Inquiry into Children's Mathematical Thinking as a Means to Teacher Change

In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's engagement with children's thinking changed dramatically in a period of only a few months; observations and interviews several years later confirm she sustained this change. Our analysis focuses on the mathematical discussions she had with her students, and suggests this talk with children about their thinking in instruction served both as an index of change, and, in combination with other factors, as a mechanism for change. We identified four phases in Ms. Statz's growth toward practical inquiry, distinguished by her use of interactive talk with children. Motivating the evolution of phases were two sorts of mechanisms: scaffolded examination of her students' thinking; and asking and answering questions about individual students' thinking. Processes for generating and testing knowledge about children's thinking ultimately became integrated into Ms. Statz's instructional practices as she created opportunities for herself, and then students, to hear and respond to children's thinking.     

Explicit and Implicit Dimensions of Adult–Child Interactions in a Quality Childcare Center

The case study presented in this article is designed to provide an in-depth understanding of how a highly trained and experienced early childhood educator thinks about her interactions with children within the context of a setting identified as providing quality childcare for 3-, 4-, and 5-year-olds. Qualitative research methods are used, including interviews, participant observation, videotaping, and the teacher's reflections on interactions with children. Verbal and nonverbal patterns emerging from videotaped observations demonstrate how the teacher integrates information about specific children into these interactions. Although children's conceptions of time and space are consistently embedded in her thinking and reflected in her behavior, she never explicitly acknowledges these dimensions. The paper concludes with a discussion of the implications of the discrepancy between the teacher's implicit and explicit understanding of her interactions with children to childcare and the preparation and development of early childhood practitioners.     

诚与雅的执着追求——宗璞创作论

宗璞是一位沐浴在西方艺术之中,又深受中国传统文化熏陶的知识型女作家,其文学创作坚持“诚”与“雅”的原则,执着于知识分子生活的描写,并从中升华出哲思和理意,在艺术上追求“外观手法”和“内观手法”、再现和表现相结合。从整体上审视,宗璞的创作呈现出真性情、理趣化、含蓄蕴藉的特征。     

Inclusive education at a BRAC school – perspectives from the children

Tahiya Mahbub is a lecturer in English studies at North South University located in Dhaka, Bangladesh. In this article, she presents some of the data on which her MPhil thesis, completed at the University of Cambridge Faculty of Education, was based. This research was carried out in Bangladesh, focusing on a primary school run by the non-governmental organisation (NGO) BRAC. Tahiya Mahbub adopted a case study approach in order to investigate this single-teacher, single-room school in Tongi, a suburb of Dhaka, the capital of Bangladesh. The work she reports here explores children's understandings about the culture, policy and practice at their school. Tahiya Mahbub argues that this sort of inquiry is necessary to the development of inclusion. She advocates equality and togetherness not only for children in school, but also between children and adults in educational research and eventually in the bigger picture of society itself. Finally, she proposes, it is essential to listen to children's experiences of school, their suggestions for change and their ideas in order to lift children's low social status in Bangladesh.     

一切为了边缘人 为了边缘人的一切——赛珍珠文学创作动因探究

赛珍珠拥有多重身份:她是父母不幸婚姻的见证者,是不幸婚姻的受害者,是智障儿童的母亲,是通晓中西文化却不被任何一方所接受的文化边缘人。这种多重身份无不例外的将赛珍珠置于一个令人尴尬的边缘人状态。作为一个边缘人,她关心同样处在社会边缘地位的人们———女人、儿童和包括中国、日本等在内的处于弱势地位的亚洲国家的人们。女性文学作品的创作,寄予了她对女性的同情与期望;儿童文学的创作,表明她对儿童的关心与厚爱;东西文化交流题材的写作,折射出她对中西文化平等对话的渴望。一切为了边缘人,为了边缘人的一切,是赛珍珠文学创作动因的真实写照。     

一例大学生完美主义倾向的辅导案例报告

大二学生小辛,女,20周岁。因为思维“神游”,无法集中注意力学习。真实的自己和现实的自己完全不同,无法统一,怀疑自己人格分裂,特别痛苦,抱着最后的希望来求助。通过访谈了解到,小辛的情绪情感长期压抑,有很强的完美主义倾向,始终在追求认可,其思维模式中存在不合理信念。通过三次心理分析和认知治疗。让小辛明白自己性格、认知中的偏颇是其问题的核心原因所在,从而调整认识,促其心理行为的改善。     

游走在社会的边缘——《所罗门之歌》里派拉特人物分析

小说《所罗门之歌》里具有传奇色彩的派拉特作为一个悲剧性人物,她守护着家族的历史,却并不完全了解家族的历史;她独立自强,一直坚守着黑人民族文化传统,却没能与时俱进、融入到现实社会中;她有着大爱,并随时愿意帮助别人,可却被排斥在黑人群体之外,实际上她一直游走在社会的边缘。     

论张洁早期小说中的女性意识

张洁在她早期的小说创作中，高举“女性意识”的大旗，在《爱，是不能忘记的》、《方舟）、《祖母绿）、《七巧板》等一系列小说中，执著于对女性问题的思考和探索。通过对真正爱情的深情呼唤，对独立女性的礼赞和同情，对庸俗女性和低俗男人的嘲讽，向以男性为中心的社会发起了冲击，具有鲜明的女性意识。     

Two-Year-Old Children's Sensitivity to a Parent's Knowledge State When Making Requests

These studies examined whether toddlers take their communicative partners' knowledge states into account when communicating with them. In Study 1 , 16 2-year-old children (mean age 2-7) had to ask a parent for help in retrieving a toy. On each trial, a child was first introduced to a new toy that was then placed in 1 of 2 containers on a high shelf. The parent either witnessed these events along with the child or did not because she or he had left the room or had covered her or his eyes and ears. As predicted, when asking for help in retrieving the toy, children significantly more often named the toy, named its location, and gestured to its location when a parent had not witnessed these events than when she or he had. In Study 2, 16 2-year-old children (mean age 2-3) had to ask a parent for help in retrieving a sticker dropped into 1 of 2 identical containers placed out of reach in the far corners of a table. The parent either witnessed, along with the child, which container the sticker was dropped into or did not because her or his eyes were closed. In their requests for help, young 2-year-old children gestured to the sticker's location significantly more often when the parent did not know its location than when she or he did. The implications of these findings for current characterizations of 2-year-old children's ability to assess the knowledge of others is discussed.     

汉娜·阿伦特论思的政治意义

以对20世纪的一系列政治问题的反思而著称于世的当代著名政治哲学家汉娜·阿伦特,晚年从她一直关注的政治问题转向哲学问题。在《精神生活》在这部未完成的著作中,她力图弥合传统上“精神生活”和“行动生活”的对立,阐明政治活动的精神性基础,并对“平庸罪恶”这一现象做出理论上的解释,说明思为何具有抗拒邪恶的力量。阿伦特对思的政治意义的分析得益于西方哲学史上的两位大师:康德和苏格拉底。从康德那里,她学会了思是什么;从苏格拉底那里,她学会了思的方式。     

《包法利夫人》中爱玛的爱情悲剧

爱玛是小说《包法利夫人》中的主人公,她短暂的一生是在不断追求理想爱情的过程中度过的。可她所追求的理想爱情一再破灭,最后在走投无路中死去。文章试图通过对爱玛与三个男人的爱情悲剧及悲剧原因的分析,使人们认识到爱玛的爱情悲剧主要是由社会、环境以及她自身的因素造成的,希望能给人一点新的启示和思考。     

Weaving curriculum webs: Planning,guiding, and recording curriculum activities in the day care classroom

One Monday morning, Sandra walked into her day care classroom with a heavy box filled with rocks. She announced with pleasure to her four- and five-year-old classmates that she had begun a rock collection. Other children quickly came over and began making comments about the colors and sizes of the rocks and about rocks they had found themselves.Diane E. Levin is Associate Professor of Education at Wheelock College in Boston, MA.     

A Case Study of the Development of a Beginning Chemistry Teacher's Knowledge about Models and Modelling

In this paper, we present a case study of a beginning chemistry teacher who enrolled in a project aimed to contribute to the development of teachers' knowledge of models and modelling in science. The project consisted of a series of institutional meetings in combination with an action research project the teacher conducted in her own classes. By explaining how the project was conducted and mainly by focusing on the teacher's voice, her dynamic, continuous, and non-linear process of knowledge development is discussed in detail. We were able to investigate and describe this development in terms of various types of knowledge – content knowledge, curricular knowledge and pedagogical content knowledge – which were developed simultaneously. Among other results, it became clear how certain institutional activities led to specific choices in the teacher's action research project. For instance, although initially she was reluctant to conduct a modelling activity in her class, she decided to experiment with such an activity in her action research project. Subsequently, the responses of her students during the project convinced her of the value of this modelling activity and helped her to become aware of specific views of her students. Finally, it became evident that the whole experience made her very enthusiastic and stimulated her to formulate specific intentions with respect to the future, both in terms of applying certain teaching activities and in terms of collaborating with colleagues.     

Elizabeth Anderson interviewed by John White

The distinguished US philosopher Elizabeth Anderson, who teaches at the University of Michigan, answers questions put to her by John White about educational aspects of her work in moral and political philosophy. She begins by describing her indebtedness to Dewey in his views on developing students’ capacities for intelligent enquiry and as citizens in a democracy. She elaborates on this in her emphasis on children learning fraternally together with others of diverse class, racial and ethnic backgrounds. She also discusses the control of education, looking at the role of the state and other political authorities in education, the charter school movement and home schooling. Well‐known for her views on democratic equality (as distinct from equality of fortune) and on an adequacy criterion of fairness, she shows how these ideas apply to education for a democratic society. This takes her into critical discussions of equality of educational opportunity, education as a positional good, and the rich variety of educational aims fitting a democracy of equals. Anderson has also written about the errors of theistic religion as well as two award‐winning recent books on the imperative of social integration and on the authoritarian powers of employers. Developing these thoughts in an educational direction, she writes here about religious and moral education, problems with assimilationist and multicultural approaches to schooling, and preparation for work as an educational aim.     

Understanding Teacher Educators and Their Pre-Service Teachers through Multi-Media Case Studies of Practice

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.     

浅析《呼兰河传》的叙事策略

萧红是中国现代文学史上著名的女作家。《呼兰河传》是萧红后期的代表作,她采用童年视角,反讽叙事以及女性自我悲剧的认同等多种叙事策略,其中浸透了她对人生的思考,对国民性所造成的悲剧的思考,特别是她作为一名女性对女性命运的思考。     

儿童文学是最美的事业——解读秦文君的儿童文学观

秦文君是当今创作成绩辉蝗并广受少年儿童读者欢迎和热爱的作家，她热爱儿童，热爱儿童文学创作，把儿童文学事业视为最美的事业。秦文君完全是用一颗爱心来创作的，她重视儿童文学的教育作用，强调儿童文学作家的责任感，能充分考虑儿童读者的接受能力和独特的审美趣味。秦文君又完全是用一颗童心来创作的，她极力宣扬其“儿童本位”的儿童文学观，强调创作目的的“为儿童”和创作原则上的“少儿视角”。     

Development of metacognitive concepts about thinking in gifted and nongifted children: Recent research

This article provides an overview of recent research in our laboratories on the development of metacognition in gifted and nongifted children. Research examining the development of children's metacognitive knowledge of mental activity concepts, general declarative metacognitive knowledge, and specific metacognitive attributions are reviewed. The present studies found, as had Alexander, Carr, and Schwanenflugel (1995), patterns of gifted and nongifted metacognitive development differed depending on the type of metacognitive knowledge being examined. Specifically, recent research on knowledge of mental activity concepts showed no clear advantages for gifted children over nongifted children. Declarative metacognitive knowledge research continues to support a monotonic advantage hypothesis in which gifted children show consistent advantages over nongifted children during the early elementary school years. This advantage, however, is short-lived due to the possible presence of a ceiling effect showing a closing of the declarative metacognitive knowledge gap between gifted and nongifted children around fourth grade. Finally, recent research on specific metacognitive attributions suggests that more intelligent children develop more sophisticated attributions over time but their ability to use this information may be more dependent on other individual differences variables that may or may not be related to intelligence such as knowledge base familiarity. We conclude that it is important to differentiate the types of metacognitive knowledge being measured in studies as we investigate individual differences in the development of children's metacognitive insights about thinking.     

Development of professional knowledge in learning to teach elementary science

The purpose of this research was to understand how preservice elementary teacher experiences within the context of reflective science teacher education influence the development of professional knowledge. We conducted a case analysis to investigate one preservice teacher's beliefs about science teaching and learning, identify the tensions with which she grappled in learning to teach elementary science, understand the frames from which she identified problems of practice, and discern how her experiences played a role in framing and reframing problems of practice. The teacher, Barbara, encountered tensions in thinking about science teaching and learning as a result of inconsistencies between her vision of science teaching and her practice. Confronting these tensions between ideals and realities prompted Barbara to rethink the connections between her classroom actions and students' learning and create new perspectives for viewing her practice. Through reframing, she was able to consider and begin implementing alternative practices more resonant with her beliefs. Barbara's case illustrates the value of understanding prospective teachers' beliefs, their experiences, and the relationship between beliefs and classroom actions. Furthermore, the findings underscore the significance of offering reflective experience as professionals early in the careers of prospective teachers. © 1999 John Wiley & Sons, Inc. J Res Sci Teach 36: 121–139, 1999     

Reification of instructional materials as part of the process of developing problem‐based practices in mathematics education

This teacher development study closely examined a teacher's practice for the purpose of understanding how she selected and implemented instructional materials, and correspondingly how these processes changed as she developed her problem‐based practice throughout a school year. Data sources included over 20 hours of planning and analysis meetings with the teacher and 27 video‐taped lessons with discussions before and after each lesson. Through qualitative analysis we examined the data for: students' cognitive demand for curricular materials the teacher selected and implemented; teacher's beliefs and practices for students' engagement in mathematical thinking; and teacher's and students' communication about mathematics during instruction. We found that the teacher shifted her views and use of instructional materials as she changed her practice towards more problem‐based approaches. The teacher moved from closely following her traditional, district‐adopted textbook to selecting problem‐based tasks from outside resources to build a curriculum. Simultaneously, she changed her practice to focus more on students' engagement in mathematical thinking and their communication about mathematics as part of learning. During this shift in practice, the teacher began to reify instructional materials, viewing them as instruments of her practice to meet students' needs. The process of shifting her views was gradual over the school year and involved substantial analysis and reflection on practice from the teacher. Implications include that teachers and teacher educators may need to devote more attention and support for teachers to use instructional materials to support instruction, rather than materials to prescribe instruction. This use of instructional materials may be an important part of transforming practice overall.