Students should have numerous, varied learning experiences that illuminate the cultural, historical, and scientific evolution of mathematics. These experiences should be designed to evoke students' appreciation of mathematics' role in the development of contemporary society and to promote their understanding of relationships among the fields of mathematics and the disciplines it serves: the humanities and the physical, social, and life sciences.
Skill in making conjectures, gathering evidence, and building an argument to support a theory are fundamental to doing mathematics. Therefore, sound reasoning should be valued as much as students' ability to find correct answers.
To express and expand their understanding of mathematical ideas, students need to learn the symbols and terms of mathematics. This goal is best accomplished in the context of problem solving that involves students in reading, writing, and talking in the language of mathematics. As students strive to communicate their ideas, they will learn to clarify, refine and consolidate their thinking.
Study that relates to everyday life and builds students' sense of self-reliance will lead them to trust their thinking skills and apply their growing mathematical power. School mathematics should prompt students to realize that doing mathematics is a common, familiar human activity.
Problem solving is the process through which students discover and apply the power and utility of mathematics. Skill in problem solving is essential to productive citizenship.