"I am a poor student" does indeed have two possible meanings, thus:
- 1. I am not a good student.
2. I do not have much money.
As usual, context would reveal which meaning is intended. Examples:
- 1. I am a poor student. I don't study enough, and I get bad grades.
2. I am a poor student. I can't buy new clothes. I can barely afford to stay in school.
- For Teachers