ABSTRACT
The chapter deals with the pattern-finding, numerical aspects. It offers details of what is involved in the learning of the two subject areas and presents illustrative examples from the research literature that describe features of student mathematical development in algebra and functions. The chapter attempts to put into perspective these elaborations of what is involved in the learning of algebra and functions and the accompanying examples of student cognition by drawing on a recently developed mathematical learning theory. As functions can be viewed both numerically as expressions of generality and as objects in their own right that denote change, they are treated both in the chapter on algebra and in the following one on functions. When students are pushed too quickly to understand an object perspective, pseudostructural knowledge can result: the chapter looks at how the traditional approach to teaching secondary school mathematics has been one involving the separation of the study of algebra from the study of functions.
