初中高效数学课堂探索

随着我国教育体制改革的不断深入发展,初中数学的课堂教学工作也发生了重大改变,传统的教学模式已经逐渐的成为历史。初中数学是对小学数学与高中数学的一个衔接过程,是端正学生的学习态度,培养学生学习兴趣,养成创新思维的关键时期,因此,对如何促使初中数学课堂的高效性的研究工作具有重要的实际应用价值。     

论数学教具在课堂教学中的应用

活用日常物品,巧制简略教具,借助多媒体现代教具,助学生体验探索、交流、成功、提升的喜悦,激发学习数学的兴趣,提高数学教学效果,提高学生的动手操作本领和实践创新本领,提高课堂讲授的实效性。     

Values in the mathematics classroom

Abstract

Values, moral values and democratic values are attracting the attention of education researchers in general and mathematics education researchers in particular. Little research has studied pre-service teachers’ perceptions of values in the classroom, their perceptions of the relationship between the different variables of values in the classroom, as well as their relationship with the democratic society. The present research attempts to do so. Twenty-two graduate pre-service teachers who participated in ‘New trends in mathematics education’ course discussed how to cultivated values in the mathematics classroom. Moreover, they answered survey questions related to the cultivation of values in this classroom. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers’ texts. The research results indicate that the pre-service teachers perceived values as encouraging students’ activity in the mathematics classroom. In addition, the pre-service teachers perceived values as encouraging specific categories of values needed as skills for the citizen in a democratic society, as creativity, critical thinking and metacognition.     

On implementation strategy of primary school mathematics inquiry classroom

新课程倡导“动手实践,自主探索与合作交流”的探究式教学.我们要实施主动探求知识、动手实践、合作交流、发现问题、解决问题的学习方式,以发展学生独立研究的能力.     

谈小学数学探究性课堂的实施策略

新课程倡导"动手实践,自主探索与合作交流"的探究式教学。我们要实施主动探求知识、动手实践、合作交流、发现问题、解决问题的学习方式,以发展学生独立研究的能力。     

Learning to lose in the mathematics classroom: a critique of traditional schooling practices in the UK

“Back‐to‐basics” policies fit easily within many mathematics classrooms. Features such as order, control, rule following, uniformity, and conformity are relatively commonplace and are now more generally in demand with the current political backlash against progressive forms of schooling. This paper examines some of the influences of these traditional features of classrooms through a case study of one mathematics department in the United Kingdom. Interviews with students, lesson observations, results of questionnaires, and other case study data are analysed to show the ways in which traditional forms of learning can inhibit understanding, reify the divide between school and the “real world,” and suppress the transfer of knowledge. The findings suggest that two key elements of British Conservative education policy the commitment to traditional forms of schooling and the drive to produce school leavers capable of adapting to the demands of the 21st century — are fundamentally in conflict.     

The phenomenology of the mathematics classroom

This paper describes the mathematics classroom from the perspective of social phenomenology. Here the classroom is seen as an environment of signs, comprising things and people, which impinge on the reality of the individual child. The paper introduces a framework through which mathematical work is seen as taking place in the imagined world through the filter of the world in immediate perception. This provides an approach to structuring evolving mathematical understanding. It is suggested that mathematical ideas are contained and shaped by the child's personal phenomenology, which evolves through time. Further, I argue these ideas are never encountered directly but rather are met through a circular hermeneutic process of reconciling expectation with experience.     

浅析如何在数学教学中提高课堂教学效率

在数学教学中,如何提高课堂教学效率,促进学生素质的全面发展,是长期困惑教师的问题。本文对提高课堂效率进行了初步的探索和实践:建立和谐的人际关;多途径地激发学生的学习兴趣;运用多媒体辅助教学;实施分层作业。     

Mythmaking and mythbreaking in the mathematics classroom

Constructivism has become a major focus of recent pedagogical reform in mathematics education. However, epistemological reform that is based on the constructivist referent of learning as conceptual change has a very limited viability in traditional mathematics classrooms because of its cultural insensitivity. By contrast, the social epistemology of critical constructivism addresses the socio-cultural contexts of knowledge construction and serves as a powerful referent for cultural reform. From this perspective, the social reality of traditional mathematics classrooms is governed by powerful cultural myths that restrain the discursive practices of teachers and students. The power of the repressive myths of cold reason and hard control is evident in the ways in which they act in concert to create a highly coherent and seemingly natural social reality. Epistemological reform of traditional mathematics classroom learning environments is, therefore, synonomous with cultural reconstruction. Critical constructivism, which has a central concern with discourse ethics and the moral agency of the teacher, draws on the social philosophy of Jurgen Habermas and argues for an alternative culture of communicative action to be established in mathematics classrooms. Teachers are expected to work collaboratively as agents of cultural change in forums beyond their classrooms.Religions, philosophies, arts, the social forms of primitive and historic man, prime discoveries in science and technology, the very dreams that blister sleep, boil up from the basic, magic ring of myth.(Joseph Campbell, The Hero With a Thousand Faces, 1968, p. 8.)     

浅谈学具操作在小学数学课堂教学中的作用

学具操作对小学数学课堂教学非常重要。近几年的教学实践证明,在小学数学课堂教学中,适当地引导学生动手操作,让学生通过学具操作参与知识的形成过程,对唤起学生的求知欲、帮助学生理解算理和掌握数学概念、培养学生的探索能力都起着非常重要的作用。     

Proofs and refutations in the undergraduate mathematics classroom

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.     

On some psychological aspects of mathematics achievement assessment and classroom interaction

The way students and teachers evaluate mathematics achievement differs in certain respects. To which causal performance is ascribed determines the teacher's strategy to interact with the student on the one hand and influences the student's willingness to invest additional effort on the other. Certain possible causal factors for success and failure in mathematics and their relation to teacher-student-interaction are discussed in the present article. A rather general cognitive scheme, the teachers reference norm, explains differences between the teacher's perception and assessment of student characteristics and subsequent teaching interventions.     

Non‐optimal uses of video in the classroom

This paper examines some instructional practices concerning the non‐optimal uses of video, films and other mass media in the K–12 classroom. Based on a six‐year process of observing and interviewing teachers regularly in two school districts in Massachusetts, USA, this paper presents a typology of seven common patterns of non‐optimal media use, instructional practices that diminish or weaken the value of film and video viewing as a learning tool. A telephone survey was conducted with a purposive sample of 130 middle‐school and high‐school teachers to provide additional evidence concerning teacher perceptions of the frequency of their colleagues' non‐optimal use of video. Teachers in the USA report that their colleagues frequently use media for non‐educational purposes, including to fill time, to keep students quiet, as a break from learning, or as a reward for good behavior. The implications of non‐optimal media use are considered in light of renewed interest in integrating media literacy into K–12 instruction.     

The uses and abuses of boredom in the classroom

Although the educational and psychological hazards of boredom are well documented, an increasing number of researchers have argued that boredom may be a helpful, rather than harmful, emotion for the growing individual. In this paper, we engage with this re-conception of boredom and explore its implications for contemporary education: Can boredom enhance student learning, or support certain forms of it? Can it be put to use in the classroom? What are the risks involved? In addressing these questions, we show that boredom can fulfil several important psychological functions under certain special conditions. At the same time, we argue that careful attention to the moral psychology of boredom reveals that it has significant disadvantages for helping students to develop a meaningful and fulfilling relationship to subject matter in the classroom. Against the backdrop of this analysis, we discuss the concept and experience of aspiration as a potential way of tempering and eventually obviating the psychological pitfalls of boredom. In the final section, we draw out several principles of an aspirational approach to grappling with boredom in education.     

Interactive development of subject matter in the mathematics classroom

There are considerable differences among mathematics teachers with regard to the quatlity of their way of developing mathematical knowledge in the classroom. Such differences are analysed. To develop mathematical meaning requires both a consistent presentation of the mathematical symbols and of the referential meaning of these symbols with respect to the given task. On the basis of this conception we assume that the quality of teaching will differ according to how teachers cope with the relation between these two sides of meaning. From a sample of 26 teachers, an expert teacher and a non-expert teacher were selected by means of classroom observation with scales of instructional quality variables. For each of these two teachers, two lessons introducing probability (sixth grade) are analysed. For this purpose, teacher and student contributions are coded. For the expert teacher, graphic visualizations of the development of mathematical concepts across time show soft transitions between the different aspects of mathematical meaning. These transitions are made possible by a consistent explication of the relation between formal symbols and the given mathematical task. In the case of the other teacher, explication of the relationship between the object side and the symbol side of mathematical meaning is much rarer, and there are sudden switches from one aspect of meaning to another. Further differences concern the handling of student contributions.We gratefully acknowledge the help of Wolfgang Barz, Regina Dietrich and Claudia Krüger with recording, transcribing or coding lessons. For their comments on draft versions of the paper the authors thank Deborah Ball, Jere Brophy, Willibald Dörfler, Alexander Gruza and two anonymous reviewers.     

Interaction and learning in mathematics classroom situations

An analysis of one ten minute episode in which three seven year-old students engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Particular attention is given to the establishment of a taken-as-shared basis for mathematical activity and to the attainment of intersubjectivity. From a perspective which treats communication as a process of active interpretation and mutual adaptation, learning as it occurs in the course of social interaction is characterized as a circular, self-referential sequence of events rather than a linear cause-effect chain. In addition, the relationship between individual learning and group development is such that the students can be said to have participated in the establishment of the situations in which they learned.