数学教师信念研究综述

数学教师持有的信念支配着教师的教学活动,决定教师创设的课堂规则,影响学生的数学相关信念,学生学习的主动性和情感.在教学过程中,教师的教学经验、学生的信念、工作环境等因素阻碍教师信念得以实施.教师信念的形成与发展受其在学生时代形成的信念、师范教育计划、指导教师的信念、教学环境等因素的影响.     

Mathematics Instruction in Safe Space: Prospective Elementary Teachers' Views of Mathematics Education

This article discusses findings from an investigation into 42 prospective elementary teachers' views of mathematics teaching and learning. The focus is on how the participants saw the roles of teachers, pupils,and mathematics in mathematics classes as they communicated their views in journals written during the study. I argue that some prospective teachers express a tendency to protect and relieve their future pupils from mathematics. I show how this tendency affects a shift from school being the place where teachers teach pupils toward a conception of a safe space where the teachers predominantly care for the children. This revised version was published online in September 2006 with corrections to the Cover Date.     

Mathematics Across the University: Facing the Problem

Abstract

We explore the development of a Mathematics Advisory and Co‐ordinating Service (MACS) at Hull University. We discuss a theory of learning which supports our distinction between two types of mathematics support required in universities today. These two aspects of the problem lead to two distinct teaching models which relate back to the learning theory.     

Framing the Problem: effects of wording on children's statistical inferences

ABSTRACT A total of 96 children aged 11 to 12 years were given statistical inference problems (base‐rate and law of large numbers) designed to test the effects of wording on their answers. The wording of the problems was manipulated to make the information on base‐rates and on the law of large numbers either more salient or less salient. The latter condition was established by adding extraneous information to base‐rates, or, in the case of the law of large numbers, making the context unfamiliar or focusing choice on a particular person rather than on the group. A significant main effect of wording was found across all problems in favour of the salient condition. The results indicated that the children had a high level of statistical intuition and that they knew when to reason statistically and when not to.     

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.     

Problem Solving in Mathematics: Influence of Presentation

Lesh (1979) suggested that the interplay between the manipulative, pictorial and symbolic modes of representation in mathematics' problems enhances meaningful learning. However, Behr (1976) and Khoury and Behr (1982) contend that it is in fact extremely difficult for many students to achieve this interplay. Students seem to proceed through a problem solution in mathematics in one mode or another and then if requested, solve problems in another mode (Behr, 1976).     

基础数学中的极值问题

本对基础数学中的极值(最值)问题的处理办法作了探讨。     

Learning Mathematics for Teaching: From a Teachers' Seminar to the Classroom

A successful practice grounded in the principles that guide the current mathematics education reform effort requires a qualitatively different and significantly richer understanding of mathematics than most teachers currently possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K-6 teachers' mathematical development, (a) engagement in inquiry into mathematics itself, and (b) investigation of children's mathematical thinking, illustrating how the need for these two kinds of investigations arises in classroom situations and how they can be pursued in a professional development setting.     

农村留守儿童安全问题研究

近年来,农村留守儿童存在的教育问题、心理问题、健康问题、安全问题等引起了我国党和政府以及社会各界的广泛关注,成为今年“两会”期间许多全国人大代表和政协委员关注的一个焦点。农村留守儿童种种问题的解决已到了刻不容缓的地步。本文试图通过对农村留守儿童安全问题的现状及成因的分析,从家庭、学校、政府和社会四个层面提出解决农村留守儿童安全问题的对策。     

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.     

Teachers' Conceptions of Proof in the Context of Secondary School Mathematics

Current reform efforts in the United States arecalling for substantial changes in the natureand role of proof in secondary schoolmathematics – changes designed to provideall students with rich opportunities andexperiences with proof throughout theentire secondary school mathematicscurriculum. This study examined 17 experiencedsecondary school mathematics teachers'conceptions of proof from their perspectives asteachers of school mathematics. The resultssuggest that implementing ``proof for all' maybe difficult for teachers; teachers viewedproof as appropriate for the mathematicseducation of a minority of students. Theresults further suggest that teachers tended toview proof in a pedagogically limited way,namely, as a topic of study rather than as atool for communicating and studyingmathematics. Implications for mathematicsteacher education are discussed in light ofthese findings.     

职前小学数学教师教学知识状况调查——以分数除法为例

大部分师范生认为自己对从事小学数学教学有一定的准备,但具体到分数教学,师范生的自我评价较低.师范生对学科知识中的"算法"知识掌握得较好,能够正确地向小学生解释如何计算分数除法,但对"算理"掌握较差,在数学教学法知识方面,师范生准备还不够充分.解决问题时,所使用的教学表征以言辞表征和符号表征居多,直观表征很少,只有少部分师范生根据小学生的认知特点采取恰当的表达方式.大专生和本科生在大部分调查项目上的表现比较一致.     

Effective Professional Development in Science and Mathematics Education: Teachers' and Facilitators' Views

This study compares the views of teachers and professional development facilitators about effective professional development (PD). We analyzed interviews with 72 teacher participants and 23 PD facilitators involved in nine science and mathematics PD projects. The teachers' themes for characterizing effective PD included classroom application, teacher as learner, and teacher networking. Similarly, the PD facilitators discussed effective PD as having classroom application and experiences for teachers as learners. In addition, PD facilitators shared the need to develop collegial relationships with teachers and improve teacher knowledge. These views correspond to some of the standards and recommendations described in policy and research documents on effective PD. Criteria of effective PD in these documents that the participants did not mention included: (1) challenging teachers' content and pedagogical content knowledge with transformative learning experiences, (2) encouraging teacher leadership for sustained support, and (3) focusing on student learning by instructing teachers on how to use student data to inform their teaching practice. Our findings have implications for designing PD that reflects the criteria of standards-based reform.     

谈初中数学课堂教学中教师行为评价问题

在初中数学课堂教学中,＂是否完成认知目标＂限制了数学教师对学生认知能力以外的其他发展的关注,＂丝丝入扣＂的教学设计严重束缚了教学中的灵活性和变通性,＂样样俱全＂的课堂教学常常忽略了学生在学习中的实际需要。对初中数学教师教学行为进行评价包括先进的教学理念、备课方式的改进、学生＂创新能力＂的培养、学生学习状态的评价、对课堂教学的反思。初中数学教师课堂教学过程的评价细则分为对教学思想、教学目标、教学内容、教学环节、教学方法、教学效果、教师教学艺术、教师的基本素养、教师自我反思、教师对学生课外活动的指导情况十种评价。     

问题情境的创设:基于思维发展的理解

问题情境是一类具有思考性和贴近学生现实的数学问题.创设问题情境,其主要任务就是把概念和定理中的数学关系由已知转化为需要思考和探索的未知关系,并置于与学生相关的现实背景中,其核心意义在于激发学生的问题意识,引发学生的数学思考.引导教师从衍生性主题的设计、数学内容本质的把握、数学关系的转化以及问题结构的明确等方面去创设问题情境,有助于彰显问题情境对学生思维发展的教学意义.     

Expanding the Disciplinary Expertise of a Middle School Mathematics Classroom: Re-Contextualizing Student Models in Conversations With Visiting Specialists

This article examines how conversations during design reviews in which 8th-grade mathematics students shared population models with visiting specialists expanded the disciplinary expertise of the classroom. Re-contextualizing is a conversational exchange that visiting specialists initiated to invite groups to consider their models in novel contexts. Analysis of 14 design reviews in 2 classrooms showed that re-contextualizing resulted in both the elaboration of ideas students already understood and new contributions to students' understandings of mathematical aspects of population modeling. This article presents case studies of 2 groups that differed in terms of their interest in the curricular task and the level of conceptual integrity of their population models. Despite these differences, the re-contextualizing exchanges that emerged in their design reviews led to new insights for both groups and provided them with opportunities to try on ways of thinking and acting like population biologists.     

New Look at a Persistent Problem: Inequality,Mathematics Achievement,and Teaching

ABSTRACT

The authors examined the relation of school-year teaching practices to SES and race/ethnic score gaps in mathematics by fitting an individual growth model with a representative sample drawn from the Early Childhood Longitudinal Study Kindergarten Cohort data. There were mixed findings. Teaching practices had uniform effects for all students, increasing their scores equally during the school year. Teaching mattered in maintaining proficiency during summer, although modestly. Specifically, practices emphasizing analytical and reasoning skills, thought among mathematics reformers to be most effective, were positively associated with summer learning among low-SES students. The authors explore possible reasons for the weak association between teaching practices and mathematics scores.