For more than a decade, research studies of mathematics education in high-performing countries have concluded that mathematics education in the United States must become substantially more focused và coherent in order to improve mathematics achievement in this country. To lớn deliver on this promise, the mathematics standards are designed khổng lồ address the problem of a curriculum that is “a mile wide and an inch deep.”

These new standards build on the best of high-quality math standards from states across the country. They also draw on the most important international models for mathematical practice, as well as research & input from numerous sources, including state departments of education, scholars, assessment developers, professional organizations, educators, parents & students, và members of the public.

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The math standards provide clarity and specificity rather than broad general statements. They endeavor to lớn follow the kiến thiết envisioned by William Schmidt và Richard Houang (2002), by not only stressing conceptual understanding of key ideas, but also by continually returning to lớn organizing principles such as place value and the laws of arithmetic lớn structure those ideas.

In addition, the “sequence of topics and performances” that is outlined in a toàn thân of math standards must respect what is already known about how students learn. As Confrey (2007) points out, developing “sequenced obstacles & challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate và unwise.” Therefore, the development of the standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time. The knowledge & skills students need lớn be prepared for mathematics in college, career, & life are woven throughout the mathematics standards. They vày not include separate Anchor Standards like those used in the ELA/literacy standards.

The Common bộ vi xử lý core concentrates on a clear mix of math skills & concepts. Students will learn concepts in a more organized way both during the school year & across grades. The standards encourage students lớn solve real-world problems.

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## Understanding Mathematics

These standards define what students should understand and be able to vì in their study of mathematics. But asking a student lớn understand something also means asking a teacher lớn assess whether the student has understood it. But what does mathematical understanding look like? One way for teachers to vày that is khổng lồ ask the student lớn justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding & procedural skill are equally important, & both are assessable using mathematical tasks of sufficient richness.