Concept Image and Concept Definition
Concept Image and Concept Definition
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概念图像和概念定义
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发表时间：
1988
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影响因子：
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通讯作者：
D. Tall
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文献类型：
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作者：
D. Tall
20世纪60年代的《新数学》以结构主义的数学方法为基础，认为只要我们能够正确地表述数学的定义和推论，那么这将促进数学的学习。但即使做到了这一点，困难依然存在。仔细的分析表明，这些困难不是学生的愚蠢，而是我们所有人都能发现的自然的人类现象。在过去的十年里，经验研究强调，个体以一种可能并不总是连贯一致的方式建立起他们对一个概念的心理意象，当现象在新的背景下遇到时，以前的经历可能会影响现象的含义。这一点在引入更高级的数学概念时表现得尤为明显：例如，对极限的口头定义“snφιS”，其形式是“只要我们取n足够大，我们就可以使S尽可能地接近S”，这使许多人相信S n永远不能与S相提并论(Schwarzenberger&Tall 1978)。
The “New Mathematics” of the 1960s was based on the structural approach to mathematics, assuming that if only we could formulate the mathematical definitions and deductions correctly, then this would improve the learning of mathematics. But even when this was done, difficulties continued to persist. Careful analysis suggest that these difficulties are not stupidity on the part of students, but a natural human phenomenon that is found within all of us. In the last decade, empirical research has emphasised that individuals build up their mental imagery of a concept in a way that may not always be coherent and consistent, and that previous experiences may colour the meanings of phenomena when they are met in new contexts. This is particularly in evidence in the introduction of more advanced mathematical concepts: For instance, the verbal definition of a limit “snφιs”, in the form “we can make s as close to s as we please, provided that we take n sufficiently large”, induces many individuals the belief that s n can never equal s (Schwarzenberger & Tall 1978).