4-level MathThinking

4 Levels:

L1. S&T (See & Touch) Concrete: 1 apple, 2 oranges...
e.g. Math Modeling: visualise the problem [Primary School]

L2. S~T (See, no Touch but can guess):
e.g. Guess x,y for 2x+3y=8 ? [Secondary School]
e.g. Chimpanzees can guess where you hide the banana.

L3. ~S~T&I (no See, no Touch but Imagine):
e.g. Complex i = [Junior College].

L4. ~S~T~I (no See, no Touch, no imagine)
e.g. Abstract Math: Galois Group, ε-δ Analysis, Ring, Field, etc. [University]