Two Undergraduate Students' Reinvention of the Multiplication Principle
Two Undergraduate Students' Reinvention of the Multiplication Principle
复制标题
两名本科生重新发明乘法原理
DOI：
10.5951/jresematheduc.50.3.0225
复制
发表时间：
2019
影响因子：
2.8
通讯作者：
Branwen Purdy
中科院分区：
文献类型：
--
作者：
E. Lockwood;Branwen Purdy
乘法原理是组合计数的一个基本方面，是解决计数问题的有效工具，也是许多关键的组合公式的基础。在本研究中，作者使用引导式再创造调查了两名本科生对MP的推理，并试图回答以下研究问题：学生如何理解MP并理解MP？具体地说，当两名学生重新设计了一条关于MP的陈述时，他们是如何关注MP的关键数学特征并对其进行推理的？学生们参与了一项配对的8节教学实验，在此期间，他们从一名初出茅庐的议员成长为一名成熟的议员。在这个过程中，学生得到了两个关键的数学特征，包括独立性和独特的综合结果，我们讨论了这些想法是如何影响学生重新创造语句的。此外，我们对未来的研究提出了潜在的启示和方向。
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, the authors used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and they sought to answer the following research questions: How do students come to understand and make sense of the MP? Specifically, while a pair of students reinvented a statement of the MP, how did they attend to and reason about key mathematical features of the MP? The students participated in a paired 8-session teaching experiment during which they progressed from a nascent to a sophisticated statement of the MP. Two key mathematical features emerged for the students through this process, including independence and distinct composite outcomes, and we discuss ways in which these ideas informed the students' reinvention of the statement. In addition, we present potential implications and directions for future research.