A Contemporary Theory of Mathematics Education Research

For proposal stage:

About the author

Preface

Chapter One Introduction

Chapter Two Reason to believe

Chapter Two provides a theoretical discussion of how we understand mathematical knowledge. The theory presents rationality and belief as mutually formative dimensions of school mathematics, where each term is more politically and socially embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a specific mode of activity referenced to the performance of certain substitute skills and procedures that have come to represent mathematics in the school context consequential to the demands of social management. The chapter considers alternative modes of apprehending mathematical objects derived as they are from this socially defined space. The chapter's central argument is that rational mathematical thought necessarily rests on beliefs set within a play of ideological framings that within school often partition people in terms of their proxy interface with mathematics. The challenge is then seen as being to loosen this administrative grip to allow both students and teachers to release their own powers to generate diversity in their shared mathematical insights rather than being guided by conformity.

Chapter Three The social packaging of mathematical learning.

Chapter Three considers some of the arbitrary curriculum or assessment criteria that operate in the social construction of mathematics in educational institutions. The advance of mathematics as an academic field is typically defined by the production of new ideas, or concepts, which adjust progressively to new shared ways of being. That is, mathematical concepts are created or invented to meet the diverse demands of everyday life, and this very diversity can unsettle more standardised accounts of what mathematics is supposed to be according to more official rhetoric. For example, the expansion of mathematics as a field often relies on research grants selected to support economic priorities. In schools, economic factors influence the topics chosen for a curriculum. In some countries, for instance, there is a shortage of specialist mathematics teachers that limit curriculum choices and restrict the choice of viable teaching materials, educational targets or models of practice advocated by research in mathematics education. Our evolving understandings of who we are and of what we do shape our use of mathematical concepts and thus our understandings of what they are. School mathematics has been reduced according to ideological schema to produce its conceptual apparatus, pedagogical forms and supposed practical applications.

Chapter Four The social administration of mathematics subject knowledge through teacher education

Chapter Four describes some recent empirical research in university teacher education. It considers how practices of teacher education impact on classroom practice by new teachers and thus shape the mathematics that takes place. The theme is explored through an extended discussion of how the conduct of mathematical teaching and learning is restricted by regulative educational policies that set the parameters through which teacher education takes place. Specifically, it considers the example of how mathematics is discursively produced by student teachers within an employment