Investigating the development of prospective mathematics teachers' pedagogical content knowledge of generalising number patterns through school practicum

The purpose of this study is to investigate the development of three prospective elementary mathematics teachers' pedagogical content knowledge (PCK) of number patterns with its two components: (1) knowledge of students' understanding and difficulties and (2) knowledge of topic-specific strategies and representations. For our investigation, we use Radford's (ZDM Math Educ 40:83-96, 2008) framework called 'architecture of algebraic pattern generalisation' to redefine these two components of PCK in the context of patterns. A case study was conducted to explore the development of PCK through a school practicum course and to examine how observation of number pattern lessons in schools and discussions of these observation contribute to prospective teachers' PCK. Analysis of the data indicated that observations and discussions of number pattern lessons resulted in considerable change in the way prospective teachers take into account students' understanding of and difficulties with patterns, as well as in the way they use pattern-specific strategies such as algebraic pattern generalisation during their lessons. © 2012 Springer Science+Business Media B.V