National Council for Teachers of Mathematics 
Curriculum Standards
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STANDARD 1: MATHEMATICS AS PROBLEM SOLVING In grades 9-12, the mathematics curriculum should include the refinement and extensions of methods of mahtematical problem solving so that all students can-
  • use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content; 
  • apply integrated mathematical problem-solving 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 real-world problem stiuations..
STANDARD 3: MATHEMATICS AS REASONING In grades 9-12, 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 10: STATISTICS  In grades 9-12, the mathematics curriculum should include the continued studey of data anlysis and statistics so that all students can- 
  • construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations.