Odd behaviour of the even integer 2

It is always of interest when one finds a property that is true only of some given object, or some given class of objects. For example, if n > 1 is an integer, then (n − 1)! + 1 is divisible by n just when n is a prime number. In this article we look at some properties that are true only for the integer 2. Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at the national and international level for the past two decades. He is the author of several expository books and articles aimed at interested high school students.     

The adolescent novel of ideas

Peter Hollindale first developed critical interests in children's literature during postgraduate teacher training at the University of Bristol, where he was taught by Margaret Meek. After teaching for several years in secondary schools he was appointed to the University of York, where he is senior lecturer in English and educational studies. He now teaches an undergraduate special paper on children's literature in the Department of English there. His bookChoosing Books for Children, a guide for parents, was published in 1974, and he has since written extensively on children's literature in academic and professional journals. His article “Ideology and the Children's Book,” which appeared inSignal 55, received the Children's Literature Association Prize for the best essay in the field of children's literature published in 1988. In recent years he has worked closely on J. M. Barrie. His edition of the “Peter Pan” prose texts was published by Oxford University Press in 1991, andPeter Pan and Other Plays appears from the same publisher in 1995. He is interested in reworkings and adaptations of classic children's texts for film and television, and his study of Steven Spielberg'sHook was published inSignal 72 in 1993. For Thimble Press he is currently completingSigns of Childness: A Short Philosophy of Children's Literature. He has contributed a number of articles toCLE, the most recent being “Westall's Kingdom” in the 1994 Autumn issue.     

Some elementary examples from Newton’sPrincipia

This article is aimed at undergraduate students to give them a taste of thePrincipia, Newton’s famous book. I have selected some examples and results in mechanics; most of them are a part of the undergraduate curriculum. His research interests are in high energy phenomenology. He is also interested in teaching graduate and undergraduate courses.     

Where the Action Is: How Drama Contributes to the Art of the Teaching and Learning of English

This paper looks at the way drama works to bring a model of an arts curriculum into reality. He also shows how drama is valuable when discussed as a separate, autonomous subject in the school curriculum as opposed to one subsumed within English. He argues for a view of the arts and gives an example of a sequence of work in an English GCSE class based around Arthur Miller's play View from the Bridge. From this he draws out several strands about the relationship of the drama curriculum to the individual students and teachers, the school, and to culture. He also emphasises the primacy of performance in drama education.     

On sums of powers of integers

For non-negative integers k, n, let P _k (n) denote the sum {fx27-1}. We show by two different means that if k ≥ 3 and odd, then n ²(n+1)² iss a factor of the polynomial P _k (n); and if k ≥ 2 and even, then n (n+1) (2n+1) is a factor of the polynomial P _k (n). We also derive a relatively unknown result first obtained by Johann Faulhaber in the 17th century. Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at the national and international level for the past two decades. He is the author of several expository books and articles aimed at interested high school students.     

Teaching Physics to In-Service Primary School Teachers in the Context of the History of Science: The Case of Falling Bodies

Our paper presents an in-service primary school teachers’ training program which is based on the idea that the history of science can play a vital role in promoting the learning of physics. This training program has been developed in the context of Comenius 2.1 which is a European Union program. This program that we have developed in the University of Athens is based on socioconstructivist and sociocultural learning principles with the intention of helping teachers to appropriate the basic knowledge on the issue of falling bodies. Moreover, it has the aim to make explicit through the exploitation of authentic historical science events, on the above topic (Aristotle’s, Galileo’s and Newton’s theories on falling bodies) the Nature of Science (NoS), the Nature of Learning (NoL) and the Nature of Teaching (NoT). During the implementation of the program we have used a variety of teaching strategies (e.g. group work, making of posters, making of concept maps, simulations) that utilize historical scientific materials on the issue of falling bodies.

---

论余华小说创作转型后的艺术走向

余华在20世纪90年代小说创作转型后,文本主题更多的是对当代的个体人生、生存现状和人性境遇给予温情的关注。在艺术上借助单纯而丰富的叙述技巧,用朴素、准确、简洁的语言表现生活的本真面目;以随和的民间姿态、悲悯的情怀、诙谐幽默的审美趣味,使作品呈现出一种淡薄而坚毅的内在力量,成功地实现了他在文学创作方面新的升华与超越。     

Responding to diversity: the challenge of expanding basic education for young people in the south

This article explores the extent to which and how non-formal education (NFE) contributes to the development of a more diversified basic education system and thus to the achievement of EFA. It outlines the current nature of NFE, the frameworks provided by the EFA movement, and the evolution of reflection, policies and practices in NFE in relation to basic education as a whole. Based on significant developments in various countries across the South, the article also discusses some key challenges that ministries of education and their partners need to face in moving towards relevant and equitable diversity in education. The article posits that, despite the many problems faced by NFE, there is justification for building on its experiences and integrating these within a larger policy and systems framework that responds more effectively to needs and circumstances of children and young people.

Solving the Self-Transformation Puzzle: The Role of Aspiration

If the received views on self-transformation in philosophical literature are correct, then either self-transformation (1) is caused by forces beyond oneself and beyond one's control, (2) is not rational to pursue, or (3) does not ever really happen. In this essay, James Gordon highlights the philosophical puzzle known as the “self-transformation puzzle,” as raised by Ryan Kemp, who suggests that transformation of the sort educators are interested in cannot be self-caused: it is either something that happens to a person, or something that, if agent guided, is not full-fledged transformation. Next, Gordon turns to an alternative take on the puzzle that tries to recast the conceptual terrain and offer a new way of thinking about self-transformation, namely, the “aspirational” account of self-change offered by Agnes Callard. He argues that Callard's aspirational account of transformation shows that at least one of the premises of Kemp's argument is false. Finally, he suggests several ways that those interested in transformative education might appeal to the concept of aspiration to revise their educational practices.     

Geography teaching in the twenty-first century

Conclusion At a time when transnational communities are being created which extend beyond the confines of regions and natio-States, geographers are questioning the very foundations of their discipline and their function in society. Not only do they no longer avoid acknowledging their role in the transmission of spatial, regional and national identity, but they no longer act solely within the framework of the nation-State. The juxtaposition of local and world considerations prompts them to embark upon new inquiries tending towards the teaching of a conceptual and topical geography which can mobilize pupils and teachers alike according to broad social, temporal and spatial principles. Human beings, frail creatures of the earth, have only one real tool adapted to the vastness of the spaces with which we have to grapple: the mind (Ratzel, 1988). Born in 1944. Professor of geography at the University of Geneva, having taught in Canada and France. He holds a doctorate from the Sorbonne and has studied geography and regional sciences in France and the United States of America. He has been chief examiner at the International Baccalaureat Office. He is now President of the Western Regional Science Association and the Swiss Association of University Lecturers. His recent publications, as author or editor, include:Encyclopédie de géographie [Encyclopedia of geography] (2nd ed., 1995),Introduction à la géographie humaine [Introduction to human geography] (5th ed., 1995) andLes concepts de la géographie [Geographical concepts] (3rd ed., 1995). He is editor-in-chief of the series entitled ‘Géographie’ at the Anthropos publishing house, Paris.     

中国文化对伏尔泰的影响

中国文化对法国启蒙思想家伏尔泰有着不可忽视的影响,尤其是中国的儒家思想为伏尔泰反对法国的专制政权提供了有利的武器。伏尔泰对中国文化表现出极大的热情是有着深刻的社会和历史原因的。     

Fermion number fractionization

Solitons emerge as non-perturbative solutions of non-linear wave equations in classical and quantum theories. These are non-dispersive and localised packets of energy — remarkable properties for solutions of non-linear differential equations. In the presence of such objects, the solutions of Dirac equation lead to the curious phenomenon of ‘fractional fermion number’. Under normal conditions the fermion number takes strictly integral values. In this article, we describe this accidental discovery and its manifestation in polyacetylene chains, which has led to the development of organic conductors. (left) Kumar Rao is a Postdoctoral Fellow at PRL, Ahmedabad. He is interested in particle physics phenomenology as probed in particle colliders and formal aspects of quantum field theory. (right) Narendra Sahu is currently a postdoctoral fellow at Lancaster University, UK. His main research area includes Cosmology and Astroparticle physics. Currently he is working on dark matter and matter anti-matter asymmetry of the universe. (center) P K Panigrahi’s research interests are in the area of quantum computation, solitons in Bose Einstein condensates & nonlinear optical media. He is also deeply interested in science education and derives pleasure from long weekend walks.     

They＇re Ptaying Our Song

It it usual at international soccer matches to play the national anthems (国歌）of the competing teams.The players line up in the centre of the field and the anthems of their countries are played through loudspeakers.It is a kind of courtesy (礼貌）given to visitors from other countries.     

Newton and the age of reason

During the spring semester of 1987 a mathematician and a physicist from Oberlin College went with twenty-one undergraduates to London to use the resources of England as the basis for a course with the above title. This unusual interdisciplinary course is described, with emphasis on its experimental, experiential nature and the challenges and satisfactions which it provided.Joseph L. Snider is Professor of Physics at Oberlin College. He received his undergraduate degree in physics from Amherst College in 1956 and his Ph.D. in experimental physics from Princeton University in 1961. He has taught and done research at Harvard University and at Oberlin College. His areas of interest are solar physics, astrophysics, relativity, and the history and philosophy of science. Recently he has become interested in working to improve the teaching of physics and astronomy to pre-college students.Bruce Pollack-Johnson is Assistant Professor of Mathematics at Oberlin College, where he is responsible for the operations research program. He received a B.A. in sociology with a minor in education from Brandeis University in 1975, an M.A. in mathematics from Temple University in 1979, and an M.S. and Ph.D. in operations research from the University of Pennsylvania in 1980 and 1983, respectively. He has published in the areas of human resource modeling, forecasting, educational planning, simulation, and project management, and his current research includes project scheduling and conflict resolution. He has helped develop new courses for liberal arts students on introductory computer science and educational philosophy, as well as the course described in this article, and is also Co-Director of the Lorain County Peace Education Project.     

The Education of the Bravanese Community. Key issues of culture and identity

Bana M. S. Banafunzi is an Asylum seeker from Somalia, presently living in Ilford, East London. He has a wide administration experience in Somalia. He was awarded a BA in Economics from Somali National University, a post‐graduate Diploma in Development Planning at API, Kuwait and an MBA at the UWIST, Cardiff.     

‘A struggle well worth having’: the uses of theatre‐in‐education (TIE) for learning

In this article Chris Cooper conveys something of his passionate belief in the importance of attending to the preconditions of learning. He stresses the crucial role of the imagination in this, bringing, as he puts it, ‘creativity to the process of learning’. His account of a drama project based on The Tempest provides important insights into the working of these processes. Many readers, as an added bonus, will be interested in the observer role of the learning support assistant.     

Polishing up the pattern: The ending ofThe Owl Service

Andrew Taylor has worked in both Primary and Secondary schools and now teaches at North Riding College, Scarborough, in North Yorkshire, England. He is soon to begin a secondment to the National Curriculum Council in York, as a Professional Officer for English. He has published previously on the Real Books controversy in the teaching of reading and is interested in the use of literature as a support for young children's writing.     

The relation between individual interest and knowledge acquisition

The objective of this study was to examine how individual interest and knowledge acquisition are causally related. Three hypotheses were tested using a cross‐lagged panel analysis (N = 186) and two quasi‐experimental studies (N = 68 and N = 108) involving students from schools in Singapore. The first hypothesis is the broadly shared standard assumption on the relation between individual interest and knowledge: the more an individual is interested in a topic, the more (s)he is willing to engage in learning. An alternative hypothesis assumes that individual interest is not the cause but the consequence of the process of learning: individual interest as an affective by‐product of learning. Finally, a third possibility is that interest and knowledge influence each other reciprocally. The results supported the affective‐by‐product hypothesis. Our findings seem at variance with commonly held conceptions that being interested guides knowledge attainment. The implications of these findings for interest research are discussed.     

徐訏早期对西方文化思潮的接受

徐Yu早期广泛摄取诸种西方化思潮。他既对马克思主义产生了强烈兴趣，又服赝康德、柏格森的唯心主义哲学，同时也认同了弗洛伊德精神分析学，最终确立了自由主义的价值观，从而与左翼思潮分道扬镳。