Can Practical Knowledge Modeled in a Teaching Simulator Support Mathematics Teacher Learning?

本项目是教育与学习研究项目的前期研究，旨在开发和研究高中几何教学证明的智能虚拟模拟，以提高对未来中学数学教师的准备。教师准备工作中的一个主要问题是将课程学习与实际课堂实践相结合。然而，常规课堂不能提供受控的环境，让初学教师能够专注于发展他们教学实践的具体、重要方面。模拟以真实的课堂情境为基础，以教师知识理论为指导，通过学习环境的虚拟性进行控制。这种学习环境允许教师探索和排练与虚拟学生一起教学的新策略，而不会在真实教室中进行这种探索的更高后果。本研究在前人关于智能导师对学生数学学习的研究基础上，推广到教师学习中。基于模拟的方法也有可能提供一个实用的框架来进行类似的教学和学习研究，以在教学情境和学科中进行教学，并在中学数学教学以外的专业中学习实践。研究完成后，基于模拟的在线学习环境将在LessonSketch （www.lessonsketch.org）上提供，供教师教育者和教师候选人使用。本课题的目标是通过设计和探索基于教学知识理论的智能教学模拟器的知识模型，测试教学知识理论“实践理性”的运行能力。本项目将开发两个版本的模拟器：简易版，其知识模型采用教学中的数学知识；高级版，在简易版基础上加入实用理性规定的实用专业知识元素。研究小组将通过比较职前中学数学教师使用简易版模拟器的学习和职前中学数学教师使用高级版模拟器的学习，来探讨实践理性的具体贡献。该项目将首先探索在哪些地方进行比较，使用模拟器的纸质版本，使用教师候选人和教师教育者对进行比较，以完善和指定更细粒度的教学知识模型和基于实践的教师教育中的脚手架模型。然后，该项目将使用教师候选人研究两个改进版本的比较。这项工作有助于理解实践知识模型在支持学习在实践中、从实践中以及为实践而教学方面的附加价值。

This project is an early-stage research study in the Research on Education and Learning program to develop and study intelligent, virtual simulations of teaching proof in high school geometry to improve the preparation of future secondary mathematics teachers. A major concern in the preparation of teachers is bridging course-based learning with practice in real classrooms. However, regular classrooms do not provide controlled situations where beginning teachers can focus on developing specific, important aspects of their teaching practice. The simulations are based on realistic classroom situations and guided by theories on teacher knowledge, but controlled via the virtual nature of the learning environment. This learning environment allows teachers to explore and rehearse new strategies for teaching with virtual students without the higher consequences of this exploration in real classrooms. This study builds on the prior work in intelligent tutors for student learning of mathematics to generalize to teacher learning. The simulation-based approach also has the potential to provide a practical framework to conduct similar studies of teaching and learning to teach in instructional situations and subjects other than the one studied here, and of learning to practice in professions other than secondary mathematics teaching. Upon completion of the study, the online, simulation-based learning environment will be available at LessonSketch (www.lessonsketch.org) for both teacher educators and teacher candidates to use.The goal of the project is to test the operational capacity of practical rationality, a theory of teaching knowledge, by designing and exploring the use of an intelligent teaching simulator whose knowledge model is based on that theory of teaching knowledge. The project will develop two versions of the simulator: a simple version whose knowledge model uses mathematics knowledge of teaching and an advanced version that adds to the simple version elements of practical professional knowledge specified by practical rationality. The research team will explore the specific contribution of practical rationality by comparing preservice secondary mathematics teachers learning with the simple version of the simulator and preservice secondary mathematics teachers learning with the advanced version. The project will first explore where the comparison is done using paper versions of the simulators using pairs of teacher candidates and teacher educators to refine and specify a more fine-grained model of teaching knowledge and a model of scaffolding in practice-based teacher education. Then, the project will study the comparison of the two improved versions using teacher candidates. This work helps understand the added value of the practical knowledge model in supporting learning to teach in, from, and for practice.