Summary of Findings of Chapters in Part II and Introduction to Part III

Abstract

The two studies, the Singapore and the Hong Kong study, provide contrasting evidence of how two groups of teachers choose to teach factorisation. Teacher-HK in the Hong Kong study placed great emphasis on the choice of tasks used to teach factorization. By selecting suitable tasks which are related but with increasing complexity, Teacher-HK presented factorization as a reverse of expansion and how a set of unique factors could be extracted from a given expression. In fact Teacher-HK wanted to ensure that the students in the class understood why each expression had a unique set of factors and why it was necessary to extract all the factors. He used specific mathematical concepts to highlight why a given set of factors is correct. For example, although $n\left(2a+2b\right),2n\left(a+b\right)$ and $2\left(na+nb\right)$ are three equivalent sets of factors for the expression $2na+2nb,$ only $2n\left(a+b\right)$ is the acceptable form. Teacher-HK helped students relate factorization of algebraic expressions to the factorization of whole numbers. Although it is correct to express twelve as the product of two factors $4\times 3,$ it was possible to factorise 12 completely to ‘$2\times 2\times 3$’. Teacher-HK tried to ensure that the students knew when they had the complete set of factors.