This paper explores how in-service teachers enrolled in a graduate proof course interpret, understand, and use generic examples as part of their proving and justification activities. Generic examples, which are capable of proving and justifying with strong explanatory power, are particularly important for teachers considering teaching proof in their classrooms. The teachers in our study used generic examples to produce three types of proof: example-based arguments enhanced with generic language; incomplete generic examples; and complete generic examples. We found that teachers conflate generic examples and visual representations, prefer visual generic examples for teaching, and consider a generic example with symbolic representation to be more convincing than a generic example without. We conclude with implications for secondary school teaching, as well as suggestions for future professional development efforts.

中文翻译：

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通用范例在教师证明活动中的作用

本文探讨了参加研究生证明课程的在职教师如何解释、理解和使用通用示例作为他们证明和论证活动的一部分。能够证明和证明具有很强解释力的通用示例对于考虑在课堂上进行教学证明的教师尤为重要。我们研究中的教师使用通用示例来提供三种类型的证明：使用通用语言增强的基于示例的论证；不完整的通用示例；和完整的通用示例。我们发现教师将通用示例和视觉表示混为一谈，更喜欢在教学中使用视觉通用示例，并认为具有符号表示的通用示例比没有符号表示的通用示例更有说服力。我们总结了对中学教学的影响，