National Council of Teachers of Mathematics Curriculum Standards for Life Cycle of Stars
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Standard 2
Mathematics as Communication 		 Standard 3
Mathematics as Reasoning 

Standard 2: Mathematics as Communication

In grades 9-12, the mathematics curriculum should include the continued development of language and symbolism to communicate mathematical ideas so that all students can: 

  • Reflect upon and clarify their thinking about mathematical ideas and relationships;
  • formulate mathematical definitions and express generalizations discovered through investigations;
  • express mathematical ideas orally and in writing;
  • read written presentations of mathematics with understanding;
  • appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas.



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.
and so that, in addition, college intending students can: 
  • construct proofs for mathematical assertions, including indirect proof and proof by mathematical induction.