This volume examines how several key components of the mathematics education system in the United States fail to provide teachers with adequate and effective tools to teach mathematics in K-12 classrooms. These components consist of teachers’ own learning experiences as students in K-12 classrooms, their undergraduate or graduate trainings in mathematics, and their in-service professional development trainings. Newton argues that unless we improve these system components as a whole and recognize the importance of teaching future mathematics teachers explicitly and rigorously the topics they are expected to teach, teachers will continue to recycle a body of incoherent and incomprehensible mathematical knowledge to their students, because these are the only types of mathematical knowledge they have at their disposal, both in terms of what they themselves have learned as K-12 students and in terms of the mathematical resources available to them, including the textbooks they rely on to teach as mathematics teachers.