Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of structural representations in facilitating reliable performance. Connectionist models for recognizing structural features were investigated, leading to the conclusion that the cognitive system probably requires knowledge functionally equivalent to grammatical rules. Data from information processing experiments indicated that: (1) judgments about the application of an algebraic operator are influenced by low-level features recognized before a completely parsed representation is formed; and (2) recognition of individual characters in expressions is not facilitated by syntactically correct contexts, as it is by lexical contexts in letter recognition, but information about the algebraic categories of characters is obtained early in processing from the syntactic context. The conclusion is made that training in basic symbolic skill might be more effective if more attention were given to teaching the structure of information of the domain, including general features of the information presented in problems as well as general constraints and goals of the procedures to be acquired. (Author/LMO)