Students should have opportunities to formulate conjectures, prove or disprove them, and support their reasoning. Student understanding is developed through ongoing reflection about content and process. An effective program focuses on the solving of problems and promotes the pursuit of further study of mathematics. An effective mathematics program clearly demonstrates that students achieve in mathematics through problem solving, communicating, reasoning, and making connections within mathematics and across disciplines. An effective mathematics program instills in all students a solid understanding of and respect for mathematics and its important role in today's society.
Mathematical problem solving is the centerpiece of an effective mathematics program.
It embraces a core of essential skills for many of today's careers. The rapid growth of information and technology has created tremendous job opportunities for those who have the requisite skills. The ability to reason and analyze quantitative issues is necessary to cope with an increasingly complex world. Mathematical problem solving begins with a careful analysis of the problem itself and a recognition of the components of the problem. This action requires insight and practice with a spectrum of mathematical problems.