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.