ABSTRACT
The purpose of this chapter is to describe a model for categorizing students into developmental levels on the basis of their responses to particular content areas and to illustrate the model’s use with mathematics. The model grows out of a shift in the focus of research related to how children respond to particular tasks. In producing a response, two related phenomena appear to be involved. First, there is an underlying phenomenon that defines the individual’s cognitive limits termed the hypothetical cognitive structure (e.g., Piaget’s stages of cognitive development). The second phenomenon, which is a function of the hypothetical cognitive structure and of experience in a content area, is termed the structure of the learned outcome (Collis & Biggs, 1979). The former is a fixed structure at any particular time and is presumably unalterable by what teachers do (at least in the short term), whereas the latter is flexible and alterable by instruction. In fact, the latter could be used by the teacher to guide the way in which lessons and programs are designed. What is argued in this chapter is that the focus of research should shift away from a response simply implying a stage of cognitive development to consideration of the quality of each individual response per se.
