Empirical evidence consistently suggests that the single most important element in a child's success at learning is the quality of the teacher. Colleges and universities are called upon to strengthen their teacher preparation and teacher professional development programs. States and districts are also called upon to enhance their in-service opportunities. The CwM materials help teachers learn new mathematical content directly relevant to the mathematics they are teaching, and also let them revisit familiar content approached in a new way. Teachers learn novel material through mathematical problem solving in an investigative style.
Many curricula now give mathematical investigations a central role in their lessons.
This adds an element of unpredictability to the directions that a lesson might take. Students discover something unexpected, or fail to understand something that is essential to the lesson. This places new demands on a teacher's flexibility and mathematical knowledge. Teachers need to know the possible directions students might pursue. They also need to know which directions are worth pursuing and will lead to development of mathematical concepts, and which directions are most likely dead ends.