"Mathematics education is in serious trouble. Some call this problem 'mathematical miseducation.' Unsatisfactory performance in mathematics by students at all levels of education—elementary to tertiary—as evidenced through national and international test scores, teacher frustrations in mathematics teaching, and parent complaints about mathematics teaching and learning are commonplace phenomena. With the premise that improvement of mathematics education must begin with teachers, this paper addresses the issues of teachers’ understanding of 1) the nature of mathematics and 2) mathematics teaching. Teachers of mathematics need to be proficient in mathematical content as well as in the use of sound mathematical pedagogy. Preservice training of mathematics teachers should include a good balance of these two components. Since teachers teach the way they were taught, these mathematics courses should involve mathematics cognition, not just rote learning. The challenges in teaching mathematics at all levels are daunting and yet too important to ignore. Scientific constructivism is proposed as a partial solution for both the mathematics education of students and of teachers."