Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving

Is proof activity in danger with the use of dynamic geometry systems(DGS)? The papers of this special issue report about various teachingsequences based on the use of such DGS and analyse the possible roles ofDGS in both the teaching and learning of proof. This paper is a reaction tothese four papers. Starting from them, it attempts to develop a globaldiscussion about the roles of DGS, by addressing four points: the variety ofpossible contexts for proof in a DGS, the dual nature of proof (cognitiveand social) as reflected in the `milieu' constructed around the use of aDGS, from observing to proving, and the overcoming of the oppositionbetween doing and proving.     

《动态几何》课程的开设在数学教与学中的价值

有关动态几何作图的理论和应用的学科,就是《动态几何》.动态几何图形有两个基本特点:图中的某些对象可以用鼠标拖动或用参数的变化来直接驱动;其它没有被拖动或直接驱动的对象会自动调整其位置,以保持图形原来设定的几何性质.《动态几何》课程在数学教学中主要有5个方面的应用:日常学习的工具、课件制作的平台、实验探索的环境、创新思维的触媒、艺术欣赏的园地.     

Learning With Dynamic Geometry Programs: Perspectives of Teachers and Learners

Abstract

In this exploratory phenomenological study, part of a larger mixed-design research project, the authors examined teacher and student roles in, and reactions to, a student-centered instructional geometry program using the Geometer's Sketchpad. Grade 7 students worked for 2 weeks in their regularly scheduled mathematics class on activities that allowed them to explain on-screen relationships among geometric shapes. A companion computer-based instructional tutorial was available as an accessible resource. The class sessions and specific dyads were observed, students surveyed, and teacher and selected students interviewed. Findings centered on 2 overarching themes: issues of power and learning. The teacher had difficulty relinquishing control of the learning environment even though she had agreed to do so. Students, however, liked their new freedom, worked hard, and expressed greater interest in the subject material.     

The Interplay of Teacher and Student Actions in the Teaching and Learning of Geometric Proof

Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify factors that may be related to the development of proof understanding. In this paper, we identify and interpret students' actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures, justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on the students, analyze student arguments, and coach students as they reason, creates an environment in which participating students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively participate in the classroom discourse are supported as they engage in proof development activities. By examining connections between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students' understanding of proof.     

Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations

A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In geometry, forms of software usually known as dynamicgeometry environments may be useful as they can enable students tointeract with geometrical theory. Yet the meanings that students gain ofdeductive reasoning through experience with such software is likely to beshaped, not only by the tasks they tackle and their interactions with theirteacher and with other students, but also by features of the softwareenvironment. In order to try to illuminate this latter phenomenon, and todetermine the longer-term influence of using such software, this paperreports on data from a longitudinal study of 12-year-old students'interpretations of geometrical objects and relationships when using dynamicgeometry software. The focus of the paper is the progressivemathematisation of the student's sense of the software, examining theirinterpretations and using the explanations that students give of thegeometrical properties of various quadrilaterals that they construct as oneindicator of this. The research suggests that the students' explanations canevolve from imprecise, `everyday' expressions, through reasoning that isovertly mediated by the software environment, to mathematicalexplanations of the geometric situation that transcend the particular toolbeing used. This latter stage, it is suggested, should help to provide afoundation on which to build further notions of deductive reasoning inmathematics.This revised version was published online in September 2005 with corrections to the Cover Date.     

Development of a Learning Progression for the Formation of the Solar System

This study describes the process of defining a hypothetical learning progression (LP) for astronomy around the big idea of Solar System formation. At the most sophisticated level, students can explain how the formation process led to the current Solar System by considering how the planets formed from the collapse of a rotating cloud of gas and dust. Development of this LP was conducted in 2 phases. First, we interviewed middle school, high school, and college students (N?=?44), asking them to describe properties of the current Solar System and to explain how the Solar System was formed. Second, we interviewed 6th-grade students (N?=?24) before and after a 15-week astronomy curriculum designed around the big idea. Our analysis provides evidence for potential levels of sophistication within the hypothetical LP, while also revealing common alternative conceptions or areas of limited understanding that could form barriers to progress if not addressed by instruction. For example, many students' understanding of Solar System phenomena was limited by either alternative ideas about gravity or limited application of momentum in their explanations. Few students approached a scientific-level explanation, but their responses revealed possible stepping stones that could be built upon with appropriate instruction.     

自主学习理论及对外汉语教学最佳模式的研究

针对当前对外汉语教学现状，分析了自主学习理论对对外汉语教学的重要性；探讨了自主学习模式在对外汉语教学中的具体运用；强调指出对外汉语教学要从引发学生的自主性入手，从而真正达到教与学的良性互动，提高对外汉语教学水平。     

WBL框架对建设我国中小学教师在线学习系统的启示

随着计算机和网络技术的发展,人们的学习方式发生了很大变化。WBL框架对构建学习者在线学习环境有很好的指导作用,为此,作者对该框架进行了介绍,并基于该框架对中小学教师在线学习系统的开发提出了建议。     

Learning study as a clinical research practice to generate knowledge about the learning of historical primary source analysis

There is a demand for educational research that addresses questions found in teachers’ practice. This line of research can be referred to as practitioner research, and it is motivated by the realisation that teacher professionalism is one of the most influential factors in determining student achievement. One question is whether the primary purpose of practitioner research should be to improve teaching practices, or to contribute to theoretical knowledge. Some argue that the primary concern should be contributions to changing practices, whereas others suggest that contributions to theory are equally important. The purpose of the article is to discuss how Learning study, regarded as a clinical research practice, can contribute to developing teaching practices and theory of history didactics in conjunction. Learning study is commonly described as an interventionist, iterative and collaborative research approach, focusing on the teaching of an object of learning, which in this case was the learning of primary source analysis in history. Examples of how the Learning study contributed to practice and theory are presented. Contributions include the suggestion that knowing primary source analysis involves the ability to distinguish and separate three critical aspects in a temporal, human and contextual dimension, and that the students’ personal perspectives are vital and should be regarded in the design of tasks and teaching. Based on the findings it is argued that practitioner research could aim at developing educational practices in conjunction with contributions to theory, and that practice and theory are necessarily entwined in the research process.     

共建教师发展的开放学习环境--探索以网络为中介的研究型课程的教师教育模式

在上海市二期课改的进行中,增设了拓展型与研究型（探究型）课程等新的课程模式,相应地对教师提出了新的要求.如何帮助教师尽快地理解改革的新理念,适应改革的需要,承担起改革的重任,已成为教师教育的当务之急.本项目研究正是从当前新形势下教师教育面临的新问题出发,试图利用学习科学的研究成果,从共建教师发展的开放学习环境着手,探索一种新的学习型、参与型的教师教育模式.该模式的主要特点是立足真实活动,在教师与学生共同参与的过程中,在与社会的积极交往中,在整合各种形式的资源中,以主题性网络为中介,帮助教师学会学习,在学习中成长,在学习中发展.     

早期学习与发展标准的制订:又一份国家指导性文件的诞生

近年来，在联合国儿童基金会的大力支持与推动下，很多国家包括中国参与了其制订早期儿童学习与发展标准的项目，并取得了实质性进展。文章以文献综述的形式介绍了这些国家制订早期学习与发展标准的背景、进程、遇到的挑战及对后续工作的展望，以让幼教界N4=-对此标准的制订有一个整体了解。     

Testing for the Transfer of Tacit Knowledge: Making a Case for Implicit Learning

Companies are beginning to realize that simply storing data in warehouses and databases is not sufficient to ensure the usefulness of that data or information. As information is processed with a purpose ( Ackoff & Emery, 1972 ), it becomes knowledge. Knowledge exists on many planes; one is the tacit‐explicit plane described by Polanyi (1966) . Knowledge‐based applications are becoming a key factor in determining organizational value. For example, Activity‐Based Costing (ABC) and Knowledge Value Added (KVA) are two methodologies that organizations use to measure explicit knowledge. However, this interest in measuring and managing knowledge creates two important questions. First, do companies include tacit knowledge in their measurements of knowledge? Second, can educators demonstrate that they are helping increase tacit knowledge? This paper posits that companies may not be including the full range of knowledge in their endeavor to measure knowledge in their organizations. To help make a case for including tacit knowledge and implicit learning, an active learning exercise is created to demonstrate a method to quantify and test for changes in both types of knowledge. The results show that the activity created observable changes in explicit and tacit knowledge. Future research will need to concentrate further on understanding how the two types of knowledge interact. For now though, these results demonstrate one way to observe the two types of knowledge and more importantly, point out the need for organizations to find ways to value both implicit and explicit knowledge.     

提高初中思想品德课堂教学合作学习有效性的途径探析

合作学习是新课程所倡导的三种学习方式之一。本文探讨了在初中思想品德课堂教学中设计有效的合作学习模式的问题,认为有效的合作学习需要恰当地设计学习问题,进行学习方式的专项训练,提供充分的合作时间和空间,再辅助适时的组织和调控,并进行科学合理的考核评价。     

On the Pronunciation of ELT Teachers in China as a Source for Language Contact and Language Input

在外语教学中,教师发挥着越来越重要的作用.因此,对外语教师的要求也随之提高.这一点已经得到了证实.作为语言沟通和语言输入的来源,外语教师的标准发音给教学带来了很大作用.因此,应当对外语教师进行培训,然后挑选合格者任职.这样,才能教会学生标准的语音语调,促进语言的正确运用.     

《孙子兵法》对警务活动与警院学员培养的价值

《孙子兵法》作为世界上最早的军事著作,历来备受推崇,研习者辈出。其论述的谋略思想可以借鉴到警务领域,为警务活动提供指导作用。警院学员作为预备警官,学习《孙子兵法》对于构建合理的知识结构,培养科学的思维方法,锻造优良的思维品格,具有尤为重要的意义。     

产教结合,是社主义新农村建设的铺垫之石——以"花椒为龙头的村教产业开发示范基地"项目辐射效应为例

杨凌职业技术学院凤县基地建设以生态经济理论为指导,坚持产教结合,实行校企合作,通过建立林特产业开发示范基地和实施系列措施,为秦巴山区农业产业结构调整和建设社会主义新农村奠定了一定基础。     

The Use of Activity Theory as a Methodology for Developing Creativity within the Art and Design Classroom

This article discusses the use of an activity theory system as an analytical tool within the school art and design classroom. It highlights reasons for its use and makes explicit its importance for investigations into teaching and learning. It proposes that through an activity theory system, teachers and researchers are enabled to reflect on the formation of thought and develop an understanding of pedagogy, where classroom roles, rules and participation are made visible. The article draws on primary research which explores the development of creativity within the English Key Stage 3 (age 11–14) art and design classroom. Illustrations are provided to show how through the use of an activity theory system a multi‐layered analysis took place. This generated reflection on relationships and structures within and surrounding the classroom, impinging creative activity. Through using the activity theory system teachers and researchers were enabled to observe the complexity of the classroom and question socio‐cultural‐political structures which empowered change.     

构建方言复杂地区高师普通话教学模式的探索

方言复杂地区高师的普通话教学改革势在必行。本文以普通话水平测试为镜,反思传统教学的偏差与误区,提出构建分类教学,分层达标的教学新模式。它突破了传统教学不分对象的弊端,提出按中介语的区域特征、按中介语的水平层次、按学科性质分班授课的设想,根据各区域层次学生的实际语音情况来设置教学目标,选取教学内容与方法,全面贯彻因地施教,因材施教的原则。这一新模式的构建,对改变方言复杂地区师范院校的普通话教学滞后现状,提高学生的普通话水平,不失为一个带有全局性、根本性的改革措施。     

高中思想政治教材建设的实践探索——以《经济生活》《经济与社会》的编写为例

以普通高中思想政治课程为代表的哲学社会科学教材以基于学科主要问题的立德树人为目标导向,强调教学内容的集体权威性,注重综合素质与创新思维的培养,注重问题情境的真实性、典型性与丰富性,初步形成了德育为魂、智育为基、素养为重的编写特色。这是国情与学生认知发展规律等多种重要因素综合作用的结果,它们共同推动了教材特色的形成,推动了基于学科问题和学科思维方法的哲学社会科学教育教学改革。     

“中体西用”论对构建中国近代新式教育的意义

“中学为体,西学为用”在中国近代史上是一个影响很大的思想,分析这个思想对于中国近代社会的影响,不应一概而论给予否定。就它与中国近代教育的关系而言,“中体西用”论在构建中国近代新式教育上具有基础性的作用,它促进了中国教育向近代化的全面转型。这种作用表现为它为中国新式教育的兴起提供了思想基础,成为其发展的动力;它为新式教育注入了崭新的教学内容,并带来了近代教学形式。