The role of the teacher is not to tell students exactly what rules and formulas they must know or to demonstrate how to use this information to solve a mathematics problem. In Japan, teachers have often been described as mean. They don't give students the answers right away, preferring to let students struggle and try first. The struggle is part of the learning process. We want them to try and choose from a range of strategies and approaches to solve problems. Students are actively involved in making sense of mathematics tasks using varied strategies, justifying solutions and making connections to prior knowledge and experiences. They are building on concepts they have already mastered.
Most of us probably remember the "I do, you do, we do" method of teaching. First the teacher showed you how to solve the problem and then you solved the problem following the exact instructions. You were copying or mimicking what your teacher did. You memorized the information and used it to solve routine problems, perhaps without understanding why.
The role of the teacher in our classroom is to engage students in tasks that promote reasoning and problem solving. The teacher facilitates conversations that move students toward a shared understanding of mathematics.