render :action with params
render :action => "second"When you render, then your method written in :action is not called, only the view with that action name is called.
In your example, when you render, then your method second is not called but you are instead rendering the second.html.erb view.
For more details refer to this.
To call that method you have to use redirect_to, which looks something like the following:
redirect_to :action => "second", :page=> 4