ABSTRACT
Some sixth-grade teachers noticed that several of their students were making the same mistake in multiplying large numbers. All of the teachers considered the students’ mistake in multidigit multiplication, lining up the partial products incorrectly, to be a problem of mathematical learning rather than a careless oversight. However, in identifying the problem and explaining how they would help students to correct the mistake, the teachers presented various ideas. The teachers in the conceptually directed group had a different interpretation of the students’ mistake. The procedural or conceptual perspective of a teacher in defining the problem seemed to be largely determined by the teacher’s subject matter knowledge of multidigit multiplication. Limited subject matter knowledge restricts a teacher’s capacity to promote conceptual learning among students. The teachers who had a conceptual understanding of the topic tended to define the mistake as a problem of lacking conceptual understanding and tended to resolve it by addressing the students’ understanding.
