Three response types for broadening the conception of mathematical problemsolving in computerized tests

Three open-ended response types-mathematical expression (ME), generating ex amples (GE), and graphical modeling (GM)-are described that could broaden t he conception of mathematical problem solving used in computerized admissio ns tests. ME presents single-best-answer problems that call for an algebrai c formalism, the correct rendition of which can take an infinite number of surface forms. GE presents loosely structured problems that can have many g ood answers taking the form of a value, letter pattern, expression, equatio n, or list. GM asks the examinee to represent a given situation by plotting points on a grid; these items can have a single best answer or multiple co rrect answers. For the three basic types, sample items are provided, the ex aminee interfaces and approaches to automated scoring are described, and re search results are reported. It is illustrated how ME, GE, and GM can be co mbined to form extended constructed-response problems, and a description is offered of how item classes might be used as a basis for creating producti on-ready scoring keys.