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首页> 外文期刊>Journal of Mathematics Teacher Education >Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions
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Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions

机译：划分分数时，准教师的推理和对学生非传统策略的回应

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摘要

Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what we call “teacher-focused” responses, whereas those doing less analysis work tended to construct “student-focused” responses. These results and their implications are discussed in relation to the influential factors the participants themselves identified to explain their approach to the given teaching-scenario task.
机译：认识学生数学思想中的意义非常具有挑战性，特别是当这些思想与标准数学不同时。这项研究通过教学情景任务研究了预期的中小学教师对学生的非传统分数分割策略的推理和响应。构造了六类推理，从而区分了深层和表层。研究了参与者的推理，他们的教学反应以及他们对数学教学的信念之间的联系。我们发现，准小学教师和中学教师的推理和回应之间不仅存在差异，而且存在相似之处。我们还发现，那些解开学生非传统策略的数学基础的人倾向于使用我们所谓的“以老师为中心”的回答，而那些做较少分析工作的人则倾向于构建“以学生为中心”的回答。讨论这些结果及其含义时，涉及参与者自己确定的影响因素，以解释他们对给定教学场景任务的处理方式。

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