ABSTRACT In this study, we investigated teachers’ abilities correctly to identify situations that are appropriate for proportional reasoning and factors that might influence their ability using data on 148 teachers from the U.S. Learning Mathematics for Teaching assessment and other, similar items (with a smaller sample). Through a quantitative exploratory data analysis, we found middle school mathematics teachers are relatively proficient at correctly identifying situations that are proportional. However, we also found these same teachers were challenged by identifying situations as appropriate for proportional reasoning when in fact they were not, particularly in linear cases with a non-trivial constant term or inversely proportional situations. We also examined teachers’ backgrounds and perceived expertise to determine whether there were correlations between their abilities to discern proportional situations and these attributes. We found that teachers are relatively proficient at self-assessing their expertise. Our findings imply that the middle school mathematics teachers in our study seemed to over-identify situations as proportional even when the situations were not proportional.

中文翻译：

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数学教师识别适合比例推理的情况的能力

摘要 在这项研究中，我们使用来自美国学习数学教学评估和其他类似项目（样本较小）的 148 名教师的数据，调查了教师正确识别适合比例推理的情况和可能影响其能力的因素的能力）。通过定量探索性数据分析，我们发现中学数学教师在正确识别成比例的情况方面相对熟练。然而，我们也发现这些教师面临着识别适合比例推理的情况的挑战，而事实上它们并非如此，特别是在具有非平凡常数项或反比例情况的线性情况下。我们还检查了教师的背景和感知的专业知识，以确定他们辨别比例情况的能力与这些属性之间是否存在相关性。我们发现教师在自我评估他们的专业知识方面相对熟练。我们的研究结果表明，我们研究中的中学数学教师似乎过分认为情况是成比例的，即使情况不成比例。