Abstract Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its contrapositive may contribute to students’ struggles. This case study investigated the effectiveness of the eliminating counterexamples intervention in improving students’ ability to construct, critique, and validate contrapositive arguments in a U.S. eighth-grade mathematics classroom. The intervention involved constructing descriptions of all possible counterexamples to a conditional claim and its contrapositive, comparing the two descriptions, noting that the descriptions are the same barring the order of phrases, and finding a counterexample to show the claim is false or viably arguing that no counterexample exists.

中文翻译：

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消除反例：改善青少年对立推理的干预措施

摘要 学生在逆反推理方面的困难已有详细记载。缺乏对逆向推理的直觉以及对条件断言与其逆向推理之间的逻辑等价缺乏元论证可能会导致学生的挣扎。本案例研究调查了消除反例干预在提高美国八年级数学课堂中学生构建、批判和验证反驳论据的能力方面的有效性。干预涉及构建对条件声明及其反义词的所有可能反例的描述，比较这两种描述，注意除了短语的顺序外，描述是相同的，并找到一个反例来表明该声明是错误的或切实论证没有反例存在。