A Closer Look at Teachers’ Proportional Reasoning
A Closer Look at Teachers’ Proportional Reasoning
复制标题
仔细观察教师的比例推理
DOI：
10.1007/s10763-022-10249-7
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发表时间：
2022
影响因子：
2.2
通讯作者：
Doleck, Tenzin
中科院分区：
文献类型：
--
作者：
Copur-Gencturk, Yasemin;Baek, Clare;Doleck, Tenzin
教师的数学知识对他们为学生学习数学创造的学习环境的质量有重要影响。尽管比例推理是几个数学概念的基础，比例和比例关系构成了中学数学课程的主要组成部分，但对教师如何进行比例推理的了解相对较少。在这项研究中，我们调查了教师比例推理的非常规的比例任务和他们的比例推理的程度能够预测他们的整体理解的相关概念：比例和比例关系。通过对238名美国数学教师的调查，我们发现教师的比例推理可以分为四类：不正确推理、加法推理、相对推理和比例推理。我们的研究结果还表明，教师的比例和比例关系的整体知识与他们按比例推理的方式一致，这意味着在单独任务中使用不正确推理的教师在比例和比例关系测量中平均得分最低，而那些按比例推理的教师平均得分最高。这项研究的意义包括需要转移注意力的方式教师的原因比例推理的两个要素（协方差和不变性），以捕捉他们的理解比例和比例关系的细微差别。
Teachers’ mathematical knowledge has important consequences for the quality of the learning environment they create for their students to learn mathematics. Yet relatively little is known about how teachers reason proportionally, despite the fact that proportional reasoning is foundational for several mathematics concepts and that ratios and proportional relationships constitute a major component of the middle school mathematics curriculum. In this study, we investigated how teachers reasoned proportionally on a nonroutine ratio task and the extent to which their proportional reasoning was able to predict their overall understanding of the relevant concepts: ratios and proportional relationships. Using data collected from 238 US mathematics teachers, we found that teachers’ proportional reasoning could be grouped into four categories: incorrect, additive, relative, and proportional reasoning. Our results also indicated that teachers’ overall knowledge of ratios and proportional relationships aligned with the way they reasoned proportionally, meaning that teachers who used incorrect reasoning on a separate task received the lowest scores on average on the ratios and proportional relationships measure, whereas those who reasoned proportionally had the highest mean scores on average. Implications of the study include the need to shift attention to the way teachers reason in relation to the two elements of proportional reasoning (covariance and invariance) to capture the nuances in their understanding of ratios and proportional relationships.
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DOI：
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发表时间：
2015
期刊：
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影响因子：
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DOI：
10.5860/choice.51-5366
发表时间：
1994-12
期刊：
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影响因子：
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