PART II The Principles of the Psychology of Mathematics Education Espoused in this Study

In Part I a description was given of how mathematics grows either as a discipline or within the individual learner. Subsequently a philosophy of mathematics education was outlined. In this Part the focus is on outlining the psychology of mathematical thinking espoused in this study. Given that the theme of this study is the novice mathematician's thought processes, mathematical thinking is explored at its advanced level and this exploration mainly encompasses the novice's encounter with and induction into mathematical abstraction. Mathematical thinking at this advanced, abstract level is referred to as Advanced Mathematical Thinking (AMT), a name borrowed from David Tall's synonymous book (1991c) as well as from the synonymous PME Working Group. The nature of AMT and its cognitive and sociocultural dimensions are discussed in the following three sections of Part II.