试析数学建构性教学中教师的作用

建构主义的数学学习观 ,对教师在数学教学中的作用需要作出新的认识 :教师是学生数学学习活动的促进者 ;教师要为学生的数学学习活动创造一个良好的学习环境 ;教师要了解学生的需求信息 ;教师要培养学生的自我调控能力     

学校环境对数学学习的影响

在数学教学中，数学教师、数学教材、同学关系3个因素对学生数学学习的影响极大，数学教师的教学是学生学好数学的前提；数学教材是学生进行学习的主要依据；班集体的学风不仅影响学生的学习成绩，也影响它们的学习态度和价值观，良好的学校环境会激起学生对数学学习的兴趣，加深学生对数学学科的内容，特点和规律的理解。     

略论激发学生学习数学的兴趣

兴趣是最好的老师。为引导学生对学习数学产生兴趣,教师应创设情境,诱发学生的学习兴趣;运用直观教学,培养学生的学习兴趣;引导学生动手操作,激发学生的学习兴趣;多用鼓励性语言,调动学生的学习兴趣。     

我国数学教师职前教育研究综述

在数学教师职前教育的研究文献中,研究者进行了大量深入而细致的研究,在理论和实践、模式及内容上都取得了丰硕的成果．主要集中在以下几个方面：高师数学教育现状;培养目标：高师数学教育改革的理论建构;高师数学教育改革的实践．追溯教师专业化水平不高在对双专业理解水平偏低方面的渊源,奠定教师专业化形成与发展中对双专业深刻理解的基础,我们应在数学教师教育改革中为之做出不懈的努力．     

我国数学教师职前教育研究综述

在数学教师职前教育的研究文献中,研究者进行了大量深入而细致的研究,在理论和实践、模式及内容上都取得了丰硕的成果.主要集中在以下几个方面:高师数学教育现状;培养目标;高师数学教育改革的理论建构;高师数学教育改革的实践.追溯教师专业化水平不高在对双专业理解水平偏低方面的渊源,奠定教师专业化形成与发展中对双专业深刻理解的基础,我们应在数学教师教育改革中为之做出不懈的努力.     

谈充实数学教师数学史知识的必要性

现代教育倡导素质教育,作为高校数学教师,承担着培养高素质数学人才的任务,除了具备过硬的专业知识外,拥有一定的数学知识,对于更好地理解数学,提高自己的数学素质,提升课堂效果,发展学生的智力是非常必要的。     

The Development of Diploma in Education Student Teachers’ Mathematics Pedagogical Content Knowledge

Mathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the development of MPCK in their pre-service teachers. As part of a research study on the development of MPCK in primary school beginning teachers, a 16-item instrument was developed to measure some aspects of the MPCK for teaching mathematics at primary level. The instrument was administered to the 2003 Intake of the Diploma in Education student teachers at the National Institute of Education, Singapore just at the beginning of their programme. As they completed their methodology course in February 2005, the instrument was administered again. This paper will discuss the findings concerning their performance in these two tests, with reference to the overall performance as well as topic-specific and MPCK construct-specific performance. The findings indicate that student teachers at the beginning of their programmes are generally quite weak in their mathematics pedagogical content knowledge, as might be expected. There was significant improvement in some aspects of their MPCK on completion of their mathematics pedagogy course.     

A model for incorporating lesson study into the student teaching placement: what worked and what did not?

This article describes a model for incorporating lesson study into the student teaching placement and reports on the success of the implementation of such a model with student teachers and their cooperating teachers (CTs). Student teachers had the opportunity to discuss many important ideas with each other and their CTs, including “big ideas” of mathematics, and the anticipation of student questions and possible responses. Student teachers also had a built‐in opportunity for peer observation on a regular basis and the opportunity to collaborate with their peers. Certain important aspects of lesson study were not present in this implementation: the teachers involved did not discuss the gaps in their own knowledge with the goal of improving their own mathematical understanding, they did not refer outside sources for ideas for the lessons, and they did not have an overarching affective goal for students. Suggestions are made for teacher preparation in light of these findings.     

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.     

Facilitating Students’ Problem Solving in a Technological Context: Prospective Teachers’ Learning Trajectory

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working with two different groups of students. Case study methods were used to identify and analyze critical events that occurred throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies; (3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent with the nature of their interactions and perceived role with students. The implications inform the development of an expanded learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics in technology-rich environments.     

用本原性数学问题驱动课堂教学--一项改进教师数学教学的行动研究

这是一项在“本原性数学问题驱动课堂教学”理念指导下的行动研究,旨在从数学教师改进自身课堂教学的动态过程,来理解职初和经验教师实施课堂教学的差异、改变和共同之处.研究的对象是小学数学“带余数除法”的三轮课堂教学,采用匹兹堡大学“QUASAR课题”研究成果中的“数学任务框架”、“任务分析指南”、“保持和降低高认知要求任务的因素”等作为分析工具,进行横向和纵向比较,得到具体的有意义的结论.     

Before,During, and After Examination: Development of Prospective Preschool Teachers’ Mathematics-Related Enjoyment and Self-Efficacy

This article examines the stability of Norwegian prospective preschool teachers’ enjoyment of mathematics and their mathematics-related self-efficacy before, during, and after a teacher-education examination. In addition, the stability of the two constructs across countries was examined through a comparison with Germany. The data revealed partial stability (technically speaking, metric invariance) of enjoyment but not of self-efficacy. Self-efficacy increased significantly before and after the examination without decreasing enjoyment, which may be a result of increased learning time. Prior mathematical knowledge predicted the level and development of enjoyment and self-efficacy in both countries. Many Norwegian students reported low mathematics-related enjoyment and self-efficacy, including negative developments. It may be important to provide positive experiences of mathematical activities during preschool teacher education.     

中国数学教师信念研究二十年

以1998-2018年中国知网收录的数学教师信念研究的论文为基础,从相关论文发表时间、论文作者、关键词、研究主题和研究方法 5个维度进行统计分析。研究发现:数学教师信念最近十年来才引起研究者较高重视,已形成两个研究群体,取得系列研究成果,但在后续研究中仍需注意接轨国际研究、夯实理论基础、创新研究方法、拓展研究主题等。数学教师信念的特征、数学教师信念各要素间的互动机制、数学教师信念与实践的关系、数学教师信念与其他心理变量的关系、发展数学教师信念的方式等是值得关注的主题。     

关于数学教师教育的若干思考（续）

剖析了当前我国数学教师教育中存在的若干问题,并提出了一些改进的思路与方法．     

‘Come in with an open mind’: changing attitudes towards mathematics in primary teacher education

Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics.

Purpose: This paper reports on an investigation into student teachers’ self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been developed by the authors in response to a new, reformed four-year undergraduate initial teacher education (ITE) for primary teachers in Ireland. The authors aimed to use the feedback to evaluate and develop the course further.

Sample: We report on the attitudes of 345 pre-service primary teachers enrolled in a four-year undergraduate ITE programme. 281 of these participants had matched survey data before and after participating in the mathematics education programme.

Method and Design: Four evaluation criteria were used as a conceptual framework for the evaluation of the mathematics education programme. A multi-method approach was taken in investigating the students’ attitudes to mathematics by using a scale as a quantitative measure of attitude alongside open-ended survey items that provided qualitative insights into changes in attitudes.

Results and conclusions: Results from the survey data suggested overall that the participants’ attitudes towards mathematics were more positive after they had experienced the mathematics education programme. Overall, the written responses suggested that according to self-reportage, participants perceived that participation in the mathematics education programme had affected their attitudes towards mathematics positively. Comments indicated that the ‘small group’ tutorial structure was particularly well received and was associated with opportunities to actively engage, explore, interact and reflect. Suggestions offered by the participants will be used to inform planning and development of the mathematics programme.