Calendar is not simply a channel field. Calendar is a module which, upon installation, creates two channels: Calendar: Calendars, to hold Calendar data, and Calendar: Events, which are event data created under a selected Calendar (created in Calendar: Calendars). Similarly named custom field groups are also created. Both channels contain specialized Calendar custom fields.
Important: You MUST use the channels and custom field groups provided by Calendar upon installation
You cannot create another channel to hold Calendar data, nor can you create another custom field group for the Calendar channels, nor can you move/use the special Calendar custom fields to another custom field group.
A good strategy would be to create 1 calendar per student. You would therefore have a Calendar: Calendars entry for each student. On the front-end, many Calendar tags have a
calendar_name="" parameter that you can use to display event data for a single Calendar (or Student in your case).