Relational Understanding and Instrumental Understanding.
Relational Understanding and Instrumental Understanding.
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关系性理解和工具性理解。
DOI：
10.4324/9780203396391-18
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
R. Skemp
中科院分区：
文献类型：
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作者：
R. Skemp
人们在世界不同地区所说的英语之间得到了虚假的友谊。一个英国人在美国要一块饼干，他会得到我们所说的烤饼。为了得到我们所说的饼干，他必须要一块饼干。在数学和日常生活中使用的英语之间，有诸如场、群、环、理想等词。一个人如果不知道他使用的这个词是一个伪朋友，就会犯一些不方便的错误。我们希望历史是真实的，而不是一个故事。我们可以从图书馆免费借书，但不能从书店借书，等等，但在前面的例子中，有一些线索可能会让人警惕：语言、国家或语境的差异。然而，如果同一个词用在同一种语言、同一个国家和同一个语境中，有两种意义，它们的区别不是微不足道的，而是像（比如说）“histoire”和“story”的意义之间的区别一样基本的，这是事实和虚构之间的区别，人们可能会预料到严重的混乱。在数学的上下文中可以找到两个这样的词;这是附加到这些词的替代含义，
One gets faux amis between English as spoken in different parts of the world. An Englishman asking in America for a biscuit would be given what we call a scone. To get what we call a biscuit, he would have to ask for a cookie. And between English as used in mathematics and in everyday life there are such words as field, group, ring, ideal. A person who is unaware that the word he is using is a faux ami can make inconvenient mistakes. We expect history to be true, but not a story. We take books without paying from a library, but not from a bookshop; and so on. But in the foregoing examples there are cues which might put one on guard: difference of language, or of country, or of context. If, however, the same word is used in the same language, country and context, with two meanings whose difference is non-trivial but as basic as the difference between the meaning of (say) ‘histoire’ and ‘story’, which is a difference between fact and fiction, one may expect serious confusion. Two such words can be identified in the context of mathematics; and it is the alternative meanings attached to these words,