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

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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.