


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 threedimensional 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.

