Time Management in the Work Economy of A Class, A Case Study: Integration of Cabri in Primary School Mathematics Teaching

Time is a constraint but also a condition of operating within a didactic system. Don’t we need to distinguish several kinds of times? Our study will focus on teachers’ time management strategies. We will identify these strategies by taking into account two temporal dimensions – didactic time and time capital – and the rate at which the former advances relative to the latter, called the pace of an activity, a lesson or a teaching sequence. Those strategies have been identified in the specific context of the integration of the Cabri-geometry dynamic geometry software in the daily work of a French primary school.     

新序关系下模糊数的距离和模糊数列的极限

在新的序关系下,定义了模糊数的距离,并与Hausdorff意义下的距离做了比较,讨论了模糊数列的极限。     

数列极限概念的抽象度分析

首先运用抽象度分析法定量地对数列极限概念的抽象层次进行分析,然后提出核心抽象概念存在,并运用教育实验检验猜想,试图揭示概念丰富的内涵.     

ICT in the classroom: Primary education student teachers’ perceptions of the interactive whiteboard during the teaching practicum

A literature review on perceptions of the interactive whiteboard during the teaching practicum shows that there has been insufficient analysis of student teachers’ perceptions of Information and Communication Technology (ICT). However, these perceptions are highly useful to create a full picture of the effectiveness – and indeed the drawbacks – of using ICT in the classroom. In this study, we examine and analyse evidence from teaching practica to assess the success of ICT – specifically the interactive whiteboard – as a teaching tool, using a qualitative method. The accounts are first-hand, scientific reflections made by student teachers from La Serena, Chile, during their teaching practicum in primary schools; for this reason they are extremely useful in analysing this teaching tool’s effectiveness in the classroom. Among the main results for students’ perceptions of incorporating technology as part of their training, we found a set of variables for good practice when using the interactive whiteboard, including: incorporating technology as an engaging didactic resource; making the most of technology for improving learning; determining when best to use the whiteboard; and identifying any limiting factors together with students’ suggestions for improvement.     

数列极限的几种计算方法

求解数列的极限问题有时比较困难,没有一般规律可循。但只要发现和利用数列的特性,选择适当的方法和运用一些技巧就能很容易求解。通过典型例题,讨论了数列极限的几种计算方法,对求解数列极限很有帮助。     

Didactic Restrictions on the Teacher’s Practice: The Case of Limits of Functions in Spanish High Schools

The Anthropological Theory of Didactics describes mathematical activity in terms of mathematical organisations or praxeologies and considers the teacher as the director of the didactic process the students carry out, a process that is structured along six dimensions or didactic moments. This paper begins with an outline of this epistemological and didactic model, which appears as a useful tool for the analysis of mathematical and teaching practices. It is used to identify the main characteristics of the mathematical organisation around the limits of functions as it is proposed to be taught at high school level. The observation of an empirical didactic process will finally show how the internal dynamics of the didactic process is affected by certain mathematical and didactic constraints that significantly determine the teacher’s practice and ultimately the mathematical organisation actually taught.     

数列极限的几种特殊求解方法

求解数列的极限问题有时比较困难,没有一般规律可循。但只要注意发现和利用数列的特性,选择适当的方法和运用一些技巧就能很容易求解。讨论了几种数列极限的特殊求解方法：比较法、定积分法和忽略高阶无穷小法,对求解无穷项和的极限很有帮助。     

Lifting the cover: developing an analytical tool to unravel environmental education resources

Abstract

Evaluations of environmental education (EE) programmes and resources are becoming increasingly visible and important. While benefits accrue through evaluation, many programmes and resources have yet to realise these. Issues such as a lack of clear objectives, reliance on traditional, summative approaches and inattention to context have prevented rigorous evaluation occurring. This paper reports on the development of an analytical tool designed to unravel EE resources. Its theoretical basis is a socially acute questions (SAQ) approach and educational configurations teachers use when implementing this approach. Using these configurations, a series of interrogatory questions were developed to unravel a resource writer’s education intent – what type(s) of knowledge are valued, the view of science presented and the view of learning. Two contrasting resources were analysed to test this tool. This analysis revealed that one resource viewed knowledge as universal, had a scientistic epistemic posture and a doctrinal/pragmatic didactic approach whereas the other viewed knowledge as contextualised, had a relativistic epistemic posture and a problematising/doctrinal didactic approach. Consequently, this tool showed that it was able to unravel a resource writer’s intent, identify gaps so teachers could adapt a resource and build capacity for didactics of EE and its evaluation.     

Between the aesthetic and the ethical: analysing the tension at the heart of Theatre in Education

Theatre in Education is a recognized form for exploring ethical issues in schools. Although the relationship between functional, didactic objectives and theatre artistry is recognized as complex and difficult, there has been little analytical work to elucidate its nature. This article takes the form of a case study intended to illuminate this tension by analysing a play that toured recently in secondary schools in Birmingham, UK. It concentrates on two aspects of this particular performance: its transgressive elements – the way in which it played with the boundaries of institutionalised values – and the features of its narrative that tended, in Eco's term, towards an aesthetic of openness. Rather than attempting to offer a clear‐cut theory, this article examines how these essentially theatrical elements of the performance meshed with the play's ethical agenda. I conclude that, despite the risks of transgressive play, it was the playful and open aspects of the enacted narrative that energized the students' moral engagement and subsequent reflection, and suggest that this has implications for moral pedagogy beyond the field of theatre.     

数列加权平均值的极限及应用

给出了数列加权平均值的极限及其若干推论,最后研究了这些结果在证明及计算中的应用．     

一类递推数列极限问题的推广与应用

求递推数列的极限是数学分析教材和一些高校硕士研究生入学考试中经常出现的问题．通过对一类递推数列的极限问题作推广,对推广的结论给出了具体应用．     

压缩映射原理在求数列极限中的应用

介绍了压缩映射原理在求数列极限中的应用.     

Strategies and Principles for the Creation of Software in CAI

In the context of CAI, the authors present examples of didactic software or‘teachware» developed in a school of engineering, accompanied by a discussion of pedagogical and systems considerations. The 'pedagogical environment' is described as the interface (Apple-Macintosh) used in the teachware in particular in relation to Bloom's six levels of learning. The ‘system approach’emphasises each step and the proper sequence that are necessary to arrive at empirically validated and relevant software. The importance of the new information technologies for both the pedagogue and ‘the media conceptualiser’ are underlined.     

极限“M-语言”的定义及其应用

相对于传统的极限"ε-语言"的定义,我们先给出无穷大数列、无穷小数列的定义,在此基础上引入数列极限的定义,继而给出函数极限的定义,这种定义我们称为极限"M-语言"的定义,然后通过举例子对该定义加以应用.     

高等数学中数列极限的几种求法

本文针对高等数学中数列极限的初等变形求极限、利用变量替换、两边夹定理、归结原则、定积分法、单调原理、级数展开式、Stolz公式等来讲述数列极限的几种求法。     

递推形式数列极限的求解

递推形式数列极限的求解问题是高等数学中的困难问题之一．该文介绍了三种求递推数列极限的方法，即利用存在性求极限、写出通项公式求极限和运用替换与变形求极限．     

求数列极限的几种方法

众所周知,极限论包括数列极限、函数极限两类。本文针对数列极限的初等变形求极限、利用变量替换、两边夹定理、归结原则、定积分法、单调原理、级数展开式、斯笃兹公式等来讲述数列极限的几种求法。     

Grammar and text: an experiment in teacher training / Gramática y texto: un experimento en la formación de profesores

Abstract

The article describes an experiment in teaching training undertaken in the context of the Masters programme in Teacher Training (for primary school teachers) at the Lisbon College of Education. The training experiment was able to: (1) incorporate mother tongue teaching into the broader curriculum; (2) relate the teaching of texts and the teaching of grammar; and (3) integrate the theoretical and practical dimensions of teacher training. The didactic scheme adopted relies on theoretical assumptions such as the concept of the integrated curriculum, the model of didactic sequence and the principles of socio-discursive interactionism. This training experiment has proved to be particularly useful for all the participants in the process (teachers of the course; trainee teachers; children in the schools; and the form teachers of the classes where the trainees do their practice). As a result of it, there has been a clear improvement in the quality of the teaching provided by our trainees in the domains of writing and grammar. The main advantages of this approach are that: (1) it structures the teaching of writing and grammar; (2) it uses projects to socially contextualize writing tasks; (3) it develops various language skills in an integrated fashion, while at the same time working on different areas of knowledge; and (4) it defines forms of spiral progression.     

The Use of Visual Media in Renaissance Cosmography: the Cosmography of Peter Apian and Gemma Frisius

Peter Apian's Cosmography (1524) first reached a large audience through the re‐editions of the Leuven mathematician Gemma Frisius. The book seems to have been intended as a didactic tool for use in a largely auto‐didactic and non‐institutionalised context. This disciplinary situation entailed the necessity of legitimation, which was partially attained by visual reference to instruments, available from the cosmographer‐instrumentmaker. Realistic depiction as well as explicit references to linear perspective painting were important means of reinforcing the rhetorical strength of these references. A second consequence of cosmography's educational context was the necessity of efficient didacticism. Because most of the (astronomical) subject‐matter of the Cosmography draws on visual thinking, powerful visual information was equally essential from this perspective. This was implemented in paper derivatives of common astronomical instruments included in the book itself. These at once enabled readers to train themselves in the use of various instruments and—because of the visualizing nature of these instruments as such—to become acquainted with specific aspects of astronomical visual thinking.

     

关于逆序列的极限空间

讨论了当逆系统为一逆序列时其极限空间的性质，证明了任一逆序列的极限空间与任一无穷的子逆序列的极限空间是同胚的。