A mathematics university student as a future mathematician should have the ability to find "new" mathematics structures or construct theorems based on particular axioms. That ability can be created by using problem posing tasks. To do the tasks, students with different abilities will use different thinking strategies. To understand them exactly, we conducted descriptive research. The high group initiated the process of reconstructing theorems with identifying and understanding axioms, making a visual diagram or making a conjecture and constructing the "new" theorem. The modest group began with understanding information (making a definition), drawing diagrams and calculating the number of lines and parallel lines, then constructing theorems. That pattern is similar for the low group. [For complete proceedings, see ED496851.]