There are novel and valid views of what makes for students' success in school and later in life. One of these views is that a student should believe in himself/herself and the student should have "grit", or perserverance.
Beyond these characteristics, I expect that a student who looks for ways other than the ways his/her teacher or book present a topic will succeed in diverse applications.
The ways the student choses or invents should relate to prior knowledge or methods that the student has already mastered or feels comfortable with.