Confusion is rife in math classes, not just on the part of students, but often on the part of instructors. This confusion can undermine learning in a big way. There are many causes of this, and it is important for a teacher (and student) to understand these if mathematics is to be successfully learned and taught.
To start with, it is natural for students of all ages and all subjects to seek the shortest road to success. But it is most dangerous in math classes.
Look at the following exponent problem: Evaluate