Teachers' knowledge of their students as learners and how to intervene

As part of a teacher profiling instrument, 42 middle school teachers were presented with a mathematics problem dealing with fractions and wholes and asked to suggest solutions that would be given by their students. Further they were asked how they would address inappropriate responses in the classroom. The students in their classes were presented with the same question as part of a larger survey of mathematical concepts important in the middle years. This study compares the expectations of teachers and their suggested remedial actions with their years of teaching, their previous mathematics study, and the performance of students. Results suggest explicit questioning of teachers is an effective way to explore teacher knowledge for teaching mathematics.