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Guidelines produced by the National Council of Teachers of Mathematics

Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards based mathematics. The NCTM employed a consensus process that involved classroom teachers, mathematicians, and educational researchers. A total of 48 individuals are listed in the document as having contributed, led by Joan Ferrini Mundy and including Barbara Reys, Alan H. Schoenfeld and Douglas Clements. The resulting document sets forth a set of six principles (Equity, Curriculum, Teaching, Learning, Assessment, and Technology) that describe NCTM's recommended framework for mathematics programs, and ten general strands or standards that cut across the school mathematics curriculum. These strands are divided into mathematics content (Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability) and processes (Problem Solving, Reasoning and Proof, Communication, Connections, and Representation). Specific expectations for student learning are described for ranges of grades (preschool to 2, 3 to 5, 6 to 8, and 9 to 12).

The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U. S. National Science Foundation. The latest update was published in 2000. The PSSM is available as a book, and in hypertext format on the NCTM web site. The PSSM replaces three prior publications by NCTM: The PSSM makes explicit the goal that all students should learn higher level mathematics, particularly underserved groups such as minorities and women. This principle encourages provision of extra help to students who are struggling and advocates high expectations and excellent teaching for all students. They acknowledge that the relative importance of some specific topics changes over time. The NCTM proposes that mathematics taught in modern classrooms be the skills that are most important to the students' lives and careers. Teaching: In the PSSM, the NCTM promotes sound teaching methods, without prescribing a one size fits all approach. The NCTM wants teachers to be able to use their professional judgment in choosing teaching techniques. They favor professional development opportunities in both mathematics (content) and in effective teaching techniques (methods). Learning: According to the PSSM, a combination of "factual knowledge, procedural facility, and conceptual understanding" is necessary for students to use mathematics. While they state that "learning the 'basics' is important", The ability to perform mental calculations and to calculate answers on paper is "essential." Very simple algebra skills are often taught to young children. For example, a student might convert an addition equation such as 19 + 15 = ? into a simpler equation, 20 + 14 = ? for easy calculation. Formally, this is described in algebraic notation like this: (19 + 1) + (15 − 1) = x, but even a young student might use this technique without calling it algebra. The PSSM recommends that all students complete pre algebra coursework by the end of eighth grade and take an algebra class during high school. Some geometry skills are used in many everyday tasks, such as reading a map, describing the shape of an object, arranging furniture so that it fits in a room, or determining the amount of fabric or construction materials needed for a project. Teaching should be appropriate to students' developmental level: Young students should be able to explain the difference between a rectangle and a square, while older students should be able to express more complex reasoning, including simple mathematical proofs. Unlike more abstract skills, the practical importance of measurement is readily apparent to students and parents. Data analysis and probability: The PSSM says that all students should learn to "formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them; select and use appropriate statistical methods to analyze data; develop and evaluate inferences and predictions that are based on data; [and] understand and apply basic concepts of probability." These skills allow students to make sense of critical information, such as medical statistics and the results of political surveys. These skills are increasingly important as statistical data are used selectively by manufacturers to promote products. While young students learn simple skills such as ways to represent the number of pets belonging to their classmates, or traditional skills such as calculating the arithmetic mean of several numbers, older students might learn concepts that were traditionally neglected, such as the difference between the occasionally dramatic relative risk reduction figures and the more concrete absolute risk reduction, or why political pollsters report the margin of error with their survey results.

Because most education agencies in the United States have adopted the NCTM recommendations to varying degrees, many textbook publishers promote their products as being compliant with the publishers' interpretations of the PSSM. However, the NCTM does not endorse, approve, or recommend any textbooks or other products and has never agreed that any textbook accurately represents their goals.