Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics (NCTM) to set forth a national vision for pre college mathematics education in the United States and Canada. The controversial document would be largely adopted by most education agencies from local to federal levels by the mid 2000s and also serve as a basis for most states' mathematics standards, as well as an influence on standards in other nations. It would later be fiercely opposed by many parents and mathematics professionals, and rejected by many states and school districts who complained about replacing instruction in arithmetic with writing, coloring, counting, and inventing mathematics unrecognizable to any previous generation of mathematicians or educators. While the standards are available on the internet, full access by the public is only available by an expensive purchase or subscription.

In 2006, NCTM issued a document called "Focal Points" which presented a more concise set of goals and objectives on a grade by grade basis, for grades K through 8. The "Focal Points" were perceived by the press (notably the Wall Street Journal (Sept 12, 2006), the New York Times, the Chicago Tribune and other newspapers to be an admission that previous standards had permitted the creation of curricula such as "Investigations" which had almost completely omitted any instruction in traditional arithmetic methods. In response to a firestorm of criticism over the 1989 standards, the NCTM replaced its call for de-emphasis with a strong emphasis of direct instruction of basic skills.

While the PSSM was championed by education theorists and administrators as raising standards for all students, it was sharply attacked by mathematicians, parents, and even some teachers over the new teaching methods which inspired lampooned exercises such as Mathland's Fantasy Lunch, Rainforest Algebra, and academic papers finding that teaching arithmetic harmed mathematical understanding. Some officials were quoted as valuing understanding processes more than learning one correct way to get one correct answer. Although still widely adopted in the United States and abroad by the mid-2000s, some states such as California and many local districts such as Tacoma, Washington would reject the standards as a massively misguided mistake in favor of more traditional approaches such as Singapore Math and Saxon math.

Mathematics in this style have also been called "standards-based" instruction or "standards-based mathematics, or simply "reform mathematics".

Less favorable terminology which have appeared in press and web articles include fuzzy math, "Where's the math", "anti-math", "math for dummies", "no-math mathematics", , rainforest algebra , "Math for women and minorities, and "new new math".

Traditional mathematics education has been called "Parrot Math" by critics. The direct instruction method has been criticized as "drill and kill".

Based on a consensus process that involved classroom teachers, mathematicians, and educational researchers from across the country, but later criticized by many people who actually used advanced mathematics for a living, the document sets forth a set of six principles that describe high-quality mathematics programs. Mathematical equity was a principle previously unseen in the field of mathematics, reflecting the influence of the politics of race, gender, and class of the 1960s and 1970s. Ten general strands or standards of mathematics content and processes were defined that cut across the school mathematics curriculum.

Specific expectations for student learning derived from beliefs of outcome-based education are described for ranges of grades (preschool to 2, 3 to 5, 6 to 8, and 9 to 12). The draft standards and the final standards make explicit goals that all students should learn higher level mathematics, particularly under-served groups such as minorities and women. These standards were made an integral part of nearly all outcome-based education and later standards-based education reform programs that were widely adopted by consensus across the United States by the 2000s.

Previously, de-facto standards had been set by textbook publishers. Mathematics texts were largely devoid of goals such as social justice and race and gender issues (equity). The new mathematics would reflect thinking in education since the activism of the 1960s and 1970s. Across education came the new context of the rise of multiculturalism and affirmative action as the primary goals of education rather than just academic content. This document built on several earlier standards documents produced by the National Council of Teachers of Mathematics— including the Curriculum and Evaluation Standards for School Mathematics (1989), the Professional Standards for Teaching Mathematics (1991), and the Assessment Standards for School Mathematics (1995).

Critics decried the dumbing "down" of mathematics, and called for giving minorities the same standards and instruction which had served previous generations of mathematics and engineering professionals. Reformers pointed to the "basics" as being the dumbed down alternative to teaching representation, relating and communicating higher order thinking skills. The standards introduced new terminology such as mathematical power, which should be given to all students, not merely the successful few who were tracked into technical college majors, and number sense, which would go far beyond memorizing a few traditional computing methods.

As parents and math / science professionals revolted against curriculums which in the case of Mathland and Investigations in Number, Data, and Space dispensed with instruction of traditional arithmetic as obsolete by calculators in favor of writing, cutting, pasting, singing and coloring, the New York Times and Wall Street Journals made "Math Wars" a new headline story. While the standards were widely and nearly universally adopted by the mid-2000s, at the same time many schools, school districts and even states such as California effectively rejected the standards, instead adopting rigorous traditional content and skill based standards and supplementing or replacing standards based curricula with Saxon math and Singapore Math which resulted in much higher test scores. Even the 2006 revision to NCTM guidelines lauded Singapore Math, though they would downplay headlines that that the standards had retreated back towards basic skills.