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1.
This study reports the learning of elementary preservice teachers regarding diversity and teaching science in diverse urban elementary classrooms. From participating in a semester-long book club, the preservice teachers reveal their cultural biases, connect and apply their knowledge of diversity, and understand that getting to know their students are important elements for teaching science in diverse classrooms. These 3 things connect in ways that allow the preservice teachers to understand how their cultural biases impede student learning and gain new knowledge of diversity as they change their cultural biases. Implications of this study reveal that preservice teachers need opportunities to reveal, confront, challenge, and change their cultural models and to develop new models for teaching science in urban elementary classrooms.
Felicia M. MooreEmail:
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2.
Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what we call “teacher-focused” responses, whereas those doing less analysis work tended to construct “student-focused” responses. These results and their implications are discussed in relation to the influential factors the participants themselves identified to explain their approach to the given teaching-scenario task.
Sandra CrespoEmail:
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3.
This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.
Tim RowlandEmail:
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4.
This paper argues for an inclusive model of science education practice that attempts to facilitate a relationship between “science and all” by paying particular attention to the development of the relationship between the teacher, students and science. This model hinges on the implementation of cogenerative dialogues between students and teachers. Cogenerative dialogues are a form of structured discourse in which teachers and students engage in a collaborative effort to help identify and implement positive changes in classroom teaching and learning practices. A primary goal of this paper is to introduce a methodological and theoretical framework for conducting cogenerative dialogue that is accessible to classroom teachers and their students. I propose that researchers must learn to disseminate their findings to teachers in ways that are practical, in that they provide teachers with information needed to make concrete connections between the research and their teaching, while continuing to make available the theories that support their findings. Using an integration research framework in conjunction with a temporality of learning model, I introduce a method of disseminating research findings that provides both classroom teachers and researchers with access to different forms of knowledge about cogenerative dialogues in the same paper. In doing so, this article examines the relationships between teacher knowledge and researcher knowledge by exploring the practical application of cogenerative dialogues for classrooms teachers and the theoretical implications of using cogenerative dialogues for researchers.
Sonya MartinEmail:
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5.
Physics teachers’ approaches to teaching physics are generally considered to be linked to their views about physics. In this qualitative study, the views about physics held by a group of physics teachers whose teaching practice was traditional were explored and compared with the views held by physics teachers who used conceptual change approaches. A particular focus of the study was teachers’ views about the role of mathematics in physics. The findings suggest the traditional teachers saw physics as discovered, close approximations of reality while the conceptual change teachers’ views about physics ranged from a social constructivist perspective to more realist views. However, most teachers did not appear to have given much thought to the nature of physics or physics knowledge, nor to the role of mathematics in physics.
Pamela MulhallEmail:
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6.
Some educators experience difficulty documenting young children’s work in early childhood settings because of a limited understanding of the importance of documentation, what or how to document, and the effective use of documentation; limited resources (time, tools, and assistance); or predetermined curricular guidelines. Some teachers, especially inexperienced early years teachers, have trouble engaging with children and documenting simultaneously, revealing a crucial misunderstanding about the purpose of documenting. Teachers at Reggio Emilia-inspired schools throughout the United States use many forms of documentation to enhance the qualities of children’s experiences in preschool classrooms. This article addresses the dilemmas teachers face in implementing documentation in order to assist them as they move from standards-based teaching and teacher-determined content to a more constructivist approach to teaching. Ideas for using documentation shared by the authors will allow young children to construct their own knowledge and curiosity, making learning more meaningful to them and more visible to others.
Janice KroegerEmail:
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7.
The main goal of the study reported in our paper is to characterize teachers’ choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied according to their level—seven classes of top level students and six classes of mixed—average and low level students. In addition, pre and post lesson interviews with the teachers were conducted, and their lesson plans were examined. Data analysis was done in an iterative way, and the categories we explored emerged accordingly. We distinguish between pre-planned and spontaneous examples, and examine their manifestations, as well as the different kinds of underlying considerations teachers employ in making their choices, and the kinds of knowledge they need to draw on. We conclude with a dynamic framework accounting for teachers’ choices and generation of examples in the course of teaching mathematics.
Orit ZaslavskyEmail:
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8.
In this article I explore research in urban science education inspired by the work of Kris Gutierrez in a paper based on her 2005 Scribner Award. It addresses key points in Gutierrez’s work by exploring theoretical frameworks for research and approaches to teaching and research that expand the discourse on the agency of urban youth in corporate school settings. The work serves as an overview of under-discussed approaches and theoretical frameworks to consider in teaching and conducting research with marginalized urban youth in urban science classrooms.
Christopher EmdinEmail: Email:
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9.
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials from the history of Chinese math in modern mathematical education.
Youjun WangEmail:
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10.
11.
This article examines Mary Budd Rowe’s groundbreaking and far-reaching contributions to science education. Rowe is best known for her research on wait-time: the idea that teachers can improve the quality and length of classroom discussions by waiting at least 3 s before and after student responses. Her wait-time research grew from and helped inform her staunch advocacy of science education as inquiry; Rowe saw wonder and excitement as central to the teaching and learning of science. She spent much of her professional life designing professional development experiences and innovative curriculum materials to help teachers, particularly elementary school teachers, enact inquiry in their classrooms.
Julie A. BianchiniEmail:
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12.
This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes and student work are used both to illustrate these challenges, as well as to demonstrate growth over time. Implications for the design of mathematics courses for prospective teachers’ are discussed. Although the study is situated in the context of multiplication, it has implications for teachers reasoning and justification in other areas of mathematics.
Judith FlowersEmail:
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13.
This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that agency and accountability were distributed in the classrooms through interactions between the teachers and students as they worked on mathematical content. In doing so, we problematize the assumption that competencies are simply attributes of individuals that can be externally defined. Instead, we propose a concept of individual competence as an attribute of a person's participation in an activity system such as a classroom. In this perspective, what counts as “competent” gets constructed in particular classrooms, and can therefore look very different from setting to setting. The implications of the ways that competence can be defined are discussed in terms of future research and equitable learning outcomes.
Melissa GresalfiEmail:
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14.
This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers’ conceptions of beginning algebra and their conceptions of their own teaching practices. The teachers’ understandings of their teaching practices were explored with a view to unravelling their conceptions of change in their teaching. Focusing on the perspectives of teachers afforded opportunities that exposed the powerful role that the teachers’ conceptions of social/institutional factors of teaching played in their conceptions of their practices. The degree to which the teachers attributed these (external) factors as crucial reasons for what they do in their teaching was the basis of a categorisation of their conceptions of the crucial determinants of their teaching practices into three types. The findings are particularly relevant to our understanding of the stability of mathematics teaching approaches in the Colombian context but have likely implications for a range of international education contexts. Specific implications for the development of the research into teachers’ conceptions of mathematics and its teaching, and for teacher education programmes are presented.
Alan J. BishopEmail:
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15.
In this article, we concentrate upon the lifeworld resources that comprise the funds of knowledge for children living in a rural community in the southeastern United States. Through interview conversations with a group of third grade children, we identified three lifeworld resources—interdependence, garbage dumping, and feral dogs—that rural teachers might draw on to generate curriculum that is connected to the community in which they teach. Through such connections rural teachers may increase the likelihood that they will remain teaching in rural schools.
Amy Suzanne JohnsonEmail:
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16.
Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics. One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has started to gain attention as an important concept in the mathematics teacher education research community, there is limited understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article, we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in both mathematics education and the learning sciences.
Jason SilvermanEmail:
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17.
Student teaching (guided teaching by a prospective teacher under the supervision of an experienced “cooperating” teacher) provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching. The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur. We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the lesson and on mathematics from the students’ point of view. These contrasting experiences suggest that student teaching can have a profound effect on prospective teachers’ understanding of mathematics in and for teaching.
Steven R. WilliamsEmail:
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18.
This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.
Jesse L. M. WilkinsEmail:
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19.
This paper focuses on efficacy beliefs with respect to teaching mathematics; it aims at testing and validating an existing scale for measuring efficacy beliefs in the domain of mathematics, examining the development of preservice teachers’ efficacy beliefs in mathematics during fieldwork, and identifying factors that contribute to the development of these beliefs. Exploratory factor analysis applied to longitudinal data collected through a questionnaire administered to almost 90 preservice teachers elicited a two-factor model, reflecting efficacy beliefs in mathematics instruction and classroom management. Using cluster analysis, we found four patterns in the development of preservice teachers’ efficacy beliefs regarding these two factors. Our analysis of semi-structured interviews with eight participants representing these four patterns suggested that preservice teachers’ efficacy beliefs were mainly informed by experimentation with teaching and interaction with mentors, tutors, peers, and pupils. Based on our findings, we draw implications for mathematics preservice teacher education and provide suggestions for future research.
Charalambos Y. CharalambousEmail:
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20.
In response to the critical shortage of qualified mathematics teachers in the U.S., the TIME 2000 Program was created with funds from the National Science Foundation, at Queens College of the City University of New York. Now institutionalized, the program is designed to support the recruitment, preparation, and retention of prospective teachers through a close-knit learning community in which participants experience an innovative and multifaceted program for their four years of undergraduate study. This article describes the innovative aspects of the program that show promise of preparing highly competent teachers whose careers span a lifetime. Short- and long-term strategies for recruiting students from high school are described as well as the program components that are designed to increase retention of candidates in the program and in teaching.
Alice F. ArtztEmail:
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