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Abstract：
This study explored the unique integration of mathematics tutors in teaching high school mathematics in a Virtual mathematics school (VMS). The tutors were three excelling STEM students who did not have any formal preparation for teaching before their work in the VMS. The goal of the study presented in this paper was to design a model of proficiency for these tutors. The model was designed using multiple case study methodology by tracking the learning through teaching of the tutors. Activity theory (Leontiev, 1978) framed the design of the study and led to a \"goal-action\" model of the tutors\' proficiency in the VMS. The goals part of the model is rooted in the construct of students\' mathematical potential (Leikin, 2021), and the action part was unraveled using the construct of a Teaching Triad (Jaworski in For the Learning of Mathematics, 12(1), 8-14, 1992). In this paper, we illustrate how our model can be used to analyze changes in the tutors\' proficiency, and how it can be applied to descriptive, explanatory, and analytical power.
摘要：
本研究探索了虚拟数学学校（VMS）中数学导师在高中数学教学中的独特整合。导师是三名优秀的STEM学生，他们在VMS工作之前没有任何正式的教学准备。本文提出的研究的目的是为这些导师设计一个熟练的模型。该模型是使用多案例研究方法设计的，方法是通过导师的教学跟踪学习。活动理论(列昂蒂耶夫，1978)构建了研究的设计框架，并导致了导师在VMS中的熟练程度的“目标-行动”模型。该模型的目标部分植根于学生数学潜力的建构(Leikin，2021),动作部分是使用教学三合会的结构展开的(Jaworski在《数学学习》中，12(1)、8-14,1992).在本文中,我们说明了我们的模型如何用于分析导师熟练程度的变化，以及它如何应用于描述性的，解释性的，和分析能力。
