This study examined the different types of
mathematical tasks used in the classroom to explore the nature of mathematics
instruction of three sixth grade teachers in an elementary school. Case
studies, instructional observations,
and classroom artifacts were used to collect data. The results showed that the
three teachers used different types of mathematical tasks and implementation
methods. One teacher focused on high cognitive demand tasks, most of which
involved substantial group discussion and students working cooperatively. Even
though the other two also used many high cognitive demand tasks, these were
mainly presented via teacher-student dialogue. By examining the types of
mathematical tasks and their implementation, it was found that the group discussion tasks were generally
all high cognitive demand tasks, in which the students fully explained the
solution process. As for the tasks administered through teacher-student dialogue, due to the usage of large
amounts of closed-ended dialogue, the students used low cognition to solve the mathematical tasks and
did not have the opportunity to completely explain their thinking about the solutions. Thus, in order to
fully understand the nature of mathematics instruction by teachers, there should be simultaneous
consideration of the types of mathematical tasks used as well as how the tasks
were implemented.

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