A comparison of the types of mathematics tasks and how they were completed during eighth-grade mathematics instruction in Germany, Japan, and the United States.

摘要

This study extends the findings of the Third International Mathematics and Science (TIMSS) Video Study, comparing eighth-grade mathematics instruction in Germany, Japan, and the United States. Using a subset of thirty lessons from each country, I coded the type of mathematics typically associated with the tasks used during instruction (Using Procedures, Making Connections, and Stating Concepts). I then compared each task as it was stated with the way it was actually completed, by coding the mathematical reasoning made explicit while working on the task (Using Procedures, Making Connections, Stating Concepts, and Answers Only). Results indicate that lessons in the U.S. include a smaller proportion of Making Connections tasks than lessons in Japan. Moreover, Making Connections tasks in the U.S. are rarely completed by Making Connections, but by providing Answers Only or by Using Procedures. However, in Germany and Japan, Making Connections tasks were more frequently implemented in a way that was consistent with the task statement. This difference may provide insight into why students in the U.S. perceive mathematics as a fixed set of rules to be followed. This perception has been identified as factor that impedes U.S. students' success in mathematical thinking, particularly problem solving. These results extend the results of the TIMSS Video Study by providing further detail about the mathematical nature of the tasks students engage in during instruction in these three countries.