Links and Gaps between Theoretical Knowledge and Perceptual Practical Knowledge of a Future Teacher When Teaching Algebraic Expressions Multiplication

Abstract Prospective mathematics teachers require an integrated education to respond to the school system demands, so that they are able to explicitly link the knowledge acquired in their training with the practice-based experiences. The purpose of this article is to investigate the links and gaps between the theoretical knowledge and the perceptual practical knowledge of a prospective teacher who participates in a Lesson Study experience in a university course, through the lesson plan, class observation and interviews. The results show situations associated with these links and gaps between the knowledge of a prospective teacher that emerge in the teaching experience of algebraic expressions multiplication, and how these influence the management understanding and learning opportunities for their students.

摘要：数学师范生需接受一体化教育以契合学校系统的各项要求，从而能够将受训期间习得的专业知识与基于实践的教学经验建立明确关联。本文旨在通过教案、课堂观察与访谈，探究一名参与大学课程内课例研究（Lesson Study）实践的师范生，其理论知识与感知性实践知识之间的关联与脱节之处。研究结果呈现了在代数式乘法教学实践中，该师范生相关知识所显现出的上述关联与脱节场景，以及这些因素如何影响其课堂管理认知与学生的学习机会。