teachers' instructional practices and their possible impact on
students' learning. In particular, the teacher tried to help students build knowledge connections and coherence through lesson
instruction. Results also suggest that coherent curriculum and the teacher's perception of the knowledge coherence facilitated
the teacher's construction of coherent classroom instruction. 相似文献
16.
This article examines how new forms of learning and expertise are made to become consequential in changing communities of practice. We build on notions of scale making to understand how particular relations between practices, technologies, and people become meaningful across spatial and temporal trajectories of social action. A key assumption of our perspective is that the scale relations that give meaning to our actions are not natural but are contested in social, cultural, and political projects. Studying these contentious activities can help us understand the nature of changing participation in dynamic and historically developed practices. Using case materials from 3 groups engaged in the local food justice movement in the western United States, we illustrate their engagement in equity-oriented scale making. Defining features of this work included identifying leverage points within inequitable systems; developing strategies for remediating scale relations to include the perspectives of historically marginalized groups; and coordinating trajectories of practice across settings, activities, and time so that these interventions became increasingly consequential. We conclude with a discussion of the significance of equity-oriented scale making as a lens for organizing design efforts and for studying their implications for nondominant communities. 相似文献
17.
18.
Julian Williams 《Educational Studies in Mathematics》2012,80(1-2):57-72
Empirical work has shown how mathematics education exhibits certain tensions between its value as being practically useful to production and consumption on the one hand and in offering access to scarce resources on the other hand. These tensions can be ultimately traced to the contradictions in the way mathematical knowledge enhances the use value and exchange value of labour power, respectively. To understand this as a social psychological phenomenon, I look to two well-known theoretical perspectives on education, first that of the Marxist psychology of Vygotsky and activity theory (and contemporary cultural–historical activity theory) which I find tends to marginalise ‘exchange value’. Second, I look to Bourdieu’s sociology of education that tends to marginalise the use value. I then bring together these two perspectives in a joint theory of education as both development and re-production of labour power, in which use and exchange value both have their place (in commodity production). This helps explain where mathematics education might be critical. 相似文献
19.
Written tasks that request an explanation can offer detailed information concerning students' knowledge to the classroom teacher.
The examination of students' written responses for the mathematical systems that are employed (referents), the connections
that are displayed (relationships) and the communication methods that are utilized (modes) provides evidence that suggests
how the student is making sense of a problem. The purpose of this article is to describe the constructs of referents, relationships
and modes and to illustrate how these constructs may be reflected in students' written responses to a decimal task that requests
an explanation. This article will also examine sets of responses from two classrooms using the proposed framework to illustrate
the type of information that teachers may acquire through the application of this framework.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Using data collected through two focus group interviews with 14- to 16-year-olds involved in a one-to-one laptop academic programme in a Singapore secondary school, this paper shows some student disengagement and dissatisfaction in class, and this poses questions about the relevance of the school's laptop programme. Our findings illustrate low productivity in the students' use of their computers as they respond to their teachers' instructional agendas. Our work indicates research into one-to-one laptop learning needs to pay greater attention to the minds, motivations and hands of students as they embark on learning they do not fully understand or can control for themselves. We determine that educators and policy-makers need to know a lot more about how growth in students' digital maturity operates. In the final analysis, we understand and explain the students' views about how their learning experiences might be improved, and their behaviour (as a digital wisdom journey centred on learning) to be digitally mature. 相似文献