学习数学的重要思想方法——联想

要提高学生的素质 ,培养适应当今高科技时代的人才 ,必须让学生学好数学 ,而学好数学要有恰当的思想方法 ,联想是学习数学的重要思想方法     

Teacher Learning in Mathematics: Using Student Work to Promote Collective Inquiry

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.     

如何做一个中学数学好教师

数学是中学阶段的基础学科,新课程改革提出了数学学科教学的基本理念:每个学生都要学习有价值和必要的数学知识,让每个学生都能在数学学习上获得不同程度的发展。新课程理念给中学数学教师提出了更高的要求和全新的挑战。文章从调动学生学习数学的积极性和提升教师的个人教学素养两个方面论述了如何做好一个中学数学教师。     

Teacher Actions to Maximize Mathematics Learning Opportunities in Heterogeneous Classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.     

教师发展的非反思路径

教师发展有反思与非反思两条途径。前者是教师在将教育教学活动对象化、课题化和教育认识显性化、公共化的前提下,通过理性方式谋求发展。后者是教师在未将教育教学活动对象化、课题化和教育认识显性化、公共化的前提下,以非理性方式谋求发展。非反思路径要么被忽视,要么被轻视,形成了反思路径的"唯一性神话"。这个神话源自理性主义认识论及建基于此的教师专业发展概念。而这两者在哲学与教育学中都遭到了批判。因此,我们应关注、重视非反思路径。它的形态包括:默会怀疑、内隐学习、悟性思维、以心识心等。     

Learning Through Reflection in Mathematics Teacher Education

This article is written from our perspective as both researchers and mathematics teacher educators, and describes how our knowledge has grown as we engage concurrently in both teaching and research. Reflection-on-action is a means for us of approaching the relationship between theory and practice that comes out of the development of our work as researchers and mathematics teacher educators. The article presents the different steps we have identified in the relationship between theory and practice during our professional development. In the discussion, we examine the whole sequence of steps showing what we have learnt. Afterwards, we use the sequence of activity of the reflective process as a framework in which we can operate and reflect about our own development.     

教师专业发展基本途径的探索

教师作为课程执行者,他们的专业发展在很大程度上决定教育教学质量,决定学生的发展程度。因此,我们有必要对教师专业发展的基本途径进行探索。     

Opportunities for Professional Learning in Mathematics Teacher Workgroup Conversations: Relationships to Instructional Expertise

Increasingly, instructional improvement efforts include teacher communities as part of their overall strategy, yet the relationship between teachers’ talk and professional learning remains underspecified. Using a discourse perspective on learning, this article compares opportunities to learn (OTLs) in the collaborative conversations of 3 mathematics teacher workgroups. We examined the differences in OTLs in 17 hr of videotaped meetings from 3 groups at different levels of instructional accomplishment in secondary mathematics. Using mixed methods, we uncovered differences in the groups’ interactions and found that OTLs were not equally distributed. Instead, teacher groups whose active participants demonstrated the greatest facility with ambitious instruction also had the richest conversational OTLs. We interpret this as an accumulated advantage developmental story: Because collaborative work in teaching involves problem posing and the articulation of practice, teachers’ conceptions get built into the framing and discussion of pedagogical problems. Accomplished teachers are thus positioned to learn more from talking with colleagues. This analysis contributes to understanding of how OTLs are constituted in teacher workgroups, with implications for making better use of teacher collaboration for professional learning.     

An Account of a Teacher's Perspective on Learning and Teaching Mathematics: Implications for Teacher Development

This report presents an account of one teacher's mathematics teaching and a perspective that underlies his teaching. Nevil was a fifth grade teacher participating incurrent mathematics education reforms in the United States. Through the account, we make distinctions about teachers' thinking and practice that can inform teacher education efforts. We constructed an account by analyzing four sets of classroom observations and interviews. We observed that Nevil decomposed his understandings of the mathematics into smaller components and connections among those components. He created situations that he believed made those components and connections transparent and attempted to elicit those connections from the students. This account illustrates a practice that is different both from traditional practice and the type of practice that we would envision as a goal for teacher development. We contribute two important aspects of mathematics teacher development from traditional to reform-oriented teaching. In particular, we describe teachers' perspectives – assimilatory structures that constrain and afford (a) the sense they make of professional development opportunities and (b) their potential learning in teacher education settings. This revised version was published online in August 2006 with corrections to the Cover Date.     

Laboratory Approach to Secondary Teacher Professional Development: Impacting Teacher Behavior and Student Engagement

Abstract

The Literacy Lab Professional Development provided a laboratory approach to professional development for 42 high school teachers in two schools. Three main activities included: (1) planning and professional development days, (2) lab and professional development days, and (3) individual coaching. The targets of the Literacy Lab Professional Development and its associated guiding questions focused on student engagement and understanding, teaching students how to make meaning from text, teaching students to write, and the structures, systems, routines, and rituals needed to create a classroom culture of thinking and learning. Results from this study point to positive differences between participating and matched-nonparticipating teachers in their instruction, student grouping, nature of tasks, task demands, types of knowledge expectations, personalization, tone, and authority structures.     

Teacher Professional Development Approach: Action Research

Theory and practice, researchers and practitioners are usually isolated in traditional education research, so much so that the research results can not solve the problems that teachers encounter in their teaching practice. As a new mode, action research provides a bridge linking theory and teaching practice as well as a way to promote teacher development.     

Learning to Learn to Teach: An ``Experiment' Model for Teaching and Teacher Preparation in Mathematics

This paper describes a model for generating andaccumulating knowledge for both teaching andteacher education. The model is applied firstto prepare prospective teachers to learn toteach mathematics when they enter theclassroom. The concept of treating lessons asexperiments is used to explicate theintentional, rigorous, and systematic processof learning to teach through studying one's ownpractice. The concept of planning teachingexperiences so that others can learn fromone's experience is used to put into practicethe notion of contributing to a sharedprofessional knowledge base for teachingmathematics. The same model is then applied tothe work of improving teacher preparationprograms in mathematics. Parallels are drawnbetween the concepts emphasized for prospectiveteachers and those that are employed byinstructors who study and improve teacherpreparation experiences. In this way, parallelsalso are seen in the processes used to generatean accumulating knowledge base for teaching andfor teacher education.     

美国《中学数学教与学》教材的特点及其对中国数学教师教育的启示

美国《中学数学教与学》是初中年级数学教师教育"数学教学法"课程的教材,其特点表现为:单元主题以数学教学理论为线索呈现,单元内容以具体数学知识为载体展开并且以参与式活动的形式组织教学活动.该教材对我国的数学教师教育有如下启示:数学教师教育课程应以数学知识为载体学习数学教育理论;数学教师教育教材应突出教学方式的示范性,体现做中学,在数学教学活动中学习数学教学方法;数学教师教育应注重教师学科专业素质的提升.     

教师合作:教师发展的一个重要路径

20世纪80年代以来,教师合作作为教师发展的一种方式获得广泛的关注,成为国际教师教育研究领域中一大热点问题。本文认为,所谓教师合作,就是教师们为了改善学校教育实践,以自愿、平等的方式就共同感兴趣的问题,共同探讨解决的办法,从而形成的一种批判性互动关系;教师合作有助于激发与强化教师发展意愿、提高教师个体反思能力、促进学校组织学习。     

Professional Development of Mathematics Teacher Educators: Growth Through Practice

In this paper we present a study conductedwithin the framework of an in-serviceprofessional development program for junior andsenior high school mathematics teachers. Thefocus of the study is the analysis of processesencountered by the staff members, as members ofa community of practice, which contributed totheir growth as teacher educators. We offer athree-layer model of growth through practice asa conceptual framework to think about becominga mathematics teacher educator, and illustratehow our suggested model can be adapted to thecomplexities and commonalities of theunderlying processes of professionaldevelopment of mathematics teacher educators.     

Reflections on an Emerging Field: Researching Mathematics Teacher Education

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education conference proceedings. Some regional sources from various parts of the world were also included. We investigated who was writing, from and in what settings, with what theoretical frameworks, and with what sorts of study designs for what core questions. We also examined the range of findings and conclusions produced in these studies. Our analysis presented here focuses on four themes that stood out from our initial investigation of almost 300 published papers, and systematically elaborated through a focused study of a 160 papers across key journals and conference proceedings in the field. From this vantage point, the paper offers a reflection on the current state of the field of mathematics teacher education research. Our aim is to stimulate discussion that can support the development of the field, not make final pronouncements about its nature. The research presented in this paper was done by five mathematics education researchers, the authors listed above, and presented at ICME10 in Copenhagen in July 2004. This Survey Team (Survey Team 3) was nominated by the International Program Committee for the Congress and asked to survey “Professional Development of Mathematics Teachers” and present this in a plenary at the Congress. A copy of the presentation can be viewed at: http://www.wits.ac.za/jadler/presentations.html. An earlier version of this paper will also appear in the ICME10 proceedings.