“Problem” has at least two meanings in mathematics education research: as a non-routine task and as a task for which solvers have been previously introduced to a solution method (Schoenfeld, 1992). In the first case “problem solving” may require that the solver create a solution method that is new to him or her. In the second case, the solver need only apply a known method to complete the task, which is considered an exercise. Which meaning is appropriate requires knowledge of the person who attempts the task. “Problem solving” is sometimes also used to mean solving a word problem. This meaning does not rely on information about the solver’s knowledge of a solution method.
In the TIMSS Video Study, “problem” encompasses all these meanings. The following summary is from Teaching Mathematics in Seven Countries:
“Problems were defined as events that contained a statement asking for some unknown information that could be determined by applying a mathematical operation. Problems varied greatly in length and complexity, ranging from routine exercises to challenging problems. Although problems could be relatively undemanding, they needed to require some degree of thought by eighth-grade students. Simple questions asking for immediately accessible information did not count as problems.” (U.S. Dept. of Ed., 2003, p. 41)
Problem statements in the TIMSS Video Study were classified as “using procedures,” “stating concepts,” or “making connections.” Implementations of problems in public class work were classified as “giving results only,” “using procedures,” “stating concepts,” or “making connections” (see Making connections).
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
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