Assessment of Student Problem-Solving on Ill-Defined Tasks
AbstractInvestigations of formal problem-solving are conducted with the expectation that they will predict or at least help understand informal or everyday problem-solving. For instance, if a student scores well on a multiple-choice physics exam, the expectation is that the student will also do well on an everyday physics problem. Traditionally the evaluation of problem-solving skills in educational testing and cognitiw psychology has been dominated by formal, 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 tests may not elicit the same cognitive processes as informal tasks because they lack the process authenticity of informal tasks (Royer, Cisero, & Carlo, 1993). To address the lack of process authenticity, problem-solving skills can be directly evaluated using tasks that are "ill defined" and therefore more likely to elicit the cognitive processes associated with informal, everyday 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 multiple approaches to problem-solving. A smaller number of students were also interviewed individually and asked to think aloud as they evaluated the solutions. Results indicate that students found multiple approaches to problem-solving desirable, while at the same time exhibiting problem-solving biases.
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