Teachers must help students realize that mathematical thinking involves dead ends and detours and encourage them to persevere when confronted with a puzzling problem and to develop the self-confidence and interest to do so. WHAT students learn is fundamentally connected with How they learn it. Students' opportunities to learn mathematics are a function of the setting and the kinds of tasks and discourse in which they participate. Their dispositions toward mathematics are also shaped by such experiences. Consequently, the goal of developing students' mathematical power requires careful attention to pedagogy as well as to curriculum.
All students can learn to think mathematically.
The goals described in the Curriculum and Evaluation Standards for School Mathematics are goals for all students. This assumption is supported by the vignettes, which were drawn from classrooms with students of diverse cultural, linguistic, and socioeconomic backgrounds. Teaching is a complex practice and hence not reducible to recipes or prescriptions. Such knowledge is general. However, teachers must also consider the particular, for teaching is context-specific.