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National Coucil of Teachers of Mathematics (NCTM) Standards

STANDARD 1: NUMBER AND OPERATION

Mathematics instructional programs should foster the development of number and operation sense so that all students—

  • understand numbers, ways of representing numbers, relationships among numbers, and number systems;

  • understand the meaning of operations and how they relate to each other;

  • use computational tools and strategies fluently and estimate appropriately.

STANDARD 2: PATTERNS, FUNCTIONS, AND ALGEBRA

Mathematics instructional programs should include attention to patterns, functions, symbols, and models so that all students—

  • understand various types of patterns and functional relationships;

  • use symbolic forms to represent and analyze mathematical situations and structures;

  • use mathematical models and analyze change in both real and abstract contexts.

STANDARD 3: GEOMETRY AND SPATIAL SENSE

Mathematics instructional programs should include attention to geometry and spatial sense so that all students—

  • analyze characteristics and properties of two- and three-dimensional geometric objects;

  • select and use different representational systems, including coordinate geometry and graph theory;

  • recognize the usefulness of transformations and symmetry in analyzing mathematical situations;

  • use visualization and spatial reasoning to solve problems both within and outside of mathematics.


STANDARD 4: MEASUREMENT

Mathematics instructional programs should include attention to measurement so that all students—

  • understand attributes, units, and systems of measurement;

  • apply a variety of techniques, tools, and formulas for determining measurements.


STANDARD 5: DATA ANALYSIS, STATISTICS, AND PROBABILITY

Mathematics instructional programs should include attention to data analysis, statistics, and probability so that all students—

  • pose questions and collect, organize, and represent data to answer those questions;

  • interpret data using methods of exploratory data analysis;

  • develop and evaluate inferences, predictions, and arguments that are based on data;

  • understand and apply basic notions of chance and probability.

STANDARD 6: PROBLEM SOLVING

Mathematics instructional programs should focus on solving problems as part of understanding mathematics so that all students—

  • build new mathematical knowledge through their work with problems;

  • develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics;

  • apply a wide variety of strategies to solve problems and adapt the strategies to new situations;

  • monitor and reflect on their mathematical thinking in solving problems.

STANDARD 7: REASONING AND PROOF

Mathematics instructional programs should focus on learning to reason and construct proofs as part of understanding mathematics so that all students—

  • recognize reasoning and proof as essential and powerful parts of mathematics;

  • make and investigate mathematical conjectures;

  • develop and evaluate mathematical arguments and proofs;

  • select and use various types of reasoning and methods of proof as appropriate.

STANDARD 8: COMMUNICATION

Mathematics instructional programs should use communication to foster understanding of mathematics so that all students—

  • organize and consolidate their mathematical thinking to communicate with others;

  • express mathematical ideas coherently and clearly to peers, teachers, and others;

  • extend their mathematical knowledge by considering the thinking and strategies of others;

  • use the language of mathematics as a precise means of mathematical expression.

STANDARD 9: CONNECTIONS

Mathematics instructional programs should emphasize connections to foster understanding of mathematics so that all students—

  • recognize and use connections among different mathematical ideas;

  • understand how mathematical ideas build on one another to produce a coherent whole;

  • recognize, use, and learn about mathematics in contexts outside of mathematics.

STANDARD 10: REPRESENTATION

Mathematics instructional programs should emphasize mathematical representations to foster understanding of mathematics so that all students—

  • create and use representations to organize, record, and communicate mathematical ideas;

  • develop a repertoire of mathematical representations that can be used purposefully, flexibly, and appropriately;

  • use representations to model and interpret physical, social, and mathematical phenomena.

 

 
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