Mystified by forms and models

API says - check_box(object_name, method, options = {}, checked_value
= "1", unchecked_value = "0")

Also give the following example:
check_box("puppy", "gooddog", {}, "yes", "no")
    <input type="checkbox" id="puppy_gooddog" name="puppy[gooddog]"
value="yes" />
    <input name="puppy[gooddog]" type="hidden" value="no" />

in light of that you can use the following:
<% for todoitem in @todoitems %>
      <%= check_box :todoitem, todoitem.done, {},, nil %>
<% end %>
This should set the id as the checked value and nil to the unchecked
vaue, but you can use whatever column you want.