It often happens that students answer (partly) a questions in an exam (lets assume this part is okay), but then add something completely off-topic or something very wrong in their answer (see examples below).
How would you deal with such an issue and why? Should one ignore the wrong things and only grade everything which is okay? Or should I bring to account that the additional part of the answer shows that he/she hasn't understood much?
Here are a few examples I have in mind:
- Assume the question is split into two parts. The answer for the first part was okay, but then on the second part the student discloses big deficits in their knowledge (e.g., he/she uses the fact that $\mathbb{R}$ is compact; or he/she calculates $(A+B)^{-1}=A^{-1}+B^{-1}$, etc., i.e., wrong arguments where you see that not much was understood).
- Assume someone answered a question right, but then add something is is which has nothing to do with the rest of the question (once when I was a TA, it happens that a question was just an exercise, the student copied the solution which was given in the exercise, but he did not finish when he arrived at the end and he also copied some part of the next exercise into his exam solution).