Assessment of student problem-solving on ill-defined tasks

Investigations offormal problem-solving ave conducted with the expectation that they will predict or at least help understand informal or everyday pro blem-solving. For instance, ifa student scores well on a multiple-choice ph ysics exam, the expectation is that the student will also do well on an eve ryday physics problem. Traditionally the evaluation of problem-solving skil ls in educational testing and cognitive psychology has been dominated by fo rmal, objectively scored tests,for example, multiple-choice tests (Garnham & Oakhill, 1994; Hambleton & Murphy, 1992). The relationship between formal and informal processes is questionable, however (Galotti, 1989). Formal te sts may not elicit the same cognitive processes as informal tasks because t hey lack the process authenticity of informal tasks (Royer, Cisero, & Carlo , 1993). To address the lack of process authenticity, problem-solving skill s can be directly evaluated using tasks that are "ill defined" and therefor e move likely to elicit the cognitive processes associated with informal, e veryday tasks. The purpose of the present study was to construct informal, performance tasks to evaluate both junior and senior high school students' problem-solving in mathematics. The task for students was to evaluate other students' solutions to two questions in mathematics. Results indicate that higher-achieving students generally preferred responses reflecting multipl e approaches to problem-solving. A smaller number of students were also int erviewed individually and asked to think aloud as they evaluated the soluti ons. Results indicate that students found multiple approaches to problem-so lving desirable, while at the same time exhibiting problem-solving biases.