Submit form in rails 3 in an ajax way (with jQuery)

I am a beginner in rails and jQuery. I have two separate forms in one page and I want to submit them separately in ajax way (with jQuery). This is how far I got. Can anybody add or fix this code to make it work. I am using Rails 3.1 and jQuery 1.6. Thank you in advance.

application.js

$(".savebutton").click(function() { 
    $('form').submit(function() {
         $(this).serialize();
    });
}); 

first form:

<%=form_for :users do |f| %>
  <fieldset>
    <legend>Basic details</legend>
    <%= f.label :school %>
    <%= f.text_field :school,:size=>"45",:class=>"round",:id=>"school" %><br/>      
  </fieldset>
  <p><%= button_to "save and continue",{:class=>"savebutton"} %></p>
<%end%>

second form:

<%=form_for :courses do |c| %>
  <fieldset>
    <legend>Your current classes</legend>
    <label>class:</label><%= c.text_field :subject,:size=>"45",:class=>"round" %><br/>
  </fieldset>
  <p><%= button_to "save and continue",{:class=>"savebutton"} %></p>
<%end%>

SchoolController

class SchoolController < ApplicationController
  respond_to :json
  def create
    @school = current_user.posts.build(params[:school].merge(:user => current_user))
    if @school.save
      respond_with @school
    else
      respond_with @school.errors, :status => :unprocessable_entity
    end
  end
end

CourseController is in the same shape as SchoolController