When solving counting problems, students often struggle with determining what they are trying to count (and thus what problem type they are trying to solve and, ultimately, what formula appropriately applies). There is a need to explore potential interventions to deepen students’ understanding of key distinctions between problem types and to differentiate meaningfully between such problems. In this paper, we investigate undergraduate students’ understanding of sets of outcomes in the context of elementary Python computer programming. We show that four straightforward program conditional statements seemed to reinforce important conceptual understandings of four canonical combinatorial problem types. We also suggest that the findings in this paper represent one example of a way in which a computational setting may facilitate mathematical learning.

中文翻译：

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通过在Python中使用循环和条件语句来丰富学生的组合推理

解决计数问题时，学生通常会费力地确定要计算的内容（以及要解决的问题类型以及最终适用的公式）。有必要探索潜在的干预措施，以加深学生对问题类型之间关键区别的理解，并有意义地区分此类问题。在本文中，我们调查了大学生在基本的Python计算机编程环境下对结果集的理解。我们表明，四个简单的程序条件语句似乎加强了对四个规范组合问题类型的重要概念理解。我们还建议，本文中的发现代表了一种计算设置可以促进数学学习的方式的示例。