NCTM Mathematics Curriculum Standards for Life Cycle of Stars
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: 

1)  Reflect upon and clarify their thinking about mathematical ideas and relationships. 
2)  formulate mathematical definitions and express generalizations discovered through investigations 
3)  express mathematical ideas orally and in writing. 
4)  read written presentations of mathematics with understanding 
5)  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: 

1)  make and test conjectures 
2)  formulate counterexamples 
3)  follow logical arguments 
4)  judge the validity of arguments 
5)  construct simple valid arguments 

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