What I think you are looking for is the alternate template feature that Umbraco provides.

You can add another template to the Umbraco backoffice which is called "Edit", and when you append that to the end of the url (and there is no node as a child with the same name), you will get that alternate template instead of the default one.

In your example it would be "/student/edit?id=2"

Then just use a surface controller to render your student edit form and and handle the submission.

Edit.cshtml:

@Html.Action("Render", "StudentForm", new {id = Request.Params["id"]})

StudentFromController.cs:

public class StudentFormController : SurfaceController
{
    [ChildActionOnly]
    public ActionResult Render(int id) {
        var studentViewModel = new StudentFormModel();        

        // Get the student to render

        return PartialView("~/Views/Partials/StudentForm.cshtml", studentViewModel );
    }

    [HttpPost]
    public ActionResult Submit(StudentFormModel model) {
        if (!ModelState.IsValid) {
            return CurrentUmbracoPage();
        }

        // Do saving stuff

        return RedirectToCurrentUmbracoPage();
    }}