Goals for mathematics instruction like those outlined in our discussion of mathematical proficiency need to be set in full recognition of the differential access students have to high-quality mathematics teaching and the differential performance they show. Those goals should never be set low, however, in the mistaken belief that some students do not need or cannot achieve proficiency. In this day of rapidly changing technologies, no one can anticipate all the skills that students will need over their lifetimes or the problems they will encounter. Proficiency in mathematics is therefore an important foundation for further instruction in mathematics as well as for further education in fields that require mathematical competence. Schools need to prepare students to acquire new skills and knowledge and to adapt their knowledge to solve new problems.

The currency of value in the job market today is more than computational competence. It is the ability to apply knowledge to solve problems.82 For students to be able to compete in today’s and tomorrow’s economy, they need to be able to adapt the knowledge they are acquiring. They need to be able to learn new concepts and skills. They need to be able to apply mathematical reasoning to problems. They need to view mathematics as a useful tool that must constantly be sharpened. In short, they need to be mathematically proficient.

Students who have learned only procedural skills and have little understanding of mathematics will have limited access to advanced schooling, better jobs, and other opportunities. If any group of students is deprived of the opportunity to learn with understanding, they are condemned to second-class status in society, or worse.

A Broader, Deeper View

Many people in the United States consider procedural fluency to be the heart of the elementary school mathematics curriculum. They remember school mathematics as being devoted primarily to learning and practicing computational procedures. In this report, we present a much broader view of elementary and middle school mathematics. We also raise the standard for success in learning mathematics and being able to use it. In a significant and fortuitous twist, raising the standard by requiring development across all five strands of mathematical proficiency makes the development of any one strand more feasible. Because the strands interact and boost each other, students who have opportunities to develop all strands of proficiency are more likely to become truly competent with each.

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