Implementing Eighth Grade Mathematics Problems in Six Countries: A Secondary Analysis of the TIMSS 1999 Video Data
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This study examined transcripts of videotaped lessons from the U.S. and five high performing countries participating in the Third International Mathematics and Science Study (TIMSS) 1999 Video Survey to investigate how eighth-grade teachers implemented mathematics problems. A coding system was developed to describe how teachers maintained or altered the potential of problems to "make connections" as they led public discussions of these problems. An analysis of the transcripts of 82 problem implementations found that when teachers or students made connections during problem discussions they most frequently did so by addressing mathematical justification, examining concepts more deeply than simply recalling or applying them, and connecting representations. Teachers most frequently led such discussions by drawing conceptual connections, taking over challenging aspects of the problems, and stepping students through arguments. Teachers much less frequently developed generalizations, compared solution methods, built on student ideas, provided scaffolding, or pressed students for justification. When connections were lost, teachers most often took over challenging aspect of the problems or shifted the focus to procedures, answers, or superficial or vague treatment of concepts. Regardless of whether or not connections were made, in about half of all implementations, teachers did most of the mathematical work, in about 8% of implementations students did it, and in the remainder, the work was shared more or less equally. This study suggests that teachers in high performing countries often make connections using approaches American mathematics educators associate with traditional teaching. Teachers in other countries may not share the assumption held by some American educators that teacher-centered instruction is ineffective for improving students' conceptual understanding and abilities in problem solving and mathematical reasoning.