Found the problem.
The mistake I was doing is using this
m => m.SchoolYears // m.SchoolYears in a list of string
When I changed it to this
m => m.SelectedYearId // m.SelectedYearId is an integer property
it worked like a charm, so finally I have this working
@Html.DropDownListFor(m => m.SelectedYearId, new SelectList(Model.SchoolYears, "YearId", "StartDates", Model.CurrentYearId), new { @class = "field_Dropdown", style = "width:100px;",onchange="return searchStudents();" })
Thanks!