How to render a partial from javascript

I have a select that gets populated depending on the selection in a different select To do this, I did what is recommended in Railscast #88 on 'Dynamic Select Menus'.

But now I need to render a partial, passing in the value selected in each of those selects. I can't figure out how to simply trigger a method call from the :onchange event in the select, so I'm thinking I need to call render :partial from within the javascript handler that detects the selects change event. But I can't figure out how. I tried the following in the javascript method (in the .js.erb file) but it doesn't work as hoped:

function staffSelected() {
    $('date_area').show();
    <% render :partial => "calendar" -%>
}

Anyone have a good solution?