Display collection stuff

Your code makes Rails do object_a.things and put the result in the
text area. when outputting an object like a string, ruby prints out
what you see, class name and the (internal ruby) object's id: #<Thing:

you will have to do something like this:
<%= text_area_tag "things", @object_a.things.map{ |t| t.name }.join("
") %>

then, when submitting the form, the content will be in params[:things]
if however you want it in params[:object_a][:things], change it like

<%= text_area_tag "object_a[things]", @object_a.things.map{ |t|
t.name }.join(" ") %>

be aware that this could lead to problems when doing mass assignment:
@object_@ =Object_a.new(params[:object]
=> "things" is no attribute of object_a (it's only an associtiaon),
and produce an error.
you can however catch this with a virtual attribute...