Thinking Deeply about Knowing Mathematics

摘要

Most prospective secondary mathematics teachers know quite a bit of mathematics, and they know that they know quite a bit of mathematics. However, they may not be aware that some of their mathematical knowledge is not conceptually deep, connected, or broad. An important part of the professional development of teachers of mathematics should be thinking deeply about "knowing mathematics," that is, prospective teachers of mathematics need to (a) think deeply about what it means to know mathematics and (b) think deeply about their own understanding of fundamental mathematical ideas.