In the book Mathematical Power: Lessons from a Classroom, Ruth Parker compares the culture of mathematics and the culture of school mathematics. She concludes that school mathematics, as most of us know it, “is unlikely to result in mathematically powerful students.” Ruth then describes a picture of what is needed as follows, “The goal of school mathematics reform is to develop students who are challenged by messy, ill-defined situations or complex problems; who are curious and have developed ‘thoughtful habits of inquiry’ (Wiggins 1989a); who are able to use important mathematical ideas to make sense of information, events, and situations in the world; and who understand the power of mathematics as a way to reveal significant patterns and relationships that surround them. Meeting this goal will require comprehensive restructuring of the content of mathematics courses, of the learning environment, of the role of the teacher, and of assessment practices.” Parker 1993.
For a look at why mathematics needs to be taught differently, dowload the PDF document, The Culture of Mathematics from the book, Mathematical Power: Lessons from a Classroom, by Ruth Parker. Reprinted with permission: Heinemann Press.