Proportional reasoning is foundational in school mathematics. Despite the importance of proportional reasoning, little has been written about the knowledge needed for teachers to teach proportional reasoning relative to its importance. In this paper, we present an initial definition for a robust understanding of proportional reasoning for teaching based on synthesizing past scholarship in conjunction with an empirical study of the knowledge resources practicing teachers use to make sense of proportional reasoning tasks. As a result of this effort, we present here an initial framing of operationalized knowledge resources based upon our definition for a robust understanding that could be used as an analytic tool. We also describe how such a framework of knowledge resources is useful in the context of teacher education, and we provide an example of how the framework was used to analyze the knowledge resources a teacher employed to make sense of a proportional reasoning task. We end by discussing possible implications our framework has for designing teacher education experiences and further research that is needed.

比例推理是学校数学的基础。尽管比例推理很重要，但是关于教师教授比例推理相对于其重要性所需的知识却很少。在本文中，我们提出了一个初步的定义，以基于对过去的学术知识的综合研究，并结合对实践教师用来理解比例推理任务的知识资源的实证研究，从而对教学中的比例推理有深入的了解。由于这项工作，在此我们根据定义给出了可操作知识资源的初始框架，以期将其作为分析工具来加以深入了解。我们还描述了这样的知识资源框架在教师教育的背景下如何有用，我们提供了一个示例，说明了如何使用该框架来分析教师用来理解比例推理任务的知识资源。最后，我们讨论框架对设计师范教育经验和所需的进一步研究可能产生的影响。