Young Peoples' Ideas of Infinity
Young Peoples' Ideas of Infinity
复制标题
年轻人的无限想法
DOI：
10.1023/a:1016090925967
复制
发表时间：
2001
影响因子：
3.2
通讯作者：
J. Monaghan
中科院分区：
文献类型：
--
作者：
J. Monaghan
本文认为，无穷大的年轻人的意见之前，教学的方法数学家在处理无穷大。为了避免与其他文件在这个特殊问题上的无限重复，参考极限概念和Cantorian无限的观点保持在最低限度。部分历史帐户的研究审查年轻人的无限的想法。获取这些想法的方法问题是本文的一个分主题。四个主要部分涉及：在这一领域的研究和皮亚杰的工作的潜在陷阱;关于无限和无限作为一个过程和作为一个对象的矛盾性质的问题;无限数;上下文和任务。
This paper considers views of infinity of young people prior to instruction in the methods mathematicians use in dealing with infinity. To avoid overlap with other papers in this special issue on infinity, reference to limit notions and Cantorian views of infinity are kept to the minimum. A partially historical account of studies examining young peoples' ideas of infinity is presented. Methodological problems in accessing such ideas is a sub-theme of this paper. The four main sections deal with: potential pitfalls for research in this area and the work of Piaget; issues concerning the contradictory nature of infinity and infinity as a process and as a object; infinite numbers; contexts and tasks.