Well-prepared beginning teachers of mathematics expect mathematics to be sensible, useful, and worthwhile for themselves and others, and they believe that all people are capable of thinking mathematically and are able to solve sophisticated mathematical problems with effort. |

Well-prepared beginning teachers of mathematics know that one's success in mathematics depends on a productive disposition toward the subject and on hard work (National Research Council [NRC], 2001a). They believe that requisite characteristics of high-quality teaching of mathematics include a commitment to sense making in mathematical thinking, teaching, and learning and to developing *habits of mind,* including curiosity, imagination, inventiveness, risk-taking, and persistence. For example, when faced with a challenge to common practice or to their current understandings or beliefs, well-prepared beginning teachers have the intellectual courage and mathematical disposition to not reject the challenge but to investigate the proposed idea, applying their own critical thinking and using all available resources.