Three Response Types for Broadening the Conception of Mathematical Problem Solving in Computerized Tests

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Abstract
Three open-ended response types—mathematical expression (ME), generating examples (GE), and graphical modeling (GM)—are described that could broaden the conception of mathematical problem solving used in computerized admissions tests. ME presents single-best-answer problems that call for an algebraic formalism, the correct rendition of which can take an infinite number of surface forms. GE presents loosely structured problems that can have many good answers taking the form of a value, letter pattern, expression, equation, 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 correct answers. For the three basic types, sample items are provided, the examinee interfaces and approaches to automated scoring are described, and research results are reported. It is illustrated how ME, GE, and GM can be combined to form extended constructed-response problems, and adescription is offered of how item classes might be used as a basis for creating production-ready scoring keys.