• That they learn to value mathematics, 
  
• That they become confident in their ability to do mathematics, 
  
• That they become mathematical problem solvers, 
  
• That they learn to communicate mathematically, and 
  
• That they learn to reason mathematically.

These goals imply that students should be exposed to numerous and varied interrelated experiences that encourage them to value the mathematical enterprise, to develop mathematical habits of mind, and to understand and appreciate the role of mathematics in human affairs; that they should be encouraged to explore, to guess, and even to make and correct errors so that they gain confidence in their ability to solve complex problems; that they should read, write, and discuss mathematics; and that they should conjecture, test, and build arguments about a conjecture's validly.