In a discussion with a physics lecturer he mentioned that one major area where students fail is understanding assumptions - for example, if we are interested in two objects hitting each other and then bouncing off, we can probably ignore gravity, since the interesting even happens very fast. That is, we may assume gravity to be zero for the calculation.
In mathematics also there are plenty of assumptions. They tend to be more explicit then in physics. Students still have problems with them - confusing what should be proven with what may be assumed, for example.
Has this phenomenon (of students failing in using assumptions) been studied, and if yes, what are the major discoveries, or where should I start reading to find out more about this?