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

本项目是教育与学习研究计划的早期研究性研究，旨在开发和研究智能、虚拟的高中几何教学验证模拟，以提高未来中学数学教师的准备。准备教师的一个主要问题是将以课程为基础的学习与真实课堂上的实践联系起来。然而，常规课堂并不提供受控的情景，初任教师可以集中精力发展他们的教学实践中具体而重要的方面。这些模拟基于真实的课堂情景，并以教师知识理论为指导，但通过学习环境的虚拟性质进行控制。这种学习环境允许教师与虚拟学生一起探索和排练新的教学策略，而不会像在真实课堂上进行这种探索那样产生更高的后果。本研究建立在前人对学生数学学习智能辅导研究的基础上，将其推广到教师学习中。这种以模拟为基础的方法也有可能提供一个实用的框架，以进行类似的教学研究，研究在教学情境和学科之外的教学，以及在中学数学教学以外的专业中学习实践。研究完成后，在线模拟学习环境将在LessonSketch(www.essonsketch.org)上提供，供教师教育工作者和教师候选人使用。该项目的目标是通过设计和探索使用智能教学模拟器来测试实践合理性的操作能力，实践理性是一种教学知识理论，其知识模型基于该教学知识理论。该项目将开发两个版本的模拟器：一个简单版本，其知识模型使用教学的数学知识；一个高级版本，添加由实践理性指定的实用专业知识的简单版本元素。研究小组将通过比较职前数学教师与简易版模拟器的学习，以及职前数学教师与高级版数学教师的学习，来探索实践理性的具体贡献。该项目将首先探索使用纸质模拟器进行比较的地方，使用教师候选人和教师教育工作者对教师候选人和教师教育人员对进行比较，以提炼和指定更细粒度的教学知识模型和以实践为基础的教师教育的脚手架模型。然后，该项目将研究两个改进版本的比较，使用教师候选人。这项工作有助于理解实践知识模型在支持在教、从教和为实践中学习方面的附加值。

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.