The Labeling Strategy: Moving Beyond Order in Counting Problems
The Labeling Strategy: Moving Beyond Order in Counting Problems
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标签策略：在计数问题中超越顺序
DOI：
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发表时间：
2013
期刊：
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通讯作者：
Todd D. Cadwalladerolsker
中科院分区：
文献类型：
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作者：
Todd D. Cadwalladerolsker
摘要排列和组合用于解决某些类型的计数问题，但许多学生很难区分哪些概念适用于给定问题。一个“顺序启发式”通常被用来区分这两者，但是当问题没有明确提到顺序时，这种启发式可能会引起混淆。本文提出了一种基于应用标签的替代策略，这是一种更通用的方法。这种策略用“标记”和“选择”取代了排列和组合，并允许学生超越顺序启发式来解决更广泛的问题。本文基于此策略开发了公式，并给出了如何使用此方法的几个示例。
Abstract Permutations and combinations are used to solve certain kinds of counting problems, but many students have trouble distinguishing which of these concepts applies to a given problem. An “order heuristic” is usually used to distinguish the two, but this heuristic can cause confusion when problems do not explicitly mention order. This article suggests that an alternative strategy, based on applying labels, is a more general approach. This strategy replaces permutations and combinations with “labeling” and “choosing,” and allows students to move beyond the order heuristic to solve a wider range of problems. This article develops formulas based on this strategy, and gives several examples of how this approach can be used.