ABSTRACT
Skilled professional mathematicians who work with elementary algebra solved a set of problems previously attempted by students of varying skill. The strategic choices, use of operators, and mistakes made by the experts are discussed. In general, the experts’ performance was not sharply different from that of the students, and reasons for this are considered. It is proposed that some streamlined procedures used by experts and less skilled solvers may be developed using only general facts about procedures, without any specifically mathematical insight. It is also shown that composition of productions cannot account for some of the streamlining observed, which takes the form of conversion of multiple-pass to single-pass procedures.
