首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 593 毫秒
1.
In this series of articles, we intend to have a glimpse of some of the landmarks in ancient Indian mathematics with special emphasis on number theory. This issue features a brief overview of some of the high peaks of mathematics in ancient India. In the next part we shall describe Aryabhata’s general solution in integers of the equationax -by =c. In subsequent instalments we shall discuss in some detail two of the major contributions by Indians in number theory. The climax of the Indian achievements in algebra and number theory was their development of the ingeniouschakravala method for solving, in integers, the equation x2 -Dy2 = 1, erroneously known as the Pell equation. We shall later describe the partial solution of Brahmagupta and then the complete solution due to Jayadeva and Bhaskaracharya.  相似文献   

2.
As a first step of a project on learning difficulties in elementary set theory, we carried out a study aimed at identifying some of the difficulties encountered by a group of 21 mathematics majors taking a course on logic and set theory. In this paper, we shall discuss one of the difficulties that we observed, namely a difficulty in conceiving a set as an object distinct from its elements, i.e. failing to fully grant sets the status of objects. This difficulty may be related to the following three types of errors that we observed in the students' first assignment: (1) confusing belonging and inclusion, (2) confusing the union of sets A, B, C, ... with the set whose elements are A, B, C, … and (3) adding or deleting curly brackets. We shall present excerpts from the students' work illustrating these three types of errors and explain how they may be related to a difficulty in conceiving a set as an object distinct from its elements.  相似文献   

3.
The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.Written version of a Survey Lecture given jointly at the Sixth International Congress on Mathematical Education (ICME-6, Budapest 1988). A condensation was published in a volume with contributions from the ICME-6 Theme Groups on Problem Solving, Modelling and Applications and on Mathematics and Other Subjects (Blum/Niss/Huntley 1989, pp. 1–21).  相似文献   

4.
We shall some day be heeded, and when we shall have our amendment to the Constitution of the United States, everybody will think it was always so, just exactly as many young people believe that all the privileges, all the freedom, all the enjoyments which a woman now possesses always were hers (Susan B. Anthony on February 15, 1894). (Sherr, 1995, p. xi)  相似文献   

5.
Whereas supra‐national higher education policies in the past decade have been criticised for their possible harm to the national governments’ autonomy, the Bologna process — as an international agreement — has received much more positive reactions from national governments, at least in the rhetoric sense. Nevertheless, a variety of approaches of governments can be noted to do justice to the agreements made in the Bologna Declaration (1999) . In this article, we shall try to explain the (gradual) change from Euroscepticism to acceptance of harmonisation attempts in higher education. We shall furthermore exemplify this change process by looking at developments in a number of European countries: UK, Greece, the Netherlands, Norway, Portugal, Austria and Germany.  相似文献   

6.
1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ａ .Ｍ .Ｗ .Ｇｌａｓｓｈａｓｓｈｏｗｎｔｈｅｆｒｅｅｌ ｇｒｏｕｐＦη ｏｆｍｏｓｔｉｎｆｉｎｉｔｅｒａｎｋηｔｏｂｅｉｓｏｍｏｒｐｈｉｃｔｏａｄｏｕｂｌｙｔｒａｎｓｉ ｔｉｖｅｌ ｓｕｂｇｒｏｕｐｏｆｔｈｅｌ ｐｅｒｍｕｔａｔｉｏｎｇｒｏｕｐＡ(Ｑ) [1,2 ] .Ｓ .Ｈ .ＭｃＣｌｅａｒｙｈａｓｐｒｏｖｅｄｔｈａｔｔｈｅｆｒｅｅｌ ｇｒｏｕｐＦηｏｆｆｉｎｉｔｅｒａｎｋηｈａｖｅｐｏｓｓｅｓｓｅｄａｆａｉｔｈｆｕｌｌｙ 2 ｔｒａｎｓｉｔｉｖｅｒｅｐ ｒｅｓｅｎｔａｔｉｏｎｏｎｔｈ…  相似文献   

7.
Editor's note: At present and for a period to come, a most important and urgent task in basic education is to bring about the "switching of tracks" from exam-oriented education, (or yingshi jiaoyu) to quality education (or suzhi jiaoyu). We have often said that the hope for reviving the nation lies in education, and the hope of reviving education lies with teachers. If we are to bring about this "switching of tracks" from exam-oriented to quality education, we shall have to successfully cultivate group after group of new teachers capable of carrying out quality education. In today's issue of this paper, we deliver the following report on the experience of one school—the Lingling Teachers' Vocational College—in cultivating new lower middle school teachers who will carry out quality education; this report and the experience it describes should hold, for us, a certain significance of leading us in thinking about the subject.  相似文献   

8.
The definition of ‘definition’ cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of concept definition and concept image, conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to construct definitions. This paper will deal with ‘definition construction processes’ and aims more specifically at proposing a new approach to the study of the formation of mathematical concepts. I shall demonstrate that the study of the defining and concept formation processes demands the setting up of a general theoretical framework. I shall propose such a tool characterizing classical points of view of mathematical definitions as well as analyzing the dialectic involving definition construction and concept formation. In that perspective, a didactical exemplification will also be presented.  相似文献   

9.
Koundinya Vajjha 《Resonance》2010,15(9):843-849
A Pythagorean triple is a triad of positive integers (x, y, z) which satisfy the Pythagoras’ equation x 2 + y 2 = z 2. In this article, we shall consider triples of the form (i, i + 1, k), and the recurrence relations governing them. In the process, we also solve completely the equation i 2+ (i + 1)2 = k 2.  相似文献   

10.
V. K. Wadhawan 《Resonance》2009,14(8):761-781
The characteristic feature of complex systems is the emergence of unexpected properties or behaviour. Complexity, beyond a certain threshold, may even lead to the emergence of new principles. It is a one-way traffic: The new principles and features may be sometimes deducible from, but are not reducible to, those operating at the lower levels of complexity. Reductionism stands discounted. Complexity is rampant in the animate world. It arises in inanimate systems also, some examples being multiferroic materials and certain nanocomposites, as also a variety of soft-matter systems. Our ecosphere is also a giant, highly complex, open system, which we do not understand much at present. Mastering complexity is the next big challenge for science. Conceptual breakthroughs are needed. In the first part of this article, we introduce the basic of information theory, chaos theory, and computational complexity. In the second part, we shall describe complex materials as well as some terrestrial and cosmic aspects of complexity.  相似文献   

11.

The growth of work‐experience as part of the school curriculum in such schemes as TVEI, has led to a growing body of literature concerned with the educational, social and political consequences of this trend. However, one aspect of analysis has been neglected by those working in this area. There has been a marked lack of investigation into factors which affect the supply of work placements to schools. Behind this lies an assumption that the participation of industry with schools is a straightforward and easy to accomplish process.

By focusing on some of the approaches exhibited by firms towards the provison of work‐experience, this paper seeks to make problematic the supply of work placements by industry in a market economy. I shall suggest that eductionalists and policy makers may have cause to be concerned not only with the quantity of placements which might be available to them in the future, but with the educational quality of these placements.  相似文献   

12.
Too difficult, too abstract, too theoretical – many first-year engineering students complain about their mathematics courses. The project MathePraxis aims to resolve this disaffection. It links mathematical methods as they are taught in the first semesters with practical problems from engineering applications – and thereby shall give first-year engineering students a vivid and convincing impression of where they will need mathematics in their later working life. But since real applications usually require more than basic mathematics and first-year engineering students typically are not experienced with construction, mensuration and the use of engineering software, such an approach is hard to realise. In this article, we show that it is possible. We report on the implementation of MathePraxis at Ruhr-Universität Bochum. We describe the set-up and the implementation of a course on designing a mass damper which combines basic mathematical techniques with an impressive experiment. In an accompanying evaluation, we have examined the students' motivation relating to mathematics. This opens up new perspectives how to address the need for a more practically oriented mathematical education in engineering sciences.  相似文献   

13.
Conclusion Change is not an abnormal or even intermittent state in education. It is an essential and permanent part of any system. True, the rate of change may be greater or less at different times but it is always present in some measure. Change at the present time in English education is rapid and, if a mere list is to be avoided, some of the trends and developments have to be omitted from a short account. Partly the movement is a reflection of the rate at which society as a whole is changing, partly the result of a belief that the system as at present constituted does not entirely meet the needs of contemporary society, even less the society of the future in which the children now at school will be adults and earn their livings. We shall have to run quite fast to stay in the same place. We shall have to run even faster if we want to get anywhere else.
Neue Tendenzen und Entwicklungen im Primar- und Sekundarschulwesen in England
Tendances et developpements recents dans l'enseignement primaire et secondaire en Angleterre
  相似文献   

14.
Abstract

The main objective of this article is to analyze the conceptual connection between the Doctrine of Children’s Education, briefly mentioned in Spinoza’s Tractatus de Intellectus Emendatione (TIE), and the concept of emendation present at the very center of this Treatise’s title. A close textual exegesis of the opening paragraphs of TIE reveals why such a doctrine cannot be the ascetic renunciation of the content of ordinary life. We shall see instead that a new institution of life shall be possible only through a deep plunge into the understanding of ordinary confused life. A Spinozan Doctrine of Children’s Education shall then be conceived as a pedagogy guided by an error mapping principle, i.e., a pedagogy capable of amending the mistaken beliefs of students through their understanding of the way these are produced as real events in the world. This would be an immanent pedagogy, which could be relevant to any form of contemporary thought that seeks a truly liberating education.  相似文献   

15.
Summaries

English

In this article, which is based on a paper read at the International Institute for Educational Planning, Paris in July 1979, we shall first review the impact of science curriculum development on Third World countries and the effect of Western science education on those changes.

We shall then outline some of the ways of thinking that the pupils of different cultures bring to school that appear to differ from, or even to conflict with Western scientific modes of thought.

This will lead us to an analysis of the factors responsible for the predicament in science education today. In the light of this analysis we shall suggest some courses of action for the future progress of science teaching in the Third World.  相似文献   

16.
Article 7, Clause 1. The state shall adopt measures to develop rural vocational education and to support the development of vocational education in ethnic minority areas and in border, remote, and poverty-stricken regions.  相似文献   

17.
本文就~(194-195)Pt,~(194—195)Hg核,在原子核的u(12/12)超对称性群下进行了能谱计算并与实验作了比较。结果表明,这些核可能是N=7超多重态成员的“候选者”  相似文献   

18.

Over the last decade, historico-educational studies of the Franco regime in Spain have undergone a remarkable development, even though the first studies of interest date back to the 1980s and even earlier. In consequence, we shall take these as our starting point although we shall, on occasion, refer to earlier studies, either for their relevance or for the scientific prestige of their authors. A thematic criterion has been preferred to a chronological one, after referring to certain studies of a general historiographic nature, essential for a first approximation to the theme. "Ideology and Education" "Educational Policy" and "New Themes" are the blocks into which the monographical studies have been distributed. This is, nevertheless, a methodological and flexible division, it being obvious that there can be no impermeable barriers between the analytic perspectives of a single question - in our case, that of education - and therefore some of them could well fit in two or even all three of the sections.  相似文献   

19.
Truisms have the disadvantage that by dulling the senses they obscure the truth. Almost nobody will become alarmed when told that in times of continuity the future equals the past. Only a few will become aware that from this follows that in times of socio-cultural change the future will not be like the past... At any moment we are free to act toward the future we desire. In other words, the future will be as we wish and perceive it to be. This may come as a shock only to those who let their thinking be governed by the principle that demands that only the rules observed in the past shall apply to the future. For those the concept of change is inconceivable, for change is the process that obliterates the rules of the past (Von Foerster, 1972).  相似文献   

20.
Abstract

This article will highlight the distinctive role of Cavell in renewing a dawn of American philosophy. Following Emerson’s remark, ‘the inmost in due time becomes the outmost’, Cavell develops his distinctive line of antifoundationalist thought. To show how unique and valuable Cavell’s endeavor to resuscitate Emerson’s and Thoreau’s voice in American philosophy is, this paper discusses the political implications of Cavell’s Emersonian moral perfectionism. This involves a reconsideration of what measures justice and what justifies happiness. While Cavell is sometimes said to be too personal and too subjective to be political, I shall argue that his Emersonian perfectionism, with its concomitant idea of the conversation of justice, is in fact thoroughly political and democratic. I shall illustrate this by examining his writing on a Hollywood film, Mr. Deeds Goes to Town (1936). The film shows vividly that happiness is a condition for achieving democracy from within. In conclusion, I shall propose that a readiness for the risk inherent in speech, rather than, say, acquiescing in received ideas or hiding behind the words of others, is at the heart of perfectionist education for globally minded citizens.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号