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. The issue of teacher knowledge in relation to teaching mathematics and students’ understanding of mathematics has long been a vexing question in mathematics education. What kinds of knowledge do teachers need in order to ensure learning for their students? Shulman (1987a, 1987b) began addressing issues of teachers ’ knowledge by suggesting seven types of knowledge that were required for teachers: content knowledge, general pedagogical knowledge, curriculum knowledge, pedagogical content knowledge, knowledg