This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and in-service teachers. The paper considers interpretations of the results under various theoretical frameworks and argues that these interpretations can be synthesized around the anthropological theory of the didactic. The paper ends with implications for what is taught under the name ‘mathematics’.

中文翻译：

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集合知识：一个教学现象

本文研究了一种教学现象，即认为集合的元素具有共同属性的感知，例如 {1, 2, 3} 和 {a, b, c} 是集合，但 {1, 2, 3, a, b, c} 不是一个集合。该论文报告了这一现象在一个国家的表现形式：教科书和课程中的一系列学校学生以及职前和在职教师。本文考虑了在各种理论框架下对结果的解释，并认为这些解释可以围绕教学的人类学理论进行综合。这篇论文以对以“数学”为名的教学内容的暗示结束。