ABSTRACT
This chapter discusses general cognitive science techniques for modeling complex human behavior. It proposes an experimental test of the model by using it to design instruction. The chapter addresses only the symbol system of algebra—understanding and manipulating expressions and equations that include symbols for variables. It explains cognitive modeling techniques to develop a simple model of competent performance in algebra. The chapter considers typical errors made by people who do not perform competently and argues that a model which can produce such errors must be radically different in important ways from the competent model. The central technique of cognitive science is modeling problem-solving behavior in the following way: A problem is considered as a data structure that includes whatever information is available about the problem. The chapter proposes a strong hypothesis the nature of at least some learners' difficulties in applying algebra with understanding and reliability.
