Teachers' Knowledge of Students' Knowledge in Mathematics Problem Solving: Correlational and Case Analyses

This study examined the relationship of teachers' knowledge of students' knowledge to teachers' mathematics instruction and to students' mathematics problem solving. First-grade teachers (N = 20) participated in a 4-week workshop in which they were given access to research-based knowledge on children's mathematics learning. Teachers were observed for 16 days throughout the school year. In May, teachers completed interviews and questionnaires about their knowledge and beliefs: their students completed achievement tests. Correlational analyses showed significant positive relationships between teachers' knowledge of students' knowledge and students' mathematics problem-solving achievement. Teachers with more knowledge of their students questioned students about problem-solving processes and listened to their responses. Teachers with less knowledge of their students explained problem-solving processes to students or observed students' solutions. Case analyses of knowledge and behavior of the most effective teacher and the least effective teacher supported these conclusions and showed important differences in how these teachers thought about and used students' knowledge.