1) rigorousness by students’ beat gesture; 2) rigorousness by students’ metaphoric gesture; 3) economy by students’ deictic gesture; 4) economy by students’ iconic gestures; 5) freedom by students’ deictic gesture; 6) freedom by students’ iconic gesture; and 7) freedom by students’ deictic and iconic gestures in explaining students’ Mathematical Ideas, and the most commonly used economically by deictic gestures, and students’ self learning in Open Approach.