Séance Séminaire

From University Mathematics to Mathematics Education

Didactic Transposition in College and School Mathematics: Novice Teachers’ Understanding of Factorization

The factorization of polynomials is a basic concept for solving problems in various domains of school mathematics. It is relevant to the greatest common divisors and least common multiples of polynomials, and is needed to solve equations and inequalities. However, although the concept of factorization comprises important content, it is recognized only as procedural knowledge required to solve equations. Thus, students memorize the formula as the inverse process of expansion without necessarily understanding its importance. From an advanced standpoint, polynomial factorization in school mathematics could be related to the unique factorization domain (UFD). Thus, I examine the understanding of polynomial factorization of novice teachers with relatively vivid advanced mathematical experience, in order to compare the relationship between school and college mathematics, and to investigate what influence these teachers’ advanced mathematical experience has on their teaching of polynomial factorization. In the first part of the presentation, I will present the curricula for mathematics teacher education and teacher employment tests focusing on teacher knowledge in Korean context. In the second part of the presentation, I will examine how the content of school mathematics is described from an advanced standpoint and how teachers utilize their college mathematics knowledge in the context of school mathematics. Focusing on the UFD in college mathematics and polynomial factorization in school mathematics, I will analyze school and algebra textbooks, and explored teacher knowledge of the UFD and how teachers’ factorization concepts occur in the teaching context in particular the issue of Klein's second transition.