Preservice teachers' beliefs about students' mathematical knowledge structure as a foundation for formative assessments

In an experiment, we studied beliefs about the structure of students' mathematical knowledge that may affect teachers' formative assessments. Using a novel approach that simulated an assessment situation, we measured the beliefs of N = 42 preservice mathematics teachers. Teachers' responses revealed that they predominantly thought of students' conceptual and procedural knowledge as being symmetrically related but not identical, which is in line with recent findings about students' knowledge. Their assessments may, thus, not be biased by incorrect beliefs. Teachers, however, did not believe conceptual and procedural knowledge to be more interrelated as a result of students' increased expertise.