Advanced Mathematical Thinking and the Way to Enhance IT
This journal discuss about Advanced Mathematical Thinking (AMT) and how to enhance it.  AMT is ability in representing, abstracting, creative thinking, and mathematical proving.  The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student’s life. The advantage in developing AMT among others are: 1) student capable to deliver idea which is possessed in verbal, symbol, table, graphic and diagram.  2) Find deep connection among mathematic branches, 3) know the outcome in one of branch which can trigger conjecture in branch which is related, 4) technique and method from one branch can be applied to prove the outcome in branch which is related, 5) capable to find new idea in problem solving, and 5) capable to understand and construct the proof.   One of theory which not only enhance student’s learning outcome but also can construct knowledge through student’s mental activity, enhance creativity, create class atmosphere which is enjoyable and challenging, and capable to enhance student’s AMT ability is APOS approach. Keywords: Advanced Mathematical Thinking, Representation, Abstraction, Creative Thinking, Mathematical Proving, APOS