Improving mathematics instruction through lesson study: a theoretical model and North American case

This article presents a theoretical model of lesson study, an approach to instructional improvement that originated in Japan. The theoretical model includes four lesson study features (investigation, planning, research lesson, and reflection) and three pathways through which lesson study improves instruction: changes in teachers’ knowledge and beliefs; changes in professional community; and changes in teaching–learning resources. The model thus suggests that development of teachers’ knowledge and professional community (not just improved lesson plans) are instructional improvement mechanisms within lesson study. The theoretical model is used to examine the “auditable trail” of data from a North American lesson study case, yielding evidence that the lesson study work affected each of the three pathways. We argue that the case provides an “existence proof” of the potential effectiveness of lesson study outside Japan. Limitations of the case are discussed, including (1) the nature of data available from the “auditable trail” and (2) generalizability to other lesson study efforts.

浅谈新课程理念下学生数学审美能力的培养

在传统的数学教学中 ,由于审美意识不强 ,教与学的不得法 ,学生往往形成一种数学不是数字就是公式的枯燥印象 ,难以对数学产生兴趣 ,部分学生甚至有恐惧心理 ,不能产生强烈的求知欲望。即使有些学生学习兴趣较浓 ,如数学“好玩”、“能使人动脑子”、“数学有无穷的奥秘”等 ,他们也只是初步感受到美 ,一般都是无意识的 ,也仅停留在严谨的推理和运算方法的认识上 ,对数学中美的意蕴、美的表现和美的启迪还缺乏明确的理解和探求 ,并非知道有数学美的存在。数学教育对数学美学内容重视不够 ,热情不高 ,是数学教育的一个薄弱环节。站在课程改革…     

Pre-service teachers in mathematics: Struggling with the Standards

The purpose of this paper is to describe a two-year investigation of pre-service teachers in mathematics. Of particular interest is the degree to which the NCTM (1989) Curriculum and evaluation standards for school mathematics, the NCTM (1991) Professional standards for teaching mathematics, and other reform agendas impact pre-service teachers' thinking and practices. The beliefs, perceptions, philosophies, and classroom actions of four cohorts of student teachers (n = 44) were examined throughout this 2year study. Of particular interest were the pressure student teachers felt to implement the Standards in their teaching, their perceptions of their own teaching with respect to the Standards, the content of their lessons, and the impact of cooperating teachers on the development of the student teachers. Data was collected through a variety of sources, organized and analyzed in the spirit of ethnographic work. Data was generated through classroom observations, pre- and post-lesson conferences, lesson plans, seminar sessions, survey questionnaires, and informal conversations. A minimum of four classroom observations were made for each participant. Analysis of the data revealed general agreement among the student teachers in their regard for the Standards. Although they appeared to affirm the goals, content and recommendations contained therein, they almost uniformly suggest that they lack the tools to implement the Standards appropriately in the classroom. The consistency in the types and content of lessons observed appeared to validate this concern. An overwhelming majority of the lessons observed bore little or no resemblance to the values so highly espoused by the student teachers. Student teachers perceived notable pressure from the education program to include the Standards in their teaching practices, while feeling little pressure from cooperating teachers. They also point to cooperating teachers as the most significant influence on their teaching.     

Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching

This article is based on one of the several case studies of recent graduates of a teacher education programme that is founded upon inquiry-based, field-oriented and learner-focussed principles and practices and that is centrally concerned with shaping teachers who can enact strong inquiry-based practices in Kindergarten to Grade 12 classrooms. The analysis draws on interviews with one graduate, and on video data collected in his multi-aged Grade 1/2 classroom, to explore some of the ways in which this new teacher enacted inquiry-based teaching approaches in his first year of teaching and to consider his capacity to communicate his understanding of inquiry. This article presents implications for beginning teachers’ collaborative practices, for the assessment of new teachers and for practices in preservice teacher education.     

论禅宗在中国书法艺术中的审美体悟

现代以来,禅与审美和艺术的关系受到学术界广泛重视。本文试以中国最具审美代表性的书法艺术为例,运用禅宗文化来加以体会和论证,以把握和解释禅思想与审美和艺术的内在关联,领略禅悟的美学特征。     

Classroom interaction as reflection: Learning and teaching mathematics in a community of inquiry

This article aims to contribute to the theory of mathematics instruction by highlighting and analysing Leen Streefland's work as a teacher in a primary school. Core ideas of Streefland's are discussed as part of a recent wave of educational innovations using the idea of learning communities. I present a case study of a lesson co-taught by Streefland and a primary school teacher (students between 11 and 13 years of age). Streefland addressed the students as `researchers' and gave them realistic problems to work on. Since they provided occasions for increasingly sophisticated solutions, the tasks given to the students stimulated processes of vertical mathematization. The students' role as researchers required them to construct novel ideas and present these to their classmates. The various solutions proposed by the students were used by the teachers to structure the learning activities in the classroom. The interaction between the common understandings in the classroom and the learning process of individual students shows that the classroom activities amount to a process of collective reflection. This revised version was published online in August 2006 with corrections to the Cover Date.     

Learning by progressive inquiry in a physics lesson with the support of cloud-based technology

ABSTRACT

Background

Inquiry-based learning has been widely adopted in educational practice especially in science education. Scaffolding plays an important role in fostering learning in sophisticated inquiry. Meanwhile, it is important not to undermine the open-endedness of inquiry activities and the nature of student-centred learning.     

探究性教学在中学数学例题教学中的应用

探究性教学旨在以学生为教学主体,通过教师的积极引导,让学生能够更好进行数学实践活动,对数学知识的学习能有质的飞跃。本文通过对探究性学习在中学数学例题教学中的应用进行合理分析,提出了一些有效的建议。     

New materialist ontologies in mathematics education: the body in/of mathematics

In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners’ bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic material, and we suggest a “pedagogy of the concept” that animates concepts as both logical and ontological. We draw on the philosopher of mathematics Gilles Châtelet in order to pursue this argument, elaborating on the way that mathematical concepts partake of the mobility of the virtual, while learners, in engaging with this mobility, enter a material process of becoming. We show how the concept of virtuality allows us to look at mathematical concepts in school curriculum in new ways.     

中俄数学教育目标的差异及缘由探析

本文论述了中俄两国数学教育目标在数学知识的理解、对数学能力的要求、对数学的态度和观念等方面的差异。探析了形成这些差异的原因 (包括学科教育观念不同 ,知识价值观不同 ,教育培养目标不同等几方面 ) ,并提出了对研制我国数学教育目标的几点启示。     

学习和研究数学哲学和数学史

从初出茅庐漫无边际的自学 ,到确定以数学哲学和数学史为研究方向 ;从 2 0年的准备阶段 ,到集中力量进行研究 ;从论文不能发表到出书 ;从参加省级的学术会议到参加国际学术会议 ,作者学习和研究数学哲学和数学史的道路是不平坦的。     

Teacher collaborative learning through the lesson study: identifying pathways for instructional success in a Singapore high school

Research shows teacher collaborative learning to be a powerful vehicle to mobilise teacher instructional change and pedagogical practices, and to improve student achievement. For such undertakings to have positive impact, understanding the visible features of collaborative structures may not be sufficient to ensure sustainable practice. Instead, there is a need to identify underlying pathways that provide for successful instructional improvement. The purpose of this qualitative study is to obtain deeper insights into teacher outcomes arising from this practice and to identify aspects of the lesson study structure and processes that afford such opportunities. Three subject groups consisting of ten teachers from a Singapore high school participated in this study. Implications on staff development programs will be discussed in the light of these findings.     

由数学直觉谈数学教学中学生创造力的培养

一、数学直觉及其意义 数学界历来以数学的绝对严谨而自豪,把数学的严密性作为数学的生命.因此,大多数数学教师的讲解,通常局限于教科书中的逻辑演绎,过多强调数学形式上的严谨.这当然是重要的.但是,这只抓住了数学活动的一个方面,即逻辑性的一面,却忽视了数学活动的另一个方面,即数学直觉层面,致使学生认为,数学就是逻辑演绎.     

高中数学教学中对学生研究性学习进行分层指导的探索

研究性学习就是在教学过程中以问题为载体,创设一种类似科学研究的情景和途径,让学生通过收集、分析和处理信息,体验和认识知识的生产和应用过程,培养分析问题、解决问题的能力和创新能力。在数学教学中,通过研究性学习,主要培养学生的数学能力和创新能力。以往由于认识上的偏差,研究性学习的设计更多地适合优秀学生的学习能力与需要,导致部分学生无法参与到研究性学习中去。为了使各层次学生都能参与研究性学习,在高中数学教学中进行“研究性学习分层指导”,是一个很好的途径。一、对研究性学习分层指导的基本涵意研究性学习是学生对某一问…     

Integrating social justice with mathematics and science: An analysis of student teacher lessons

Student teachers have difficulty planning lessons that fully integrate social justice with mathematics/science content. This study was a content analysis of 26 poster presentations of mathematics or science lessons incorporating social justice issues made by student teachers (20F, 6M) at a mid-sized college in central New York State. The presented lessons applied four pedagogical approaches to integration (data collection followed by graphing analysis; discussion of text/video; modeling; library/internet investigation) and addressed three major social justice themes (diversity, system disparities in human communities, and in stewardship of earth). Deeper content knowledge, faculty lesson modeling/reflection and practice delivering lessons are recommended.     

高中数学探究教学与学生问题意识的培养

问题意识既是探究教学所必需的,同时又是可以在探究教学中进行培养.论题从心理认知规律和教学过程规律方面,探讨在高中数学探究教学中培养学生问题意识的一些方法.     

Educational theories and computer game design: lessons from an experiment in elementary mathematics education

Although educational games have been used for a considerable time, their true potential for enhancing achievement and motivation is still being explored. We argue in this paper that we may get closer to realizing this potential if the theoretical underpinning of educational games is improved. We developed a simple interactive math game based on insights from cognitive load and game design theory, in which players solve mathematical problems competitively and creatively. To investigate the effects of the game on achievement and motivation, we ran an experiment with fifth- and sixth-grade students. Our results show that students who played the game achieved better math results than those who did not. We did not find any significant differences in math motivation. Another promising finding, albeit beyond the scope of our hypotheses, relates to the potential effects of math games on student behavior.

     

Designing and building an on-line community: The struggle to support sociability in the inquiry learning forum

In this paper we describe the sociotechnical structures of the Inquiry Learning Forum (ILF), a Web-based professional development tool designed to support a community of inservice and preservice mathematics and science teachers creating, sharing, and improving inquiry-based pedagogical practices. Founded in our previous research and consistent with our pedagogical commitment, the technical structures of the ILF have been designed around a “visiting-the-classroom” metaphor. This decision was based on our belief that teachers need to be full participants in, and owners of, their virtual space for meaningful interaction to occur. The hallmark of this environment is that teachers with a broad range of experience and expertise can come together in an on-line environment to observe, discuss, and reflect on pedagogical theory and practice anchored to actual teaching vignettes. The goal of this paper is to share how we instantiated our pedagogical commitments and to describe the challenges we faced during the design, development, implementation, and analysis of the ILF. Toward this end, we walk the reader through our design and implementation process, highlighting our change in focus from usability to sociability issues, and movement from conceiving the ILF as an electronic structure to a sociotechnical interaction network. The ILF Design Team consists of Brian Beatty, Tom Duffy, Geraldine Haas, Chris Keslin, Sun-Myung Lee, Justin Marquis, and Kirk Sluder