I'm often asked why I deduct points for not simplifying answers, or for using decimal (calculator) approximations instead of exact values (usually involving radicals, logarithms, trigonometry, e or pi).

Remember that if no points are deducted, it means that you are earning an A+, and that no improvement is necessary. If you are not able to simplify answers, or give exact values, then there is certainly room for improvement.

To help you understand what I consider to be an A+, A, B, C, D or F student, it's useful to understand how I view the process of learning math (or any subject that is based on finding and using patterns that occur in our world).

the process of learning

• intuition 1 = F
  
  you don't know how things work, so you try things you knew before from other situations
  
  
• patterns / rules = D or C
  
  you begin to notice there are patterns to how things work, and you learn rules about those patterns
  
  
• mechanics = C or B
  
  you practice using the rules and making sure you can use them correctly without referring back to the rules
  you realize that some rules work most, but not all, of the time
  you begin to wonder why the rules work the way they do
  
  
• speed = A
  
  you get even more practice using the rules so you can use them very quickly
  you realize that the rules can be written and used in different ways
  you can see clearly how the rules are based on prior rules
  
  
• intuition 2 = A+
  
  you can use the rules so quickly you barely have to think about how to use them
  you start creating new rules based on finding new patterns
  
  

Be careful to note that the beginning (F) and ending (A+) stages are both about being intuitive, but that there is a world of difference between them. An F intuitive student finds it nearly impossible to do what the D/C/B/A students do, whereas an A+ intuitive student can do what the D/C/B/A students do without much thought.