I suppose you want to rebind the RadScheduler based on the selected text in the DropDownList. Following is the sample code that I tried based on your scenario.
Because I have the dates linked to a database so when a new term starts it automatic adds to the dropdown so I couldn't use the if statements linked to a certain date.
Here is my code which I used instead.
privatevoidDropDownDisplayYearChange ()
{
DateTime value = newDateTime(2000 + Convert.ToInt32(AcademicYearDropDown.SelectedValue.ToString().Substring(0, 2)), DateTime.Today.Month, DateTime.Today.Day);