Knowledge and representations : the meaning making process in the curriculum of mathematics

Abstract

The purpose of this study is to understand the representations of mathematical knowledge in a series of co-related pedagogic discourses in the curriculum of mathematics in Hong Kong. Pythagoras' Theorem was selected as the focus of this study. Co-related pedagogic discourses such as the mathematics syllabus (EDB, 1999), the mathematics curriculum guideline (HKEAA, 2007), mathematics textbooks (e.g. Wong & Wong, 2009) and the mathematics examination paper (HKEAA, 2012), were selected as the source of data from which instances of the representation of Pythagoras' Theorem were examined and compared. As for the theoretical framework of this study, recontextualisation (Bernstein, 1990) has been reconciled with reinstantiation (Painter et al., 2012) in order to model the phenomenon of knowledge representation from a linguistic perspective. The findings of this study will contribute to the understanding of knowledge delocation and relocation in mathematics and other subjects from a linguistic perspective. Chapter One introduces the need to understand mathematics, the changes of the secondary mathematics school curriculum in Hong Kong and the rationale for studying the relations between the curriculum documents. Chapter Two reviews the research in mathematical knowledge structures and the semiotic nature of mathematics. Chapter Three connects social semiotics to sociological perspective, offering the understanding of the relationship between different pedagogic discourses from a linguistic perspective. Chapter Four is concerned with the research methodology and provides the analytical models to understand research data. Chapter Five analyses research data, focusing on the multisemiotic phenomenon in the curriculum of mathematics. Chapter Six discusses the findings of this research, presenting the reasons for using systemic functional theory and sociological approaches to investigate knowledge structures in mathematics and other areas. Chapter Seven concludes this research and provides insights that will illuminate other studies interested in understanding the knowledge and representation of knowledge in school system.