Loading AI tools
Guidelines produced by the National Council of Teachers of Mathematics From Wikipedia, the free encyclopedia
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.[1][2] 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.[3] The original draft was widely reviewed at the end of 1998 and revised in response to hundreds of suggestions from teachers.
The PSSM is intended to be "a single resource that can be used to improve mathematics curricula, teaching, and assessment."[3] 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:[3]
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 the philosophy of outcome-based education, are described for ranges of grades (preschool to 2, 3 to 5, 6 to 8, and 9 to 12). These standards were made an integral part of nearly all outcome-based education and later standards-based education reform programs that were widely adopted across the United States.[citation needed]
In 2006, NCTM issued a document called "Curriculum Focal Points" that presented the most critical mathematical topics for each grade in elementary and middle schools. American mathematics instruction tends to be diffuse and is criticized for including too many topics each year. In part, this publication is intended to assist teachers in identifying the most critical content for targeted attention. More such publications are planned.
NCTM stated that "Focal Points" was a step in the implementation of the Standards, not a reversal of its position on teaching students to learn foundational topics with conceptual understanding.[15] Contrary to the expectation of many textbook publishers and educational progressives, the 2006 Curriculum Focal Points strongly emphasized the importance of basic arithmetic skills in lower and middle grades. Because of this, the "Curriculum Focal Points" was perceived by the media[16][17] as an admission that the PSSM had originally recommended, or at least had been interpreted as recommending, reduced instruction in basic arithmetic facts.
The 2006 Curriculum Focal Points identifies three critical areas at each grade level for pre-kindergarten through Grade 8.[15] Samples of the specific focal points for three grades are below. (Note that the Simple Examples below are not quotes from the Focal Points, but are based on the descriptions of activities found in the Focal Points.)
Focal points | Related content standard | Simple example |
---|---|---|
Pre-Kindergarten Focal Points[18] (student age: 4 or 5 years old) | ||
Developing an understanding of whole numbers | Number and Operations | How many blue pencils are on the table? |
Identifying shapes and describing spatial relationships | Geometry | Can you find something that is round? |
Identifying measurable attributes and comparing objects by using these attributes | Measurement | Which one is longer? |
Fourth Grade Focal Points[19] (student age: 9 or 10 years old) | ||
Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication | Number and Operations, Algebra | An auditorium has 26 rows of 89 seats. How many seats are there? |
Developing an understanding of decimals, including the connections between fractions and decimals | Number and Operations | Draw a picture of 0.2. What fraction is this? |
Developing an understanding of area and determining the areas of two-dimensional shapes | Measurement | How could we find the area of this L-shaped room? |
Eighth Grade Focal Points[20] (student age: 13 or 14 years old) | ||
Analyzing and representing linear functions and solving linear equations and systems of linear equations | Algebra | The equation y = 4x + 4 shows the cost y of washing x windows. How much more will it cost each time I add 2 more windows to the job? |
Analyzing two- and three-dimensional space and figures by using distance and angle | Geometry, Measurement | Use the Pythagorean theorem to find the distance between the two points on the opposite corners of this rectangle. |
Analyzing and summarizing data sets | Data Analysis, Number and Operations, Algebra | What is the median price in this list? Does the median change if I lower the most expensive price? |
The Focal Points define not only the recommended curriculum emphases, but also the ways in which students should learn them, as in the PSSM. An example of a complete description of one focal point is the following for fourth grade:
Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication
Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multidigit whole numbers. They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.
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.[21][22][23][24] 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.[25]
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.