Conceptualizing and justifying sets of outcomes with combination problems
Conceptualizing and justifying sets of outcomes with combination problems
复制标题
通过组合问题概念化并论证一组结果
DOI：
10.1080/19477503.2017.1392208
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发表时间：
2019
影响因子：
--
通讯作者：
P. Galarza
中科院分区：
文献类型：
--
作者：
Nicholas H. Wasserman;P. Galarza
抽象组合问题是组合学课程的基石，但很少有研究考察学生感知和区分不同组合问题的方式。在这篇文章中，我们调查了离散数学课程中的数学教育专业学生(n=18)如何看待两个截然不同的组合问题(第一类和第二类组合问题)。特别是，我们考察了参与者如何概念化每个问题的结果集、计算过程和公式，同时也探索了学生证明他们的关系的方法。对收集的数据的回顾表明，学生往往不太一致，比起与无序的可区分对象的集合(类别I)，他们更难利用和证明与有序的不可区分对象的集合(类别II)的组合。基于这些发现，我们对组合学教育中组合的教与学提出了建议。
ABSTRACT Combination problems are a cornerstone of combinatorics courses, but little research has been done examining the ways that students perceive and differentiate among different combination problems. In this article, we investigate how mathematics education students (n = 18) in a discrete mathematics course view two categorically different combination problems (Category I and II combination problems). In particular, we look at how participants conceptualized each problem’s sets of outcomes, counting processes, and formulas, while also exploring the means by which students justified their relationships. Review of the data collected suggests that students tend to be less consistent and have more trouble utilizing and justifying combinations with a collection of ordered indistinguishable objects (Category II) than they do with a collection of unordered distinguishable objects (Category I). Based on these findings, we provide recommendations for the teaching and learning of combinations in combinatorics education.