数学教学内容知识(MPCK)的构成成分表现形式及其意义

MPCK是由数学学科知识(MK)、一般教学法知识(PK)、关于学生的知识(CK)和关于教育技术的知识(TK)融合而成,其本质是教师如何将数学知识的学术形态转化为教育形态,以促进学生的数学理解、提高学生的数学能力和提升学生的数学素养.若从微观和宏观层面上看,可把MPCK分为话题MPCK和课堂MPCK.对于话题MPCK而言,其表现形式是:针对特定内容和特定学生,教师"呈现"数学问题的方式;对于课堂MPCK而言,其表现形式是:针对特定内容和特定学生,教师"组织、呈现、调整"数学课堂教学的方式.MPCK对数学教师的专业发展意义重大,它有助于数学教师进一步加深对教师专业的认识,有助于数学教师进一步发展专业知识.     

论数学课堂预设提问的策略

预设提问是数学教学设计的重要内容,是数学课堂有效提问的关键,教师预设提问的策略主要有:(1)明确提问的目的;(2)摸清学生的知识储备;(3)把握学生的思维特点;(4)确定学生的"最近发展区";(5)寻找数学知识的生长点;(6)关注数学思想与方法.     

数学教师专业发展的新视角——数学教学内容知识(MPCK)

数学教学内容知识(MPCK)是关于某一特定的数学内容该如何进行表述、呈现和解释,以使学生更容易接受和理解的知识.它作为数学教师知识结构的核心,是区别数学教师与数学家、数学教师与其它学科教师的重要特征,是数学教师专业成长的重要体现.依据我国数学教师的特点,通过数学知识向数学教学内容知识的转化不失为一条发展教师MPCK的直接而有效的途径.     

发展数学教师知识结构的若干策略

数学教师的知识结构面临着教师专业化和基础教育数学课程改革的挑战.发展数学教师知识结构的策略有:经历数学问题解决过程,发展数学知识;构建与学生的数学对话,发展学生学习数学的知识;开展合作式探究活动,发展数学教学的知识;组织教师叙事研究,发展数学教师的个体知识.     

基于学生应用能力发展的高中数学教学创新策略研究

近年来随着数学教育改革的不断深入,学生的知识应用能力和学科核心素养越来越受到重视.数学课程具有工具性、人文性和实践性等特点,如何在有限的数学课堂时间内提高学生的知识学习和应用能力,是数学课程教学改革的关键问题.自从李吉林先生提出数学应用能力以来,中小学数学教师都在努力改革课堂教学,高中数学课堂教学也不例外.培养学生的数...     

中学数学课堂师生话语权的量化研究——基于LPS项目课堂录像资料

师生关系是数学课堂教学中的重要研究内容.对师生话语的绝对数量、师生话语量之比以及师生话语长度进行定量分析,得到(1)不同教师的数学课堂师生话语容量存在较大差异;(2)不同教师的数学课堂师生话语之比有较大差异:(3)中国数学课堂中教师的话语平均量是学生的6.6倍;(4)中国大陆的数学课堂师生话语量之比与国际平均水平没有显著差异;(5)数学课堂中师生的话语长度呈现一定的规律.     

高中数学课后作业的现状调查及应对策略

学生喜欢做数学课后作业,并希望通过作业检验自己对知识的理解、掌握情况。数学教师怎样才能真正设计出适合学生的数学课后作业呢?经过共同研讨后发现,作业的设计至关重要。教师在设计数学课后作业前要研究学生的知识储备、学习水平、课堂知识的理解程度和可能达到的学习预期等,再根据学生现有学习水平选择有针对性训练和能力提高的题目布置课后作业。     

如何激发农村学生学习数学的兴趣

众所周知,学生学习数学的兴趣并不是天生的,而是依靠后天的培养和指导.作为一个农村数学教师,尤其是新教师,课堂上怎样吸引学生,怎样启发学生,怎样提问学生,怎样导人等,都是非常基本的常用的课堂教学技能.教与学是师生心灵的交往,成功的教学不是靠教师单方面的传授.通过多年的教学经历,本人认为培养学生学习数学的兴趣可以从以下几方面着手:(一)立足课堂,激发兴趣课堂上如何吸引学生的注意力,我认为首先教师     

农村小学数学教学之我见

小学数学是一门基础学科,也是我们从事生活、工作和劳动的一门工具学科.要想培养学生养成良好的数学学习习惯和学习方法,提高小学生的数学素养和实践能力,丰富学生的知识储备,我们小学数学教师,尤其是农村小学数学教师,必须研读新课程标准,把握新课标的基本要求,从三个维度设定教学目标.发挥信息技术手段和生活课程资源的优势作用,实实在在提高教学质量.     

让生活浸润数学课堂

在数学教学中,让生活浸润数学课堂,让数学回归生活,引领学生感悟数学知识与现实生活的联系,用数学的眼光去观察生活实际,培养解决实际问题的能力,成为每位数学教师应重视的问题。在小学数学教学中,教师要基于学生的生活经历,联系学生和社会生活的实际帮助学生在生活中学习数学,感悟数学和体验数学,提高学习数学的有效性。一、生活素材浸润数学课堂,让学生在生活中学习数学     

Using an Undergraduate Geometry Course to Challenge Pre-service Teachers' Notions of Discourse

This investigation uses classroom discoursein an undergraduate mathematics course tochallenge pre-service secondary mathematicsteachers' notions about mathematical discourse,what it might resemble in the classroom, andhow its various forms can be cultivated byclassroom teachers. The research setting was arequired geometry course taught by the author.Eleven pre-service mathematics teachers intheir junior or senior year of an undergraduate program participated. Results indicated participants made a transition toward an image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and developed in their ability to participate in such discourse.This awareness, along with participants'analyses of their own habits of discourse asclassroom teachers, prompted shifts in theirprojected image of the role of discourse intheir future practices of teaching. Resultssuggested further that the undergraduatemathematics classroom (as opposed to themethods classroom) offers a powerful and uniqueforum in which pre-service secondary teacherscan practice, articulate, and collectivelyreflect on reform-minded ways of teaching.     

Building on student mathematical thinking in whole-class discourse: exploring teachers’ in-the-moment decision-making,interpretation, and underlying conceptions

Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.

     

Comparative analyses of discourse in specialized STEM school classes

ABSTRACT

The authors detail the discourse patterns observed within mathematics and science classes at specialized STEM (science, technology, engineering, and mathematics) high schools. Analyses reveal that teachers in mathematics classes tended to engage their students in authoritative discourse while teachers in science classes tended to engage students in dialogic discourse. The authors examined variations in the type of discourse in relationship to the discipline being taught, the educational level of the teacher, and course requirements were also explored.     

An emerging community in online mathematics teacher professional development: an interactional perspective

Online collaborative and content-focused professional development (PD) is becoming an increasingly important setting for supporting mathematics teachers’ professional learning. The purpose of this study was to better understand the process by which a community emerges in such a PD setting by examining how the cohesiveness of 21 mathematics teachers’ social network evolves and associated shifts in the quality of mathematics teachers’ mathematical discourse. We employed social network analysis (SNA) to examine the evolving cohesiveness of mathematics teachers’ social network and coding procedures to examine teachers’ mathematical discourse. A key finding was the documentation of an emergent divide between participation in the core and periphery during initial weeks of the PD and then a reduced divide and emergence of a social network that resembles a community. We argue that the instructor’s pattern of participation that included distributing their interactions across the subgroups while sending a common message regarding expectations for mathematical discourse in the PD may have contributed to the community formation process. We propose the Interaction Assessment Model, which outlines an approach for PD facilitators to use SNA as a feedback mechanism to differentiate facilitation of online collaborative and content-focused PD and build online communities.

     

Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom?

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and support the professional development of these teachers? Eighteen such textbooks for use by 7 to 11-year-old children in England were examined for their potential to help teachers attend to reasons. It was found that they were unlikely to point teachers towards reasons for patterns and procedures. Although some had the potential to help in introducing and structuring a lesson, they were unlikely to induce the teacher to address matters of understanding in their discourse. Their implicit message tended to be that mathematics education is about computational skill development through routines, algorithms and practice.     

In-service training programmes for mathematics teachers nested in transnational policy discourses

Results in mathematics on international knowledge surveys like Programme for International Student Assessment and Trends in International Mathematics and Science Study have become one of the most important factors for the perceived success or failure of schools and even entire education systems in the policy arena. In this article, we explore the complex recontextualising processes that occur when translating educational policy into actual programmes for teachers’ education. First, the transnational education policy discourse(s) of teachers’ in-service training with a focus on mathematics will be explored. Second, we examine how this transnational discourse is recontextualised in a national policy discourse resulting in a national reform programme for in-service training of mathematics teachers in Sweden. In a third step, concrete teacher training courses in mathematics are examined. The result shows a convergence between the official policy discourse and the pedagogic recontextualising field in terms of a broad teaching repertoire and peer discussions about reflections on certain common objects of learning.     

教师变量对小学生数学学习成绩影响的多水平分析

32名小学数学教师与这些教师所教班级的1691名学生参与了本研究。两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像,并按照学习任务的认知水平与课堂对话的特点进行了编码,同时测查了学生的期末数学学习成绩。多水平分析结果表明:教师的学科教学知识、课堂学习任务的认知水平、课堂对话中教师提问问题的类型与对话的权威来源对学生的数学成绩具有显著的预测作用;而教师的学科知识对学生数学成绩的影响未达到显著性水平。     

Troubling “understanding mathematics in-depth”: Its role in the identity work of student-teachers in England

In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop “understanding mathematics in-depth” in students in order for them to become successful mathematics teachers. We take a poststructural approach, so we are not interested in asking what such an understanding is, about the value of this approach or about the effectiveness of the MECs in developing this understanding in their participants. Instead we explore what positions this discourse of “understanding mathematics in-depth” makes available to MEC students. We do this by looking in detail at the “identity work” of two students, analysing how they use and are used by this discourse to position themselves as future mathematics teachers. In doing so, we show how even benign-looking social practices such as “understanding mathematics in-depth” are implicated in practices of inclusion and exclusion. We show this through detailed readings of interviews with two participants, one of whom fits with the dominant discourses in the MEC and the other who, despite passing the MEC, experiences tensions between her national identity work and MEC discourses. We argue that it is vital to explore “identity work” within teacher education contexts to ensure that becoming a successful mathematics teacher is equally available to all.