Characterizing introduction to proof courses: a survey of U.S. R1 and R2 course syllabi
Characterizing introduction to proof courses: a survey of U.S. R1 and R2 course syllabi
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证明课程介绍的特征：美国 R1 和 R2 课程大纲调查
DOI：
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发表时间：
2020
影响因子：
0.9
通讯作者：
Dov Zazkis
中科院分区：
文献类型：
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作者：
Erika J. David;Dov Zazkis
摘要 许多设有数学课程的高等院校都提供证明课程简介，以方便数学学生从微积分和微分方程等主要基于计算的课程过渡到实分析和数论等以证明为中心的课程。然而，与大多数高等教育数学课程不同，其数学内容直接由课程名称暗示，证明课程的介绍可能在讨论的数学内容方面存在实质性差异。在这项研究中，我们通过检查美国 176 所 R1/R2 大学最近的教学大纲和其他相关课程文件，记录了证明课程简介内容的变化。由于美国出现了越来越多的关于本科介绍性证明和证明的数学教育研究，这些介绍性证明课程涵盖的内容的广泛样本对于可能不知道存在跨机构差异的美国证明研究人员以及旨在更好地了解美国证明教育研究中所研究的学生群体的国际证明研究人员来说都具有启发性。
ABSTRACT Many tertiary institutions with mathematics programmes offer introduction to proof courses to ease mathematics students’ transition from primarily calculation-based courses like Calculus and differential equations to proof-centred courses like real analysis and number theory. However, unlike most tertiary mathematics courses, whose mathematical content is directly implied by their course titles, introduction to proof courses may vary substantively in terms of the mathematics content discussed. In this study, we document the variation in content of introduction to proof courses by examining recent syllabi and other relevant course documents from introduction to proof courses at 176 R1/R2 universities across the United States. Since there is a growing number of mathematics education studies on undergraduate introductory proof and proving emerging from the U.S., this broad sample of what content these introductory proof courses cover is illuminating for both U.S. proof researchers, who are likely unaware of what cross institution variation exists, as well as international proof researchers aiming to better contextualize the student populations studied in U.S. proof education research.