ActiveRecord::UnknownAttributeError in rails application

I have two model, one as follow

class Course < ActiveRecord::Base
  has_many :assignments, class_name: 'Assignment', foreign_key: :assignment_id, dependent: :destroy
  has_many :groups, class_name: 'Group', foreign_key: :group_id, dependent: :destroy
end

And another model

class Assignment < ActiveRecord::Base
  belongs_to :course, class_name: 'Course', foreign_key: :course_id
  has_many :questions, class_name: 'Question', foreign_key: :question_id, dependent: :destroy
end

These two has relationship one to many i.e a course can have many assignments but an assignment belongs to a course.

In my assignment/index.html.erb view I have following form

<%= form_tag({controller: "assignments", action: "new"}, method: "get", class: "nifty_form") do %>
    <%= select_tag "course", options_from_collection_for_select(Course.all, :id, :name) %> <br /><br />
    <%= submit_tag("New Assignment") %>
<% end %>

New method of my assignments_controller.rb

def new
    @course = Course.find(params[:course])
    @assignment = @course.assignments.build
  end

When I submit the above form I get error at this line @assignment = @course.assignments.build

ActiveRecord::UnknownAttributeError in AssignmentsController#new
unknown attribute: assignment_id

assignment_id and course_id are not a column in the any of the table. How to fix this error?

Also I am new to rails. Since I have one to many relation, I am trying to create database as @assignment = @course.assignments.build is this the right way? I mean do I have to write @course.assignments.build or just @assignment = Assignment.new is okay? Also the way I wrote the relationships with foreign key is it correct?