An Unexpected Outcome: Students’ Focus on Order in the Multiplication Principle
An Unexpected Outcome: Students’ Focus on Order in the Multiplication Principle
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意想不到的结果：学生对乘法原理中顺序的关注
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Branwen Purdy
中科院分区：
文献类型：
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作者：
E. Lockwood;Branwen Purdy
乘法原理（MP）是组合计数的一个基本方面。为了更好地理解学生对MP的推理，我们让两名本科生在教学实验中重新发明了MP的陈述。在本文中，我们采用了行动者导向的视角（Lobato，Educational Researcher，32（1），17-20，2003，Educational Psychologist，47（3），1-16，2012），并借鉴洛克伍德的《数学行为杂志》，32，251-265（2013）学生的组合思维模型来追踪学生关于顺序的某种概念的发展-MP的陈述应该允许计数过程的阶段的任何排序。值得注意的是，这一概念与MP的教科书陈述中如何处理顺序不同。我们报告这种概念如何持续的学生，我们解释了研究人员（采访者）和学生如何设法通过教学实验，同时保持不同的概念的秩序。学生对顺序的推理揭示了学生思考顺序的方式，并突出了值得关注的乘法的潜在微妙之处。
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration. In an effort to better understand students’ reasoning about the MP, we had two undergraduate students reinvent a statement of the MP in a teaching experiment. In this paper, we adopt an actor-oriented perspective (Lobato, Educational Researcher , 32 (1), 17–20, 2003 , Educational Psychologist, 47 (3), 1–16 2012 ) and draw on Lockwood’s, Journal of Mathematical Behavior, 32 , 251–265 ( 2013 ) model of students’ combinatorial thinking to trace the students’ development of a certain conception about order – that a statement of the MP should allow for any ordering of the stages of a counting process. Notably, this conception differs from how order is treated in textbook statements of the MP. We report on how this conception persisted for the students, and we explain how the researchers (interviewers) and students managed to proceed through the teaching experiment while maintaining different conceptions of order. The students’ reasoning about order sheds light on ways in which students may think about order and highlights potential subtleties about multiplication in counting that deserve attention.