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1962年,联合国教科文组织曾在布达佩斯举行了一次有关中学数学改革的国际会议.自此以后,由美、英首先发动起来的西方数学教学改革的浪潮席卷了半个地球.本文作者理查德·斯根普是英国富有声望的哲学家和心理学家,出身于中学数学教师,现任教于英国曼彻斯特大学心理学系,对数学教学的心理学颇有研究,是出席1962年布达佩斯会议英国的两名代表之一.西方这场轰轰烈烈的改革运动,到了七十年代初,遭到了严重挫败.失败的原因在哪里呢?西方学者众说纷云,莫衷一是.理查德·斯根普于1971年发表的《学习数学的心理学》,仍然坚持数学改革的结构化方向,即由集合、关系、映射、函数等现代基础概念统率全部数学教材,形成一种结构体系,而把这场改革运动的失败归罪于教学方法上的失慎和心理学上的原因,强调改革“不一定能使情况转好,新课题的推广不会自动获得很好理解的,如果它们还是用同样坏的老办法来教的话.”当今,在我国深入研究中学数学现代化的问题当中,借鉴外国的经验和教训,或许是有益的.现将其中的一章译载于此,供数学工作者和数学教师研究参考.
UNESCO held an international conference on mathematical reform in secondary schools in Budapest in 1962. Since then, a wave of reforms in western mathematics teaching, first launched by the United States and Britain, has swept half of the globe. Spenpro, a prestigious philosopher and psychologist in the United Kingdom, was born in a middle school math teacher and now teaches at the Department of Psychology at the University of Manchester, England. He studied psychology in mathematics teaching very well and attended two meetings in Budapest in 1962 One of the representatives, the vigorous reform movement in the West, was severely defeated by the early 1970s .What is the reason for the failure? Western scholars say a lot of things, neither .If Richard Scunt published in 1971 The “Psychology of Learning Mathematics” still insists on the structural direction of mathematics reform. That is, all mathematics teaching materials are ruled by the modern basic concepts of aggregation, relationship, mapping and function, forming a structural system. However, the failure of this reform movement Attributed to the failure of teaching methods and psychological reasons, stressed that reform “may not be able to make the situation better, the promotion of new topics will not If they still use the same bad old ways to teach them. ”Nowadays, it is perhaps useful to learn from the experience and lessons learned by foreign countries in our in-depth study on the modernization of mathematics in secondary schools. A chapter is here for reference by maths and math teachers.