NCTM Mathematics Curriculum Standards for Galactic Inquiry
Standard 2
Mathematics as Communication 
Standard 3
Mathematics as Reasoning 
Standard 4
Mathematical Connections 
Standard 7
Geometry from a Synthetic Perspective


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 



Standard 4: Mathematical Connections 

In grades 9-12, the mathematics curriculum should include investigation of the connections and interplay among various mathematical topics and their applications so that all students can: 

1)  recognize equivalent representations of the same concept 
2)  relate procedures in one representation to procedures in an equivalent representation 
3)  use and value the connections among mathematical topics 
4)  use and value the connections between mathematics and other disciplines. 



Standard 7: Geometry from a Synthetic Perspective

In grades 9-12, the mathematics curriculum should include the continued study of the geometry of two and three dimensions so that all students can: 

1)  interpret and draw three dimensional objects 
2)  represent problem situations with geometric models and apply properties of figures 
3)  classify figures in terms of congruence and similarity and apply these relationships 
4)  deduce properties of, and relationships between, figures from given assumptions 

and so that, in addition, college intending students can 
1)  develop an understanding of an axiomatic system through investigating and comparing various geometries.