No, in principle the student retains the copyright in their work.
If the student's work was on behalf of the education institution as part of a course, the institution can stipulate certain user rights in this regard. For example, the work can be placed in an electronic learning environment to be assessed by a lecturer or commented on by fellow students. An education institution can also stipulate that a work must stay available for a certain period of time as part of an e-portfolio. From a legal point of view, this means the student grants a licence to the institution for this intended use. This can be put in writing, but mostly this is done tacitly, as an electronic assignment has to be disclosed in some way to have it assessed by others.
In order to give students clarity about the type of use they agree to when they upload an assignment, the intended forms of use in the electronic learning environment in question can be clearly stated in the general terms and conditions. The students only grant a licence for certain types of use and they retain the copyright in their work themselves. However, the institution may make arrangements with the students for the assignment of copyright. This can only be done in a written agreement that is signed by the student.