Obviously, there are probably many unidentified species, so I think the question must be read to include only identified species. I guess I’d also rule out extinct species. Even so, I’d think there should be a precise number of currently identified species.
I was pretty close. Consulting Nelson, JS. 1994. Fishes of the World (3rd Ed.) there are about 25,000 identified species and 55,000 named species and subspecies. That’s over 10 years old, so it must be more than that by now (depending on the splitters, not the lumpers, winning the taxonomic battle).
It’s never possible to come up with a precise number of species for any group, since different authorities may disagree as to which forms are full species and which are subspecies. However, 25,000 is a good estimate for the total of described species, with estimates of about 30,000 or so for total species including undescribed forms.
Note that “fishes” include members of 4 different vertebrate classes: Myxini, or hagfish; Cephalaspidomorphi, or lampreys; Chodrichthyes, or cartilaginous fishes; and Osteichthyes, or bony fishes.
You/your student(s) might have some fun looking at Fishbase.org, which lists a number disturbingly close to those posted by Colibri. I like this site because it tends to attract contributors from around the globe, not just U.S. / Western researchers.