National
Council of Teachers of Mathematics
Curriculum
Standards

STANDARD
1: MATHEMATICS AS PROBLEM SOLVING 
In grades 912, the mathematics
curriculum should include the refinement and extensions of methods
of mahtematical problem solving so that all students can
 use, with increasing
confidence, problemsolving approaches to investigate and understand
mathematical content;
 apply integrated mathematical
problemsolving strategies to solve problems from within and outside
mathematics;
 recognize and formulate
problems from situations within and outside mathematics;
 apply the process
of mathematical modeling to realworld problem stiuations..

STANDARD
3: MATHEMATICS AS REASONING 
In
grades 912, the mathematics curriculum should include numerous and
varied experiences that reinforce and extend logical reasoning skills
so that all students can
 make and test conjectures;
 formulate counterexamples;
 follow logical arguments
 judge the validity
of arguments;
 construct simple valid
arguments.

STANDARD
4: MATHEMATICAL CONNECTIONS 
In grades 912, the mathematics
curriculum should include investigation of the connections and interplay
among various mathematical topics and their applications so that
all students can
 recognize equivalent
representations of the same concept;
 relate procedures
in one representation to procedures in an equivalent representation;
 use and value the
connections among mathematical topics;
 use and value the
connections between mathematics and other disciplines.
