Topics such as recursion, iteration, and the comparison of algorithms have emerged and deserve increased attention because of their relevance. Students should have opportunities to learn increasingly more sophisticated mathematical ideas as they progress through the grades. They should not spend a significant part of their instructional time reviewing mathematics content. A well-articulated curriculum is necessary for teachers at each level to know what mathematics their students have already studied and will study in future grades. The Teaching Principle Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.
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.