Answer: No, the student does not do any work on the wall.
Explanation: The work is defined as the movement of an object done/caused by a force.
And it can be calculated as:
W = F*d
where W is work, F is force and d is the displacement of the object
In this case, the student is applying force on the wall, so we have the first part, but we also know that the wall does not move, so in this case, d = 0, which would imply that the work applied to the wall must be equal to zero
(because W = F*0 = 0)
So the answer is no, the student does not do any work on the wall.