Testing Mathematical Problem Solving

The topic of testing mathematical problem solving lies at the intersection of two powerful educational movements. In 1980 “problem solving” was chosen to be the focus of school mathematics for the remainder of the decade (National Council of Teachers of Mathematics, 1980). Although some would argue that the focus has remained more rhetorical than real, many teachers have made genuine efforts to include more problem-solving activities in their instruction, and curriculum materials have been revised to incorporate such activities. At the same time, national reports on the status of education (Stanic, 1984) have stepped up efforts to compare student performance by state, by district, by school, and even by teacher, and such efforts have often resulted in more instructional time than ever before being given over to testing. Mathematics educators concerned about increasing the attention given to problem solving in school mathematics instruction have sought instruments that would convince teachers and students alike that the students were improving their problem-solving performance. Testers concerned about measuring all the desired outcomes of instruction have sought to develop instruments that would tap problem solving as one of the “higher order skills” in which many students are presumably deficient. The result has been a flurry of activity to improve the measurement of problem-solving performance in mathematics.