Educating the Young Mathematician: A Historical Perspective Through the Nineteenth Century

Educational programs for young children emerged reasonably early in the history of the United States of America. Its theoretical foundation was based on the thoughts and principles of various early European scholars who differed from one another in their educational theories and how they viewed experiences that would impact on young children’s education, including their mathematics experiences. The movements of Children’s Arithmetic, Mental Arithmetic, the infant school, and the Froebel kindergarten all influenced mathematics in early childhood education. This article reviews the history of mathematics education in relation to the history of early childhood education through the nineteenth century. It also discusses how research in mathematics education attempted to gain its own identity. Throughout history, researchers have identified issues in mathematics education and addressed them, defining the field, and generating a cadre of mathematics researchers.     

An Orientation on the Mathematics Classroom that Emphasizes Power and Identity: Reflecting on Equity Research

In this paper, I reflect on equity research in order to describe a perspective on the mathematics classroom as a non-neutral place where issues of power and identity play out in teaching and learning processes. This view of the mathematics classroom takes seriously issues of equity in the form of power and what becomes constituted as legitimate mathematics while attending to the out-of-school practices in which students engage. This orientation and its related issues are significant in that they provide an alternative perspective on investigating equity in mathematics classrooms that is in contrast to efforts that focus specifically on comparing standardized test scores of specific groups based solely upon racial classifications.Lynn Liao Hodge is an assistant professor in mathematics education. Her research interests include issues of equity and identity in mathematics education and how classroom practices create opportunities for students to develop both an appreciation and a deep understanding of mathematics. Additionally, she is interested in investigating experiences that support the increased participation of women and minorities in mathematics, science, and engineering related professions. Address correspondence to Lynn Liao Hodge, Department of Theory and Practice in Teacher Education, The University of Tennessee, Knoxville, TN 37996-3442, USA; e-mail: lhodge4@utk.edu     

Primary Mathematics Teacher Education in Greece: Reality and Vision

This paper focuses on two main issues concerning the mathematics education of prospective primary school teachers in Greece: the integration of mathematics and pedagogy and the relation of theory to practice. In particular, specific teaching approaches are discussed concerning the problem of integration both in mathematics and in mathematics education courses. The problem of "theory – practice" is examined through an analysis of the kind of teaching practice in which the prospective teachers are involved. Finally, the constraints that the mathematics educators face and the impact of their work on the professional life of the teachers in the future are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

基础教育阶段现代学校制度的基本类型

我国正在建设的基础教育阶段现代学校制度,正在逐步形成下列一些基本类型:第一,按照“公共教育政策取向的不同”来划分,可分为:公平优先、效率第二的现代学校制度基本类型;效率优先、公平第二的现代学校制度基本类型;同等对待公平与效率的现代学校制度基本类型。第二,按照“建设过程中主导者身份的不同”来划分,可分为:政府主导的现代学校制度基本类型;市场主导的现代学校制度基本类型;专家和学术力量主导的现代学校制度基本类型。第三,按照“学校内部治理结构的不同”来划分,可分为:以“学校民主管理委员会领导下的校长主持制”为主轴的现代学校制度的基本类型;以“校长负责制”为主轴的现代学校制度基本类型;以“董事会(理事会)领导下的校长主持制”为主轴的现代学校制度基本类型;以“教育集团、企业集团领导下的校长主持制”为主轴的现代学校制度基本类型;以“党组织领导下的校长负责制”为主轴的现代学校制度基本类型等。     

Troubling teacher identity: preparing mathematics teachers to teach for diversity

This paper reports on an action research project designed to explore the complexities of pre‐service mathematics teacher resistance to social justice issues. Research on equity and mathematics education has indicated that such resistance seems particularly strong for mathematics teachers. Twelve pre‐service mathematics teachers participated in a course‐based research project to explore this issue. Participants completed a classroom discourse analysis and a self‐study narrative as part of their secondary mathematics methods course. The findings suggest that attention to issues of identity construction within school mathematics can be successfully embedded in methods courses in order to better prepare mathematics teachers to teach for diversity.     

Building the wall brick by brick: one prospective teacher’s experiences with mathematics anxiety

Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.     

Developing Self-Efficacy in Teaching Mathematics: Pre-Service Teachers’ Perceptions of the Role of Subject Knowledge

ABSTRACT

Two major concerns in mathematics teacher education are the role of subject matter knowledge and the development of self-efficacy in pre-service teachers. This article brings these issues together in an exploration of the interaction between pre-service teachers’ perceptions of their subject matter knowledge and their accounts of university and placement experiences as potential sources of self-efficacy. Reporting on a group of ten pre-service teachers in Norway, we explore variations in the ways in which they perceived the role of subject knowledge in relation to experience, particularly “mastery experiences”, over a period of nearly two years. We suggest that recognition of the role of “understanding why” in mathematics is crucial in the experience of mastery, and that there is a need to focus more on the role of subject matter knowledge in all sources of self-efficacy in teaching mathematics.     

我国农村教育效益的理论内涵与指标体系研究

农村教育效益是关系整个农村教育发展的重要议题,建构农村教育效益指标体系对于科学测评农村教育效益有积极意义。本研究在深入剖析农村教育发展效益理论内涵的基础上,对教育效益与教育效率、教育经济效益与教育非经济效益、教育效益与教育公平之间的关系进行了必要梳理。我国农村教育发展效益指标体系的构建,主要体现在农村教育发展的贡献率、农村义务教育阶段绩效工资、学校标准化建设以及农村家庭教育支出4个维度。     

Speaking out: perspectives of gay and lesbian practitioners in outdoor education in the UK

Outdoor education has been shaped historically and culturally by many influences. Physically challenging activities out of doors have been appropriated by a number of traditions. These include militaristic, educational and developmental ideologies. Arguably, central to these ideologies are heterosexual, white middle class values. While women have sought to challenge this and feminist and pro-feminist research is evident, very little research has been undertaken into sexuality in relation to teacher or practitioner perspective and experience. Consequently, gay and lesbian voices within outdoor education are all but silenced. This paper explores the perspectives of three lesbian and four gay men who work in the UK outdoor education ‘industry’.

In-depth interviews were held with the participants exploring a variety of issues relating to their life histories and their experiences of working in a predominantly heterosexist outdoor education culture. This paper focuses upon the ways in which the participants perceived the need to conceal their lesbian and gay identities and the consequential effects of managing their identities.     

数学经验主义及其对数学教育的启示

数学思维是一种高度抽象的心智活动过程.数学推理和证明并不依赖于经验事实,但数学与经验是有关系的.数学理论的突破是以经验的支持为前提的.经验是影响数学发展和数学学习的一个重要因素.数学经验主义对数学教育的启示有:应充分认识经验在教育中的价值,从学生现有经验出发组织教学,发挥经验在教学中的积极作用.在数学教育中,既要避免过分强调数学的逻辑性和抽象性,也要防止过分陶醉于学生的直接经验而忽视系统知识的学习.     

To know or not to know – mathematics, that is a question of context

As one of the so-called basic skills, 'mathematics' or 'numeracy' is at the top of the list of subjects in adult education programmes. Together with political investment in general and further education, practitioners and theoreticians focus on 'knowing and learning in different contexts'. Jean Lave's theory about 'situated learning' may be regarded as a confrontation with the idea of learning as acquisition of propositional knowledge. One characteristic of adult education in mathematics is that the participants bring with them adult life experience from their everyday and work. Another characteristic is their perspective in educating themselves. There is an apparent contradiction between many adults being blocked in relation to mathematics in formal settings and being competent in their everyday life. It is possible to make sense of this contradiction by analytically expanding the context for knowing and learning mathematics from the participants' experiences and perspectives to also include the adults' dispositions, cf. Pierre Bourdieu's concept of 'habitus' as a guiding principle for practice. By interpreting the account of her life by a 75 year old woman concerning her attitudes to mathematics, the author illustrates and discusses the two analytical concepts ('situated learning' and 'habitus') and their suitability for analysing adults knowing or not-knowing mathematics in different situation contexts. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Social Foundations Classroom

In this article, we promote the use of autobiography in the social foundations of education classroom as a means of connecting education to real life experiences, history, and fostering epistemological development of college students. Autobiography involves students' awareness of the relation between theory and lived experience. As a form of reflective knowing, autobiography may help students understand complex terms such as "learning," "knowledge," and "education" by exploring various contexts that influence such understandings. Reflective knowing explores some of the experiential and purposive contexts that influence knowledge creation. Intellectual maturity and self-awareness may arise from circumstances that can lead students to be more confident critical thinkers and problem solvers. We describe how we have used autobiography in our social foundations of education classrooms and explore how influencing the pedagogy of teacher education critiques traditional epistemologies toward a redefinition of education for a democratic society.

Now reflecting on my educational history, I realize that everything I have learned in the past has taught me something about myself. Whether I was aware of my development at the time [hinges] on individual circumstances. I have thrived on learning, brought about by major changes impacting my life. These variations and my necessary adaptations have taught me the most important skill I need to know. Because of changes in my life, I have succeeded in learning how to learn. (Rita, Bucknell University, learning autobiography, September 1999)1

If I can make present the shapes and structures of a perceived world, even though they have been layered over with many rational meanings over time, I believe my own past will appear in altered ways and that my presently lived life - and, I would like to say, teaching - will become more grounded, more pungent, and less susceptible to logical rationalization, not to speak of rational instrumentality. (Greene 1995, 77-78)     

关于中学数学教育研究的元研究——基于2005—2009年中国期刊网数据的分析

应用文献计量法,对2005—2009年中国期刊网上有关中学数学教育研究的文章进行再研究.研究内容主要涉及文章的篇数、期刊、参考文献引用情况、研究者身份、研究领域和研究方法等方面.研究表明:中学数学教师的专业发展正由外部期望转向内部需求;中学数学教育研究具有两面性;中学数学教育研究"趋同度高"、"分野度低";中学数学教育研究在方法上"程序简单的多"、"复杂设计的少"等特征.     

The Golden Rule Settlement: A Minority Perspective

In his "minority perspective," Bond takes a position opposing mechanical application of Golden Rule-like procedures but advocating that, at least in some situations, issues of equity can be introduced in item selection without doing violence to test validity.     

论"简"--中古士人的一种审美观念

本文首次提出并探讨了中古士人尚“简”的审美观念问题。“简”构成了魏晋人物品藻的一个审美标准,也是中古士人的一种重要的美学观念。“简”代表了一种人生追求,也显示了一种人生境界。这种审美观念滥觞于《周易大传.系辞上》,其在中古时代的发展与确立,与魏晋玄学有密切的关系。“简”作为文艺批评的一个最基本的美学范畴,从陆云到刘勰无不受其影响。     

可欲且可行的全球公民教育实践路径:苏格兰“全球故事情节法”探析

研究发现,全球公民教育的热度不高与其实践层面的三重困境有关。"全球故事情节法"之所以成为苏格兰实施全球公民教育的最有效路径,正是源自于其对实践困境的有效回应:其一,政府对全球公民教育的倡导营造了相对宽松的政策环境,"全球故事情节法"与现有课程体系相融合获得了灵活的实践空间,实现了安全的课程地位。其二,通过对"故事情节法"和教育戏剧的运用,使全球社会和全球议题通俗化,实现了学生的体验式学习,弥合了学生认知能力和认知需求间的矛盾。其三,西苏格兰发展教育中心通过职业培训传播了理论知识和实践能力,构建了围绕全球公民教育的共同体,为教师提供了教学支持。     

Equality or equity: Gender awareness issues in secondary schools in Pakistan

This paper focuses on gender awareness issues as a dimension of addressing the wider issue of the quality of education in Pakistan from the perspective of social justice. In Pakistan classrooms, boys and girls learn separately and therefore teachers and others tend to think that there are no gender issues once access is achieved and the learners are in the classroom. However, beyond access there are several factors that compromise quality of education and raise issues for gender equity as an element of social justice. These issues are examined in the context of a professional development intervention on promoting gender awareness among secondary mathematics teachers in disadvantaged schools in rural Pakistan.     

立足本土经验 推动国际合作——“哲学在教育和教育研究中的角色”国际学术研讨会综述

"哲学在教育和教育研究中的角色"国际学术研讨会围绕教育公平、教育改革、教育研究方法、教育哲学等议题,对在当前中国教育和西方教育所遇到的诸多价值层面和方法层面上的问题进行了反思和探讨,推进了教育哲学的研究.     

The curricular importance of mathematics: a comparison of English and Hungarian teachers’ espoused beliefs

This paper reports an interview study of 45 English and 10 Hungarian teachers of mathematics. The semi‐structured interviews focused on the teachers’ professional life‐histories and invited them to discuss their beliefs about the necessary subject content for the teaching and learning of mathematics. Substantial differences emerged between the two cohorts, which accord with well‐defined national perspectives on education in general and mathematics education in particular. They reflect, at national rather than individual levels, the expectations of the curricular frameworks within which teachers operate. English teachers tended to view mathematics as applicable number and the means by which learners are prepared for a world beyond school. Hungarian teachers privileged mathematics as problem‐solving and logical thinking.