From time to time, ask you student this question again. Prepare sets of some items. Eliminate the commonalities until only the quantity is left. If you offer counting bears and Dienes cubes and the answer is they are made of plastic, throw in a set of steel balls. Do it until the quantity is the only commonality left.
In the second or the third grade, American students can't answer what numbers stand for. Remind them: numbers stand for quantity, and a quantity can be only discovered matching one to one. As long as the kids keep this in mind, they understand what they are doing.
To count, we must be able to separate the objects, serialize them and (usually) recognize them as the members of some class. We count in space, in time and within given spatial and temporal constrains.