Analysis of constructed mathematical responses by numeric tests for equivalence

A method is described to determine if a constructed mathematical response is equivalent to the correct answer specified by the course author. Based on a combination of random evaluation and operator analysis, the method is theoretically justified for a general class of functions. Possible breakdowns due to computer arithmetic are discussed as well as the difficulties encountered when a function fails to fall in the general class. For CAI applications where a response is considered correct if it is equivalent to the correct answer, the method offers two possible advantages: (1) Only one form of the correct answer is specified. (2) Extensive and time consuming manipulation of expressions is avoided.