I don't know if walk trot canter and whoa mean the same to the horse when your sitting on top of them squeezing with your legs....
Then teach the horse to go left and right with the bridle?!
I've never trained a horse how to be ridden if that makes sense... I worked on a TB track all we did was run! Use a hot walker grooming feeding and cleaning stalls. So the teaching a green horse is new for me.
I know this could be a lengthy subject but any info would help.