Education,gift and reciprocity: a preliminary discussion

This paper analyzes the importance and role of the reciprocity relationship in education. It presents a review on the mobilization of the principle of reciprocity—in the anthropological but also sociological and economic senses—in educational processes, especially in adult education. The study is divided into three parts. The first part analyzes the importance of reciprocity in education according to Mauss and to the theory of reciprocity. The second part discusses recent contributions on the role of reciprocity relationships in adult education, expanding Piaget’s perspective on the relation between autonomy and cooperation in education and learning. The third part illustrates this approach with three case studies in Brazil.     

Recycling Piaget: Posthumanism and making children’s knowledge matter

A growing body of research incorporates children’s perspectives into the research process. If we are to take children’s perspectives seriously in education research, research methodologies must be capable of addressing issues that matter to children. This article engages in a theoretical discussion that considers how a posthuman research methodology can support such an effort. Piaget’s early and lesser known qualitative studies on children’s conception of the world are re-read along with Karen Barad’s posthuman theory, using Catherine Malabou’s concept of plasticity. Through a plastic reading of Piaget and Barad, I consider how a posthuman theoretical framework might contribute to research seeking to access children’s perspectives. Before concluding, I reflect on some ethical concerns regarding posthuman research in education.     

Researching research: mathematics education in the Political

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault’s notion of bio-politics—mainly to address the object “learning”—and ?i?ek’s ideology critique—to address the object “mathematics”. These theories, which have already been used in the field to research teaching and learning, have a great potential to contribute to a reflexivity of research on its discourses and effects. Furthermore, they enable us to present a clear distinction between what has been called the sociopolitical turn in mathematics education research and what we call a positioning of mathematics education (research) practices in the Political.     

皮亚杰认知发展理论对《计算机程序设计》课程教学的启示

皮亚杰认知发展理论体系对儿童心理发展和教育研究产生了巨大的影响,对教学活动有很好的指导作用。根据皮亚杰的理论,《计算机程序设计》课程教学应注意以下几点：根据学生需要设置课程,激发学习动机;顺应学生的认知发展情况;教学内容安排应螺旋上升;重视实践活动;通过分析学生的学习过程发现问题;鼓励学生采用小组协作方式学习。     

基于结构思想的数学教学

结构思想是皮亚杰、布鲁纳、布尔巴基学派等发展起来的现代教育理论,数学结构思想是对教育层面上数学本质的认识与处理方式。运用数学结构思想进行中学数学教学,不仅能提高学生对知识掌握的效率,而且能使学生获得全面的数学素质。而在数学教学中渗透数学思想方法,能帮助学生真正认识数学的体质,提高他们分析问题和解决问题的能力。     

Comparing variation theory with Piaget’s theory of cognitive development: more similarities than differences?

ABSTRACT

Lo’s variation theory is a learning and teaching theory based on Marton’s phenomenographic approach and is one of the most important backbones of learning studies. The proponents of variation theory demarcate their approach from constructivist learning approaches, stressing constructivism as philosophical framework, but not as learning theory. At the same time, the phenomenographic approach emphasizes the importance of Piaget’s work about the cognitive development, which should be considered when talking about learning and teaching. We argue that – from a theoretical point of view – Piaget’s theory of how cognitive schemata are developed and how variation theory proposes that learning can be fostered entails many similarities which are not apparent at first glance. We demonstrate the similarities and differences using a teaching example from an English as second language classroom and show the implications for practical instructional work. Finally, we discuss concrete suggestions how variation theory could benefit even more from Piaget’s theory.     

论涂尔干道德教育论及其主要特色

相对于涂尔干的社会理论而言,其道德教育理论受到了一定程度的冷遇。涂尔干提出的"道德三要素"即纪律精神、对群体的依恋和自主性是其道德教育理论的总纲。他对教师权威在道德教育中的作用及其局限性的讨论也是很深刻的。从成年人与未成年人所构成的代际关系角度讨论道德的代际传承和道德教育的代际机制,无疑是其最具特色的理论之一。道德心理学家如皮亚杰和科尔伯格对涂尔干道德教育论的批评,既有片面性,但也十分深刻。     

MATHEMATICS TEACHER EDUCATION AND QUALITY

‘Quality’ in mathematics teaching does not relate solely to pupil achievement, to teaching approaches or to deeply held beliefs about the nature of mathematics and its teaching and learning, but to all of these. A model of a teacher's mathematics‐related belief‐system is presented, and the issue of the contrast between espoused and enacted beliefs is discussed. ‘Quality’ in mathematics teacher education raises all of these issues, as well as the aims, goals and means of the teacher preparation process itself. The paper concludes by arguing against the ‘apprenticeship’ model of mathematics teacher education, for depriving student teachers of theory and of practical research experience. A well known dictum paraphrased states that theory without practice is empty, but that practice without theory is blind. ‘Quality’ in mathematics teaching and teacher education depends on both theory and practice in systematic cooperation.     

Reframing the Debate About the Relationship Between Learning and Development: An Effort to Resolve Dilemmas and Reestablish Dialogue in a Fractured Field

The field of early childhood education (ECE) is currently unable to reach consensus on the extent to which ECE should be based on child development. One manifestation of this situation is the dilemma that early educators purportedly face between teaching the whole child and the curriculum, between developmentally appropriate practice (DAP) and standards. The source of this dilemma is attributed to a one-dimensional understanding of children’s development in which development is privileged over learning. Addressing this dilemma begins by discussing a theoretical difference between Piaget and Vygotsky: for Piaget, development drives learning; for Vygotsky, learning drives development. This seemingly dichotomous difference is reframed, however, by the insight that Piaget and Vygotsky focused on different types of development: Piaget studied universals (e.g., object permanence); Vygotsky studied nonuniversals (e.g., cultural tools often learned in schools). Their dispute stems, therefore, from this factor: development drives learning in nonuniversal developmental sequences, but learning drives development in universal sequences. Teachers who adopt a multi-dimensional developmental framework—a framework that makes visible how the relationship between learning and development may vary within universal versus nonuniversal developmental sequences—may be better prepared to (1) make informed decisions about the extent to which they should guide children’s activities and (2) avoid the DAP versus standards dilemma. The most recent iteration of DAP moved toward adopting a multi-dimensional developmental framework when it encouraged teachers to base instructional judgments on the extent to which children’s emerging capacities will likely require greater versus lesser degrees of adult guidance, structure, and support.     

Mathematics as Liberal Education: Whitehead and the Rhythm of Life

In several of his works, Alfred North Whitehead (1861–1947) presents mathematics as a way of learning about general ideas that increase our understanding of the universe. The danger is that students get bogged down in its technical operations. He argues that mathematics should be an integral part of a new kind of liberal education, incorporating science, the humanities, and “technical education” (making things with one’s hands), thereby integrating “head-work and hand-work.” In order to appreciate the role mathematics plays in modern science, students should understand its diverse history which is capable of bringing abstract ideas to life. Moreover, mathematics can discern the alternating rhythms of repetition and difference in nature constituting the periodicity of life. Since these same rhythms are to be found in his theory of learning as growth, there appears to be a pattern linking Whitehead’s approach to mathematics and his educational philosophy.     

Sociological tools in the study of knowledge and practice in mathematics teacher education

In this paper, we put Basil Bernstein’s theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is our focus, the particular example provides a compelling story at the heart of which is the problem of integration of knowledge(s) within a pedagogic practice. Here, a constructivist pedagogy is at work, but differentially with respect to teaching/learning mathematics and teaching/learning mathematics teaching. The example illuminates mathematics and teaching, and their co-constitution in a particular pedagogic context.     

2-3岁幼儿自我中心化与去自我中心化行为表现的个案分析

相比于2岁以前的幼儿来说,2岁之后的幼儿迎来了更高水平的自我中心化,表现为叛逆、自我中心语言、泛灵现象等。同时幼儿的去自我中心化在幼儿心里开始生根发芽,准备成为继自我中心化之后的第二棵“大树”。根据皮亚杰的认知发展理论,在儿童与周围环境作用时,环境会对儿童产生同化与顺应的作用。这两种作用是导致幼儿出现自我中心化与去自我中心化相互交织、此消彼长的原因。笔者尝试以皮亚杰的同化顺应平衡理论来解释幼儿的行为。     

国内数学元认知的研究与思考

数学元认知是数学教育研究中的重要话题。国内近20年数学元认知研究主要围绕数学元认知概念、数学元认知对数学学习的影响、数学元认知水平、数学元认知能力培养等话题展开。数学元认知相关研究虽取得较大进展,但也存在一些亟待解决的问题,需要从理论本身和方法论两个层面进行思考。     

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

This article offers a new interpretation of Piaget’s decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget’s theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.     

Decentering: A construct to analyze and explain teacher actions as they relate to student thinking

Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus. Specifically, we extend previous work in this area by utilizing Piaget’s construct of decentering (The language and thought of the child. Meridian Books, Cleveland, 1955) to explain teachers’ actions relative to both their thinking and their students’ thinking. In characterizing decentering with respect to a teacher’s focus on student thinking, we use two illustrations that highlight the importance of decentering in making in-the-moment decisions that are based on student thinking. We also discuss the influence of teacher decentering actions on the quality of student–teacher interactions and their influence on student learning. We close by discussing various implications of decentering, including how decentering is related to other research constructs including teachers’ development and enactment of mathematical knowledge for teaching.     

Sameness-difference judgments inSaimiri sciureus based on volumetric cues

The rationale was to apply Piaget’s theory and methods to the study of the phylogenetic development of cognitive abilities. It was asked whether squirrel monkeys have the prerequisite skills for conservation of quantity, and, specifically, whether they might respond differentially to equivalent and unequivalent volumetric cues. All monkeys responded significantly and differentially to pairs of identical objects or pairs of objects similar only in volume vs. pairs of objects which differed in volume. It was concluded that squirrel monkeys have the prerequisite skills for the conservation of quantity. Discussion included methodological problems associated with demonstrating conservation in nonhumans as well as the potential usefulness of Piaget’s theory for phylogenetic studies of intelligence.     

高校体育工作质量评价指标体系研究

文章基于模糊数学理论构建了一个由9个类别共27项指标构成的高校体育工作质量评价指标体系,并以浙江某普通本科院校为实例加以验证。实例研究表明,评价结果与该高校体育工作的实际情况基本相符,可以为高校管理决策提供依据。     

Lacan,subjectivity and the task of mathematics education research

This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud’s psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan’s subjectivity initially in relation to the work of Piaget and Vygotsky who have been widely cited within mathematics education research, but more extensively it is shown how Lacan’s conception of subjectivity provides a development of Peircian semiotics that has been influential for some recent work in the area. Through this route Lacan’s work enables a conception of subjectivity that combines yet transcends Piaget’s psychology and Peirce’s semiotics and in so doing provides a bridge from mathematics education research to contemporary theories of subjectivity more prevalent in the cultural sciences. It is argued that these broader conceptions of subjectivity enable mathematics education research to support more effective engagement by teachers, teacher educators, researchers and students in the wider social domain.

皮亚杰的儿童心理发展观及教育启示

皮亚杰的儿童心理发展观是新课程改革的重要理论依据。文章对皮亚杰儿童心理发展观具体内容进行阐述,旨在为课程改革和教育实践提供启示和借鉴。     

基于MQI评估系统的大班数学集体活动质量分析及其启示

数学是学前儿童学习和入学准备的重要领域,也是学前教育质量监测的重要方面。MQI评估系统作为一种评估数学课堂教学质量的框架,体现了最新数学教育观念,突出了数学的学科特性和认知要求,强调儿童的主动参与和生成性的教学过程,可同时对教师的教和儿童的学进行评估。本研究使用MQI评估系统对我国幼儿园大班数学集体活动的质量进行考察,结果表明除数学意义建构和数学语言之外,数学丰富度领域各维度表现水平不高;教师对儿童行为进行处理和反馈的水平较低;大多数活动片段中不存在数学表达和语言上的错误及不严密性问题;儿童参与有意义的解释或者提问和推理较少,参与活动的认知要求不高。幼儿园大班数学集体活动质量受到集体教学中"教"与"学"的关系、教师对数学领域知识和儿童数学发展目标的认知、教师评价儿童数学思维的能力及师幼互动技巧、教师培训与考核的侧重点等因素的影响。我国学前教育界应重视数学教育活动的过程性质量,关注儿童数学学习过程性能力的发展,并应在借鉴MQI评估系统的基础上开发适合我国幼儿园数学教育实践的质量评估系统。