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.This revised version was published online in September 2005 with corrections to the Cover Date.     

Constructing Learning Environments for Complex Social Skills

This article addresses issues faced in the construction of computer programs that teach complex social skills. We describe a software architecture called Guided Social Simulation (GuSS). GuSS combines a simulation in which students can practice social skills with guidance that enhances the simulated experience. One of the applications of GuSS, called YELLO, teaches how to sell Yellow Pages advertising. YELLO is described in detail. The social simulation and guidance components of GuSS each present a set of technical and theoretical challenges. We discuss both sets. In discussing the techniques we use for constructing a social simulation, we emphasize the mechanisms that implement social agents as simple social planners. We then focus on one particular guidance component of GuSS—the storyteller. The storyteller is a teaching module that contains the real-life stories of experienced practitioners captured on videodisk. The storyteller monitors the student's actions in the simulation and interjects stories that are relevant to the student's experience.     

从几何角度证明代数不等式

不等式是数学竞赛中的常见题型之一,证明的方法也多种多样．笔者发现,有一类不等式可以结合代数式的几何意义去证明．这类问题主要是根据几何图形的凸凹性寻求不等关系,其特点是让多组对称式的求和化归成面积或长度等几何量．下面通过实例来介绍．     

一个几何定理的证明方法初探

用三角形面积公式先证明推论 ,再用推论结果去证明定理 ,定理和推论都得以严格证明 ,学生易于理解和接受。     

Teachers as Designers of Learning Environments

Abstract

This study examined how six Singapore teachers approached the design and implementation of a unit of work (topic) to demonstrate exemplary classroom practices that engage learners and use ICT in knowledge-generative rather than presentational activities. After a reflection and feedback session on the first lesson observation involving the researcher and the teacher, the teacher redesigned the lesson to enhance ICT use and involve students more actively in their learning. Our study revealed that there is a difference between students' physical engagement and cognitive engagement in a task and that the teacher, as a designer of the learning environment, needs to make explicit the cognitive processes involved in using the tool to ensure students' effective use of ICT. The teachers' understanding of what constitutes effective learning and their roles in students' learning determine how they design the learning environment. In essence, it is the teacher's skill in managing the “tripartite” partnership of IT tool, learning task, and teacher support that brings about higher levels of student engagement.     

Transfer of Learning as a Specific Case of Transition between Learning Contexts in a French Work-Integrated Learning Programme

The aim of this article is to discuss transfer of learning in a tertiary technical course in the French educational context. The focus is on a pedagogical sequence (i.e. a complex problem-solving activity) requiring different types of knowledge that students are expected to have learnt previously in the different parts of their training course (both at university and in the workplace). The theoretical approach considers transfer of learning as a complex transition, including not only cognitive but also social and identity changes. This type of transition can be more or less difficult according to the types of knowledge and the pedagogical organisation of the training course, including more or less connective activities between its different components. We recorded two groups of students during the pedagogical sequence and analysed their collective activity during the problem solving. Our findings show that students can easily transfer concrete knowledge from the workplace whereas they have great difficulty in using theoretical concepts and methods coming from the academic teachings at the university. We propose an interpretation of the students?? difficulties by analysing the characteristics of these different social learning contexts. We also discuss the way in which such types of connective activities can be designed and managed by teachers to improve their efficiency.     

联赛加试几何题证明随想

2001年全国联赛加试第一题:图1如图1,在ABC中,O为外心,三条高AD、BE、CF交于点H.直线ED和AB交于点M,FD和AC交于点N.求证:     

《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.     

四成分教学设计模型——面向复杂学习环境的多媒体原理

四成分教学设计模型认为要实现复杂学习需要借助学习任务、支持性信息、程序性信息和子任务练习等因素.本文探讨运用这一模型设计多媒体学习环境及相关的14条多媒体原理.学习者可以在一个模拟的环境下完成学习任务,利用相关的多媒体原理有利于促进归纳学习过程;学习者还可以在超媒体系统中掌握支持性信息,相关的多媒体原理有利于促进信息的提取和精细加工过程;学习者也可以通过电子绩效支持系统来获取程序性信息,相关的多媒体原理有利于知识处理;最后,学习者能通过基于计算机练习程序来进行子任务的练习与训练,相关的多媒体原理有利于促进知识技能的巩固.本文还讨论了四成分模型框架的启示和不足.     

Living and Learning at the Intersection: Student Homelessness and Complex Policy Environments

In urban districts, homeless and highly mobile students are an important contributor to achievement disparities—and their numbers are rising. To date there has been little inquiry into how broader education and housing policies shape the schooling experiences of homeless and highly mobile families. Using semi-structured interviews with 132 key community stakeholders (parents, school social workers, other school staff, and community/service personnel) in one urban area, this study explored how families living at the policy intersection of the McKinney-Vento Homeless Assistance Act and federal rehousing policies, such as the HEARTH Act, experience the schooling process. These policies have important impacts on students; the McKinney-Vento Act provides them with a range of supports while recent federal policies such as the HEARTH Act are shifting where and how they are living. Taking a policy perspective and drawing insights from Lin’s network theory of social capital, the findings suggest that these policies both independently and concomitantly shape families’ life opportunities. Implications for schools, communities, and scholars are addressed.     

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.     

网络学习环境设计的十个要素

本在提出远程学习中支持体系概念的基础上，提出了一些如何为学习提供建构主义学习的例子，并提出了适用于不同教学环境的学习支持体系的设计准则。     

利用直线系方程证明平面几何问题

(本讲适合高中)解析法证明平面几何问题已备受关注,而直线系方程的巧妙利用,既可摆脱求交点、直线方程等烦琐运算,又能较简单地得到所需结论,充分体现了整体处理问题的解题策略.本文从六个方面介绍直线系方程在证明平面几何问题中的应用.若直线a1x b1y c1=0与a2x b2y c2=0相交于点P,则通过点P的直线系方程可写成λ(a1x b1y c1) μ(a2x b2y c2)=0(λ、μ∈R).1证明三线共点用直线系方程表示过其中两直线交点的直线,然后,取特殊的λ0、μ0时就是第三条直线,从而证明三线共点.图1例1如图1,⊙O与△ABC的边BC、CA、AB分别交于点A1和A2、点…     

Three Cases of Hashtags Used as Learning and Professional Development Environments

Hashtags offer exciting opportunities for professional development, teaching, and learning. However, their use reflects users’ needs and desires. To illustrate and problematize the ways hashtags are used in professional development settings, this study reports on users’ participation patterns, users’ roles, and content contributed to three unique hashtags. This mixed methods research employs data mining techniques to retrieve data. Using a collective case study methodology, the study compares and contrasts the use of three hashtags and offers insights into the use of hashtags as emerging learning and professional development environments. Results show that hashtags exhibit similarities, such as unequal user participation. Findings also reveal differences between hashtags. For instance some hashtags are used on an ongoing basis while others have well-defined start and end dates. Ultimately, these results question deterministic thinking with respect to emerging technologies and novel professional development environments.     

Self-Regulated Learning in Technology-Enhanced Learning Environments: lessons of a European peer review

This article first describes the state-of-the-art of model building and empirical research in the field of self-regulated learning (SRL) and then focuses on self-regulated learning in Technology-Enhanced Learning Environments (TELEs). We present recent research results obtained in a European project (TELEPEERS) in the context of which we evaluated TELEs in a peer review manner with respect to their potential for supporting self-regulated learning. In addition, data were obtained on a sample of TELEPEERS students working in these environments and comparative analyses were made across the European project partners.     

Developing an Initial Learning Progression for the Use of Evidence in Decision-Making Contexts

This paper outlines an initial learning progression for the use of evidence to support scientific arguments in the context of decision-making. Use of evidence is a central feature of knowledge evaluation and, therefore, of argumentation. The proposal is based on the literature on argumentation and use of evidence in decision-making contexts. The objective is to develop a construct map describing a trajectory of evidence use in a decision-making context. The levels in the initial learning progression are characterised by students’ performance in practice. The framework is applied to a multiple-case study in 10th grade (66 students), structured around a marine resource management task. Data included audio and video recordings, as well as students’ written artefacts. Five levels of complexity in student performance are described; on the lowest level, students are able to identify and extract information in response to a problem and recognise general features in a set of data; on the uppermost level, they are able to articulate arguments by synthesising evidence from multiple sources and evaluate options based on evidence and scientific content. The framework also shows potential for recognising students’ difficulties in identifying and integrating data and evidence in their justifications and in drawing from domain knowledge to interpret evidence. Implications for educational practice are discussed.     

论学习环境设计的理论基础

如何为学习者创设良好的学习环境以支持和促进学习者的学习已逐渐成为教育技术领域的前沿研究课题。本文对“社会-文化观”下的情境认知理论、活动理论、分布式认知理论等三种理论的主要观点加以概括,并详细分析了它们为学习环境设计所提供的指导原则。笔者认为,好的学习环境设计应该得到理论的指导但不能成为理论的奴隶,设计者应该根据具体学习情境的约束和给养,为学习者尽可能地提供真实的情境、活动和任务。     

Epistemic Frames as an Analytical Framework for Understanding the Representation of Scientific Activity in a Modeling-Based Learning Unit

Research in Science Education - Set in the context of modeling-based learning (MBL), this research investigated the potential of epistemic frames as a theoretical and analytical framework for...