Students learn mathematics through the experiences that teachers provide. Teachers must know and understand deeply the mathematics they are teaching and understand and be committed to their students as learners of mathematics and as human beings. Nevertheless, much is known about effective mathematics teaching. The teacher is responsible for creating an intellectual environment in the classroom where serious engagement in mathematical thinking is the norm. Effective teaching requires deciding what aspects of a task to highlight, how to organize and orchestrate the work of students, what questions to ask students having varied levels of expertise, and how to support students without taking over the process of thinking for them.
Effective teaching requires continuing efforts to learn and improve.
Teachers need to increase their knowledge about mathematics and pedagogy, learn from their students and colleagues, and engage in professional development and self-reflection. Teachers need ample opportunities to engage in this kind of continual learning. The working lives of teachers must be structured to allow and support different models of professional development that benefit them and their students. The Learning Principle Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Research has solidly established the importance of conceptual understanding in becoming proficient in a subject.