NCTM Mathematics Curriculum Standards for Searching for New Planets
Standard 3
Mathematics as Reasoning 

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