Teachers who listen to students, and who plan instruction based on what they learn from listening, transform student learning. For example, two children may arrive at the same solution of a problem but with different strategies. These strategies may reflect different levels of understanding and suggest different follow-up activities. Moreover, teachers who listen carefully to students' mathematical explanations often find that their students know a great deal of mathematics at an informal level. By building upon this informal knowledge, teachers can help their students construct more sophisticated concepts.
Effective teachers listen carefully to how students go about solving problems.
They know their students' mathematical strengths and weaknesses and they can develop a teaching strategy based on this understanding. Research shows that when teachers act upon their knowledge of student thinking, their beliefs about learning and instruction, their classroom practices and, most importantly, their students' learning and beliefs can be affected profoundly. Reference Philipp, R., A. Flores, and J. Sowder. Reflective Practitioners of Mathematics Teaching . National Center for Research in Mathematical Sciences Education, 1992.