In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations - problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered sequences of two (or more) indistinguishable objects (a less obvious application of combinations). We hypothesized that novice students may recognize combinations as appropriate for the first type but not for the second type, and our results support this hypothesis. We briefly discuss the mathematics, share the results, and offer implications and directions for future research.

中文翻译：

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对组合进行分类：调查大学生对不同类别组合问题的反应

在本文中，我们报告了一项旨在测试学生是否区分涉及组合的两种不同类型问题的调查，即组合用于计算无序不同对象集的问题（一种自然的，通用的组合使用方式），以及使用组合来计算两个（或多个）无法区分的对象的有序序列的问题（组合的不太明显的应用）。我们假设新手学生可能会认为组合适合于第一种类型，但不适用于第二种类型，并且我们的结果支持了这一假设。我们简要讨论数学，分享结果，并为将来的研究提供启示和方向。